WorldWideScience

Sample records for nonlinear finite deformation

  1. NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD

    Institute of Scientific and Technical Information of China (English)

    Liu Zhifang; Zhang Shanyuan

    2006-01-01

    A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.

  2. GEOMETRICAL NONLINEAR WAVES IN FINITE DEFORMATION ELASTIC RODS

    Institute of Scientific and Technical Information of China (English)

    GUO Jian-gang; ZHOU Li-jun; ZHANG Shan-yuan

    2005-01-01

    By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave.If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.

  3. Three kinds of nonlinear dispersive waves in elastic rods with finite deformation

    Institute of Scientific and Technical Information of China (English)

    ZHANG Shan-yuan; LIU Zhi-fang

    2008-01-01

    On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis.

  4. Mixed and Penalty Finite Element Models for the Nonlinear Behavior of Biphasic Soft Tissues in Finite Deformation: Part II - Nonlinear Examples.

    Science.gov (United States)

    Almeida, EDGARD S.; Spilker, ROBERT L.

    1998-01-01

    This two-part paper addresses finite element-based computational models for the three-dimensional (3-D) nonlinear analysis of soft hydrated tissues, such as articular cartilage in diarthrodial joints, under physiologically relevant loading conditions. A biphasic continuum description is used to represent the soft tissue as a two-phase mixture of incompressible inviscid fluid and a hyperelastic, transversely isotropic solid. Alternate mixed-penalty and velocity-pressure finite element formulations are used to solve the nonlinear biphasic governing equations, including the effects of strain-dependent permeability and a hyperelastic solid phase under finite deformation. The resulting first-order, nonlinear system of equations is discretized in time using an implicit finite difference scheme, and solved using the Newton-Raphson method. Details of the formulations were presented in Part I [1]. In Part II, the two formulations are used to develop two-dimensional (2-D) quadrilateral and triangular elements and three-dimensional (3-D) hexahedral and tetrahedral elements. Numerical examples, including those representative of soft tissue material testing and simple human joints, are used to validate the formulations and to illustrate their applications. A focus of this work is the comparison of the alternate formulations for nonlinear problems. While it is demonstrated that both formulations produce a range of converging elements, the velocity-pressure formulation is found to be more efficient computationally.

  5. Mixed and Penalty Finite Element Models for the Nonlinear Behavior of Biphasic Soft Tissues in Finite Deformation: Part I - Alternate Formulations.

    Science.gov (United States)

    Almeida, EDGARD S.; Spilker, ROBERT L.

    1997-01-01

    This paper addresses finite element-based computational models for the three-dimensional, (3-D) nonlinear analysis of soft hydrated tissues, such as the articular cartilage in diarthrodial joints, under physiologically relevant loading conditions. A biphasic continuum description is used to represent the soft tissue as a two-phase mixture of incompressible, inviscid fluid and a hyperelastic solid. Alternate mixed-penalty and velocity-pressure finite element formulations are used to solve the nonlinear biphasic governing equations, including the effects of a strain-dependent permeability and a hyperelastic solid phase under finite deformation. The resulting first-order nonlinear system of equations is discretized in time using an implicit finite difference scheme, and solved using the Newton-Raphson method. Using a discrete divergence operator, an equivalence is shown between the mixed-penalty method and a penalty method previously derived by Suh et al. [1]. In Part II [2], the mixed-penalty and velocity-pressure formulations are used to develop two-dimensional (2-D) quadrilateral and triangular elements and 3-D hexahedral and tetrahedral elements. Numerical examples, including those representative of soft tissue material testing and simple human joints, are used to validate the formulations and to illustrate their applications. A focus of this work is the comparison of alternate formulations for nonlinear problems. While it is demonstrated that both formulations produce a range of converging elements, the velocity-pressure formulation is found to be more efficient computationally.

  6. Anisotropy, inhomogeneity, and tension-compression nonlinearity of human glenohumeral cartilage in finite deformation.

    Science.gov (United States)

    Huang, Chun-Yuh; Stankiewicz, Anna; Ateshian, Gerard A; Mow, Van C

    2005-04-01

    The tensile and compressive properties of human glenohumeral cartilage were determined by testing 120 rectangular strips in uniaxial tension and 70 cylindrical plugs in confined compression, obtained from five human glenohumeral joints. Specimens were harvested from five regions across the articular surface of the humeral head and two regions on the glenoid. Tensile strips were obtained along two orientations, parallel and perpendicular to the split-line directions. Two serial slices through the thickness, corresponding to the superficial and middle zones of the cartilage layers, were prepared from each tensile strip and each compressive plug. The equilibrium tensile modulus and compressive aggregate modulus of cartilage were determined from the uniaxial tensile and confined compression tests, respectively. Significant differences in the tensile moduli were found with depth and orientation relative to the local split-line direction. Articular cartilage of the humeral head was significantly stiffer in tension than that of the glenoid. There were significant differences in the aggregate compressive moduli of articular cartilage between superficial and middle zones in the humeral head. Furthermore, tensile and compressive stress-strain responses exhibited nonlinearity under finite strain, while the tensile modulus differed by up to two orders of magnitude from the compressive aggregate modulus at 0% strain, demonstrating a high degree of tension-compression nonlinearity. The complexity of the mechanical properties of human glenohumeral cartilage was exposed in this study, showing anisotropy, inhomogeneity, and tension-compression nonlinearity within the same joint. The observed differences in the tensile properties of human glenohumeral cartilage suggest that the glenoid may be more susceptible to cartilage degeneration than the humeral head.

  7. Nonlinear viscoelastic response of highly filled elastomers under multiaxial finite deformation

    Science.gov (United States)

    Peng, Steven T. J.; Landel, Robert F.

    1990-01-01

    A biaxial tester was used to obtain precise biaxial stress responses of highly filled, high strain capability elastomers. Stress-relaxation experiments show that the time-dependent part of the relaxation response can be reasonably approximated by a function which is strain and biaxiality independent. Thus, isochronal data from the stress-relaxation curves can be used to determine the stored energy density function. The complex behavior of the elastomers under biaxial deformation may be caused by dewetting.

  8. -Deformed nonlinear maps

    Indian Academy of Sciences (India)

    Ramaswamy Jaganathan; Sudeshna Sinha

    2005-03-01

    Motivated by studies on -deformed physical systems related to quantum group structures, and by the elements of Tsallis statistical mechanics, the concept of -deformed nonlinear maps is introduced. As a specific example, a -deformation procedure is applied to the logistic map. Compared to the canonical logistic map, the resulting family of -logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors – a phenomenon rare in one-dimensional maps.

  9. SOLITARY WAVES IN FINITE DEFORMATION ELASTIC CIRCULAR ROD

    Institute of Scientific and Technical Information of China (English)

    LIU Zhi-fang; ZHANG Shan-yuan

    2006-01-01

    A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also.

  10. Non-linear elastic deformations

    CERN Document Server

    Ogden, R W

    1997-01-01

    Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.

  11. Finite Deformation of Magnetoelastic Film

    Energy Technology Data Exchange (ETDEWEB)

    Barham, Matthew Ian [Univ. of California, Berkeley, CA (United States)

    2011-05-31

    A nonlinear two-dimensional theory is developed for thin magnetoelastic lms capable of large deformations. This is derived directly from three-dimensional theory. Signi cant simpli cations emerge in the descent from three dimensions to two, permitting the self eld generated by the body to be computed a posteriori. The model is specialized to isotropic elastomers with two material models. First weak magnetization is investigated leading to a free energy where magnetization and deformation are un-coupled. The second closely couples the magnetization and deformation. Numerical solutions are obtained to equilibrium boundary-value problems in which the membrane is subjected to lateral pressure and an applied magnetic eld. An instability is inferred and investigated for the weak magnetization material model.

  12. Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method

    Directory of Open Access Journals (Sweden)

    Emir Gülümser

    2014-01-01

    Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.

  13. Nonlinear Deformable-body Dynamics

    CERN Document Server

    Luo, Albert C J

    2010-01-01

    "Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...

  14. Finite elements of nonlinear continua

    CERN Document Server

    Oden, J T

    2000-01-01

    Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s

  15. Leukocyte deformability: finite element modeling of large viscoelastic deformation.

    Science.gov (United States)

    Dong, C; Skalak, R

    1992-09-21

    An axisymmetric deformation of a viscoelastic sphere bounded by a prestressed elastic thin shell in response to external pressure is studied by a finite element method. The research is motivated by the need for understanding the passive behavior of human leukocytes (white blood cells) and interpreting extensive experimental data in terms of the mechanical properties. The cell at rest is modeled as a sphere consisting of a cortical prestressed shell with incompressible Maxwell fluid interior. A large-strain deformation theory is developed based on the proposed model. General non-linear, large strain constitutive relations for the cortical shell are derived by neglecting the bending stiffness. A representation of the constitutive equations in the form of an integral of strain history for the incompressible Maxwell interior is used in the formulation of numerical scheme. A finite element program is developed, in which a sliding boundary condition is imposed on all contact surfaces. The mathematical model developed is applied to evaluate experimental data of pipette tests and observations of blood flow.

  16. A study on nonlinear finite element analysis of laminated rubber bearings. Pt.1. Development of evaluation method for mechanical properties of laminated rubber bearings for horizontal base isolation system considering volumetric deformation of rubber material

    Energy Technology Data Exchange (ETDEWEB)

    Matsuda, Akihiro; Ohtori, Yasuki; Yabana, Shuichi; Hirata, Kazuta [Central Research Inst. of Electric Power Industry, Abiko, Chiba (Japan). Abiko Research Lab

    1999-04-01

    The purpose of this research is to develop the evaluation method for mechanical properties of laminated rubber bearings by nonlinear finite element method (FEM) considering the volumetric deformation of natural rubber material. Relationship between pressure and volumetric strain of the natural rubber is obtained from the volumetric tests and is introduced into user-subroutine of the FEM code (ABAQUS). Finite element analyses of natural rubber bearings (NRB) and the natural rubber bearing with lead plug (LRB) are carried out. The results may be summarized as follows; 1) Horizontal, vertical stiffness and effect of shear deformation on vertical stiffness of natural rubber bearings that have various shape are simulated with enough accuracy. 2) Horizontal and vertical stiffness of LRB are also simulated well. (author)

  17. Wetting on a deformable substrate with finite deformations and asymmetrical substrate surface energies

    Science.gov (United States)

    Limat, Laurent; de Pascalis, Riccardo; Dervaux, Julien; Ionescu, Ioan; Perthame, Benoit

    2016-11-01

    Wetting on soft compounds is still imperfectly understood, especially when the dry and wetted parts of the substrate have two different values of surface energies (contact angle different than 90 degrees). The problem is made very complex by geometrical non-linearities arising from finite slope of the substrate and finite deformations, that must be absolutely considered, to distinguish at second order between Young law and Neuman equilibrium of surface tensions. We have developed a numerical, finite element, code that allows one to minimize surface and bulk energies, with finite deformations and asymmetry of the surface energies. The results are compared to a linear theory based on Green function theory and Fredholm integrals, and with recent experiments using X-ray visualization. The non-linear numerics reproduce very well the observed profiles, while the linear approach gives helpful analytical approximates.

  18. Deformation of Honeycomb with Finite Boundary Subjected to Uniaxial Compression

    Directory of Open Access Journals (Sweden)

    Dai-Heng Chen

    2013-11-01

    Full Text Available In this paper, the crushing behavior of hexagonal honeycomb structures with finite boundaries (finite width and height subjected to in-plane uniaxial compressive loading is studied based on the nonlinear finite element analysis. It is found that stress-strain responses for the honeycombs with finite boundaries can be classified into two types: Type I and Type II. Such a characteristic is affected by the wall thickness, the work-hardening coefficient and the yield stress for the honeycombs. Furthermore, a transition from the symmetric to asymmetric deformation mode can be observed in Type I, and these deformed cells were localized in a horizontal layer. However, for the case of Type II response, the symmetric and asymmetric deformation modes can be observed simultaneously, and the region of the asymmetric mode was formed by the cell layer along the diagonal direction. As a result, the shear deformation behavior was developed along that direction. Moreover, the effect of work-hardening on the deformation behavior for the honeycombs with finite boundaries can be explained from that for infinite honeycombs.

  19. Dependence of the frequency spectrum of small amplitude vibrations superimposed on finite deformations of a nonlinear, cylindrical elastic body on residual stress

    KAUST Repository

    Gorb, Yuliya

    2010-11-01

    We model and analyze the response of nonlinear, residually stressed elastic bodies subjected to small amplitude vibrations superimposed upon large deformations. The problem derives from modeling the use of intravascular ultrasound (IVUS) imaging to interrogate atherosclerotic plaques in vivo in large arteries. The goal of this investigation is twofold: (i) introduce a modeling framework for residual stress that unlike traditional Fung type classical opening angle models may be used for a diseased artery, and (ii) investigate the sensitivity of the spectra of small amplitude high frequency time harmonic vibrations superimposed on a large deformation to the details of the residual stress stored in arteries through a numerical simulation using physiologic parameter values under both low and high blood pressure loadings. The modeling framework also points the way towards an inverse problem using IVUS techniques to estimate residual stress in healthy and diseased arteries. © 2010 Elsevier Ltd. All rights reserved.

  20. Non-linear finite element modeling

    DEFF Research Database (Denmark)

    Mikkelsen, Lars Pilgaard

    The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...... on the governing equations and methods of implementing....

  1. EFFECTIVE STRESS AND STRAIN IN FINITE DEFORMATION

    Institute of Scientific and Technical Information of China (English)

    周喆; 秦伶俐; 黄文彬; 王红卫

    2004-01-01

    Whether the concept of effective stress and strain in elastic-plastic theory is still valid under the condition of finite deformation was mainly discussed. The uni-axial compression experiments in plane stress and plane strain states were chosen for study. In the two kinds of stress states, the stress- strain curve described by logarithm strain and rotated Kirchhoff stress matches the experiments data better than the curves defined by other stressstrain description.

  2. Introduction to nonlinear finite element analysis

    CERN Document Server

    Kim, Nam-Ho

    2015-01-01

    This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: ·         Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems ·         Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory ·    ...

  3. Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector

    Science.gov (United States)

    Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)

    2001-01-01

    Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.

  4. The Finite Deformation Dynamic Sphere Test Problem

    Energy Technology Data Exchange (ETDEWEB)

    Versino, Daniele [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Brock, Jerry Steven [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2016-09-02

    In this manuscript we describe test cases for the dynamic sphere problem in presence of finite deformations. The spherical shell in exam is made of a homogeneous, isotropic or transverse isotropic material and elastic and elastic-plastic material behaviors are considered. Twenty cases, (a) to (t), are thus defined combining material types and boundary conditions. The inner surface radius, the outer surface radius and the material's density are kept constant for all the considered test cases and their values are ri = 10mm, ro = 20mm and p = 1000Kg/m3 respectively.

  5. A nonlinear viscoelastic constitutive equation - Yield predictions in multiaxial deformations

    Science.gov (United States)

    Shay, R. M., Jr.; Caruthers, J. M.

    1987-01-01

    Yield stress predictions of a nonlinear viscoelastic constitutive equation for amorphous polymer solids have been obtained and are compared with the phenomenological von Mises yield criterion. Linear viscoelasticity theory has been extended to include finite strains and a material timescale that depends on the instantaneous temperature, volume, and pressure. Results are presented for yield and the correct temperature and strain-rate dependence in a variety of multiaxial deformations. The present nonlinear viscoelastic constitutive equation can be formulated in terms of either a Cauchy or second Piola-Kirchhoff stress tensor, and in terms of either atmospheric or hydrostatic pressure.

  6. Nonlinear Finite Element Analysis of Ocean Cables

    Institute of Scientific and Technical Information of China (English)

    Nam-Il KIM; Sang-Soo JEON; Moon-Young KIM

    2004-01-01

    This study has focused on developing numerical procedures for the dynamic nonlinear analysis of cable structures subjected to wave forces and ground motions in the ocean. A geometrically nonlinear finite element procedure using the isoparametric curved cable element based on the Lagrangian formulation is briefly summarized. A simple and accurate method to determine the initial equilibrium state of cable systems associated with self-weights, buoyancy and the motion of end points is presented using the load incremental method combined with penalty method. Also the Newmark method is used for dynamic nonlinear analysis of ocean cables. Numerical examples are presented to validate the present numerical method.

  7. Dynamic Stability of Viscoelastic Plates with Finite Deformation and Shear Effects

    Institute of Scientific and Technical Information of China (English)

    李晶晶; 程昌钧; 等

    2002-01-01

    Based on Reddy's theory of plates with higher-order shear deformations and the Boltzmann superposition principles,the governing equations were established for dynamic stability of viscoelastic plates with finite deformations taking account of shear effects,The Galerkin method was applied to simplify the set of equations.The numerical methods in nonlinear dynamics were used to solve the simplified system.It could e seen that there are plenty of dynamic properties for this kind of viscoelastic plates under transverse harmonic loads.The influences of the transverse shear deformations and material parameter on the dynamic behavior of nonlinear viscoelatic plates were investigated.

  8. Finite Deformations of Conformal Field Theories Using Analytically Regularized Connections

    OpenAIRE

    von Gussich, Alexander; Sundell, Per

    1996-01-01

    We study some natural connections on spaces of conformal field theories using an analytical regularization method. The connections are based on marginal conformal field theory deformations. We show that the analytical regularization preserves conformal invariance and leads to integrability of the marginal deformations. The connections are shown to be flat and to generate well-defined finite parallel transport. These finite parallel transports yield formulations of the deformed theories in the...

  9. ANALYSIS OF SIMPLE SHEAR ENDOCHRONIC EQUATIONS FOR FINITE PLASTIC DEFORMATION

    Institute of Scientific and Technical Information of China (English)

    江五贵; 黄明挥

    2005-01-01

    Jaumann rate, generalized Jaumann rate, Fu rate and Wu rate were incorporated into endochronic equations forfinite plastic deformation to analyze simple shear finite deformation. The results show that an oscillatory shear stress and normal stress response to a monotonically increasing shear strain occurs when Jaumann rate objective model is adopted for hypoelastic or endochronic materials. The oscillatory response is dependent on objective rate adopted, independent on elastoplastic models. Normal stress is unequal to zero during simple shear finite deformation.

  10. Some variational principles in electroelastic media under finite deformation

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    It is proposed that the universal thermodynamic energy variational principle is in-cluded in the first law of thermodynamics. Some variational principles in the elec-troelastic media under finite deformation are derived from this universal thermo-dynamic variational principle. It is suggested that in the general electroelastic analysis the environment should be considered together with the discussed elec-troelastic medium. For the variational principle of nonlinear electroelastic media the variation of the electric potential is coupled with the virtual displacement,and the variation of the initial volume should be considered. The Maxwell stress in the initial configuration is naturally derived from this variational principle and it is unique in the second order precision.

  11. Some variational principles in electroelastic media under finite deformation

    Institute of Scientific and Technical Information of China (English)

    KUANG ZhenBang

    2008-01-01

    It is proposed that the universal thermodynamic energy variational principle is in-cluded in the first law of thermodynamics. Some variational principles in the elec-troelastic media under finite deformation are derived from this universal thermo-dynamic variational principle. It is suggested that in the general electroelastic analysis the environment should be considered together with the discussed elec-troelastic medium. For the variational principle of nonlinear electroelastic media the variation of the electric potential is coupled with the virtual displacement, and the variation of the initial volume should be considered. The Maxwell stress in the initial configuration is naturally derived from this variational principle and it is unique in the second order precision.

  12. Finite Deformation by Elasticity, Slip, and Twinning: Atomistic Considerations, Continuum Modeling, and Application to Ceramic Crystals

    Science.gov (United States)

    2009-03-01

    finite shear strains associated with slip and deformation twinning and improper lattice rotations across twin boundaries . Nonlinear anisotropic...of (2) results from gradients in twin fractions, e.g. interface dislocations at tapered twin boundaries . Disclination models of twins (Clayton et

  13. Hyperelastic bodies under homogeneous Cauchy stress induced by non-homogeneous finite deformations

    CERN Document Server

    Mihai, L Angela

    2016-01-01

    We discuss whether homogeneous Cauchy stress implies homogeneous strain in isotropic nonlinear elasticity. While for linear elasticity the positive answer is clear, we exhibit, through detailed calculations, an example with inhomogeneous continuous deformation but constant Cauchy stress. The example is derived from a non rank-one convex elastic energy. Connections to conforming and non-conforming finite element implementations are drawn.

  14. DIFFERENTIAL QUADRATURE METHOD FOR BENDING OF ORTHOTROPIC PLATES WITH FINITE DEFORMATION AND TRANSVERSE SHEAR EFFECTS

    Institute of Scientific and Technical Information of China (English)

    李晶晶; 程昌钧

    2004-01-01

    Based on the Reddy' s theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature ( DQ ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert (DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated.Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.

  15. NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS

    Directory of Open Access Journals (Sweden)

    Hasan YILDIZ

    2004-03-01

    Full Text Available Deep drawing process is one of the main procedures used in different branches of industry. Finding numerical solutions for determination of the mechanical behaviour of this process will save time and money. In die surfaces, which have complex geometries, it is hard to determine the effects of parameters of sheet metal forming. Some of these parameters are wrinkling, tearing, and determination of the flow of the thin sheet metal in the die and thickness change. However, the most difficult one is determination of material properties during plastic deformation. In this study, the effects of all these parameters are analyzed before producing the dies. The explicit non-linear finite element method is chosen to be used in the analysis. The numerical results obtained for non-linear material and contact models are also compared with the experiments. A good agreement between the numerical and the experimental results is obtained. The results obtained for the models are given in detail.

  16. Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel

    Institute of Scientific and Technical Information of China (English)

    Vishesh Ranjan Kar; Subrata Kumar Panda

    2016-01-01

    In the present article, the linear and the nonlinear deformation behaviour of functionally graded (FG) spherical shell panel are examined under thermomechanical load. The temperature-dependent effective material properties of FG shell panel are evaluated using Voigt’s micro-mechanical rule in conjunction with power-law distribution. The nonlinear mathematical model of the FG shell panel is developed based on higher-order shear deformation theory and Green-Lagrange type geometrical nonlinearity. The desired nonlinear governing equation of the FG shell panel is computed using the variational principle. The model is discretised through suitable nonlinear finite element steps and solved using direct iterative method. The convergence and the val-idation behaviour of the present numerical model are performed to show the efficacy of the model. The effect of different parameters on the nonlinear deformation behaviour of FG spherical shell panel is highlighted by solving numerous examples.

  17. Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel

    Directory of Open Access Journals (Sweden)

    Vishesh Ranjan Kar

    2016-02-01

    Full Text Available In the present article, the linear and the nonlinear deformation behaviour of functionally graded (FG spherical shell panel are examined under thermomechanical load. The temperature-dependent effective material properties of FG shell panel are evaluated using Voigt’s micro-mechanical rule in conjunction with power-law distribution. The nonlinear mathematical model of the FG shell panel is developed based on higher-order shear deformation theory and Green-Lagrange type geometrical nonlinearity. The desired nonlinear governing equation of the FG shell panel is computed using the variational principle. The model is discretised through suitable nonlinear finite element steps and solved using direct iterative method. The convergence and the validation behaviour of the present numerical model are performed to show the efficacy of the model. The effect of different parameters on the nonlinear deformation behaviour of FG spherical shell panel is highlighted by solving numerous examples.

  18. Nonlinear Finite Element Analysis of Sloshing

    Directory of Open Access Journals (Sweden)

    Siva Srinivas Kolukula

    2013-01-01

    Full Text Available The disturbance on the free surface of the liquid when the liquid-filled tanks are excited is called sloshing. This paper examines the nonlinear sloshing response of the liquid free surface in partially filled two-dimensional rectangular tanks using finite element method. The liquid is assumed to be inviscid, irrotational, and incompressible; fully nonlinear potential wave theory is considered and mixed Eulerian-Lagrangian scheme is adopted. The velocities are obtained from potential using least square method for accurate evaluation. The fourth-order Runge-Kutta method is employed to advance the solution in time. A regridding technique based on cubic spline is employed to avoid numerical instabilities. Regular harmonic excitations and random excitations are used as the external disturbance to the container. The results obtained are compared with published results to validate the numerical method developed.

  19. FINITE DEFORMATION ELASTO-PLASTIC THEORY AND CONSISTENT ALGORITHM

    Institute of Scientific and Technical Information of China (English)

    Liu Xuejun; Li Mingrui; Huang Wenbin

    2001-01-01

    By using the logarithmic strain, the finite deformation plastic theory, corresponding to the infinitesimal plastic theory, is established successively. The plastic consistent algorithm with first order accuracy for the finite element method (FEM) is developed. Numerical examples are presented to illustrate the validity of the theory and effectiveness of the algorithm.

  20. SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.

    1999-03-01

    This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.

  1. Advantages of formulating an evolution equation directly for elastic distortional deformation in finite deformation plasticity

    Science.gov (United States)

    Rubin, M. B.; Cardiff, P.

    2017-06-01

    Simo (Comput Methods Appl Mech Eng 66:199-219, 1988) proposed an evolution equation for elastic deformation together with a constitutive equation for inelastic deformation rate in plasticity. The numerical algorithm (Simo in Comput Methods Appl Mech Eng 68:1-31, 1988) for determining elastic distortional deformation was simple. However, the proposed inelastic deformation rate caused plastic compaction. The corrected formulation (Simo in Comput Methods Appl Mech Eng 99:61-112, 1992) preserves isochoric plasticity but the numerical integration algorithm is complicated and needs special methods for calculation of the exponential map of a tensor. Alternatively, an evolution equation for elastic distortional deformation can be proposed directly with a simplified constitutive equation for inelastic distortional deformation rate. This has the advantage that the physics of inelastic distortional deformation is separated from that of dilatation. The example of finite deformation J2 plasticity with linear isotropic hardening is used to demonstrate the simplicity of the numerical algorithm.

  2. Finite Element Analysis of Deformed Legs of Offshore Platform Structures

    Institute of Scientific and Technical Information of China (English)

    柳春图; 秦太验; 段梦兰

    2002-01-01

    The element stiffness matrix of the equivalent beam or pipe element of the deformed leg of the platform is derived bythe finite element method. The stresses and displacements of some damaged components are calculated, and the numeri-cal solutions agree well with those obtained by the fine mesh finite element method. Finally, as an application of thismethod, the stresses of some platform structures are calculated and analyzed.

  3. Finite temperature Casimir effect in the presence of nonlinear dielectrics

    CERN Document Server

    Kheirandish, Fardin; Soltani, Morteza

    2010-01-01

    Starting from a Lagrangian, electromagnetic field in the presence of a nonlinear dielectric medium is quantized using path-integral techniques and correlation functions of different fields are calculated. The susceptibilities of the nonlinear medium are obtained and their relation to coupling functions are determined. Finally, the Casimir energy and force in the presence of a nonlinear medium at finite temperature is calculated.

  4. Compositional Finite-Time Stability analysis of nonlinear systems

    DEFF Research Database (Denmark)

    Tabatabaeipour, Mojtaba; Blanke, Mogens

    2014-01-01

    for the system but with bounded disturbance. Sufficient conditions for finite-time stability and finite-time boundedness of nonlinear systems as well as a computational method based on sum of squares programming to check the conditions are given. The problem of finite-time stability for a system that consists......This paper, investigates finite-time stability and finite-time boundedness for nonlinear systems with polynomial vector fields. Finite-time stability requires the states of the system to remain a given bounded set in a finite-time interval and finite-time boundedness considers the same problem...... of an interconnection of subsystems is also considered and we show how to decompose the problem into subproblems for each subsystem with coupling constraints. A solution to the problem using sum of squares programming and dual decomposition is presented. The method is demonstrated through some examples....

  5. Rapid Finite Element Analysis of Bulk Metal Forming Process Based on Deformation Theory

    Institute of Scientific and Technical Information of China (English)

    WANG Peng; DONG Xiang-huai; FU Li-jun

    2009-01-01

    The one-step finite element method (FEM), based on plastic deformation theory, has been widely used to simulate sheet metal forming processes, but its application in bulk metal forming simulation has been seldom investigated, because of the complexity involved. Thus, a bulk metal forming process was analyzed using a rapid FEM based on deformation theory. The material was assumed to be rigid-plastic and strain-hardened. The constitutive relationship between stress and total strain was adopted, whereas the incompressible condition was enforced by penalty function. The geometrical non-linearity in large plastic deformation was taken into consideration. Furthermore, the force boundary condition was treated by a simplified equivalent approach, considering the contact history. Based on constraint variational principle, the deformation FEM was proposed. The one-step forward simulation of axisymmetric upsetting process was performed using this method. The results were compared with those obtained by the traditional incremental FEM to verify the feasibility of the proposed method.

  6. Assessment of the non-linear behaviour of plastic ankle foot orthoses by the finite element method

    OpenAIRE

    Syngellakis, S.; Arnold, M. A.; Rassoulian, H.

    2000-01-01

    The stiffness characteristics of plastic ankle foot orthoses (AFOs) are studied through finite element modelling and stress analysis. Particular attention is given to the modelling and prediction of non-linear AFO behaviour, which has been frequently observed in previous experimental studies but not fully addressed analytically. Both large deformation effects and material non-linearity are included in the formulation and their individual influence on results assessed. The finite element progr...

  7. Finite-time disturbance attenuation of nonlinear systems

    Institute of Scientific and Technical Information of China (English)

    MO LiPo; JIA YingMin; ZHENG ZhiMing

    2009-01-01

    This paper is devoted to the finite-time disturbance attenuation problem of affine nonlinear systems.Based on the finite time Lyapunov stability theory,some finite-time H_∞ performance criterions are derived.Then the state-feedback control law is designed and the structure of such a controller is investigated.Furthermore,it is shown that the H_∞ controller can also make the closed-loop system satisfy finite-time H_∞ performance for nonlinear homogeneous systems.An example is provided to demonstrate the effectiveness of the presented results.

  8. Nonlinear Finite Strain Consolidation Analysis with Secondary Consolidation Behavior

    Directory of Open Access Journals (Sweden)

    Jieqing Huang

    2014-01-01

    Full Text Available This paper aims to analyze nonlinear finite strain consolidation with secondary consolidation behavior. On the basis of some assumptions about the secondary consolidation behavior, the continuity equation of pore water in Gibson’s consolidation theory is modified. Taking the nonlinear compressibility and nonlinear permeability of soils into consideration, the governing equation for finite strain consolidation analysis is derived. Based on the experimental data of Hangzhou soft clay samples, the new governing equation is solved with the finite element method. Afterwards, the calculation results of this new method and other two methods are compared. It can be found that Gibson’s method may underestimate the excess pore water pressure during primary consolidation. The new method which takes the secondary consolidation behavior, the nonlinear compressibility, and nonlinear permeability of soils into consideration can precisely estimate the settlement rate and the final settlement of Hangzhou soft clay sample.

  9. Prediction of the nonlinear creep deformation of plastic products

    OpenAIRE

    Spoormaker, Jan; Skrypnyk, Ihor; Heidweiller, Anton

    2015-01-01

    Based on an example of the non-linear creep deformations of an air inlet, thispaper demonstrates modern capabilities in the FEA modeling of complex 3D visco-elastic deformations in relation to the design of plastic products. The importance of such capabilities for designing complex plastic components is discussed. Because commercial FEA packages do not yet render these capabilities "off the shelf", the non-linear visco-elasticity model is incorporated through a user subroutine. The specifics ...

  10. Nonlinear electroelastic deformations of dielectric elastomer composites: II - Non-Gaussian elastic dielectrics

    Science.gov (United States)

    Lefèvre, Victor; Lopez-Pamies, Oscar

    2017-02-01

    This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response - under finite deformations and finite electric fields - of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal elastic dielectric composites within the context of a nonlinear comparison medium method - this is derived as an extension of the comparison medium method of Lopez-Pamies et al. (2013) in nonlinear elastostatics to the coupled realm of nonlinear electroelastostatics - to generate in turn a corresponding solution for composite materials with non-ideal elastic dielectric constituents. Complementary to this analytical framework, a hybrid finite-element formulation to construct homogenization solutions numerically (in three dimensions) is also presented. The proposed analytical framework is utilized to work out a general approximate homogenization solution for non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. The solution applies to arbitrary (non-percolative) isotropic distributions of filler particles. By construction, it is exact in the limit of small deformations and moderate electric fields. For finite deformations and finite electric fields, its accuracy is demonstrated by means of direct comparisons with finite-element solutions. Aimed at gaining physical insight into the extreme enhancement in electrostriction properties displayed by emerging dielectric elastomer composites, various cases wherein the filler particles are of poly- and mono-disperse sizes and exhibit different types of elastic dielectric behavior are discussed in detail. Contrary to an initial conjecture in the literature, it is found (inter alia) that the isotropic addition of a small volume fraction of stiff (semi

  11. Viscoelastic models with consistent hypoelasticity for fluids undergoing finite deformations

    Science.gov (United States)

    Altmeyer, Guillaume; Rouhaud, Emmanuelle; Panicaud, Benoit; Roos, Arjen; Kerner, Richard; Wang, Mingchuan

    2015-08-01

    Constitutive models of viscoelastic fluids are written with rate-form equations when considering finite deformations. Trying to extend the approach used to model these effects from an infinitesimal deformation to a finite transformation framework, one has to ensure that the tensors and their rates are indifferent with respect to the change of observer and to the superposition with rigid body motions. Frame-indifference problems can be solved with the use of an objective stress transport, but the choice of such an operator is not obvious and the use of certain transports usually leads to physically inconsistent formulation of hypoelasticity. The aim of this paper is to present a consistent formulation of hypoelasticity and to combine it with a viscosity model to construct a consistent viscoelastic model. In particular, the hypoelastic model is reversible.

  12. Large deformation simulation of anisotropic material using an updated Lagrangian finite element method

    NARCIS (Netherlands)

    Thije, ten R.H.W.; Akkerman, R.; Huetink, J.

    2007-01-01

    Large deformation finite element (FE) simulations of anisotropic material often show slow convergence or break down with increasing anisotropy and deformation. Large deformations are generally approximated by multiple small linearised steps. This leads to poor performance and contradicting formulati

  13. Study on finite deformation finite element analysis algorithm of turbine blade based on CPU+GPU heterogeneous parallel computation

    Directory of Open Access Journals (Sweden)

    Liu Tian-Yuan

    2016-01-01

    Full Text Available Blade is one of the core components of turbine machinery. The reliability of blade is directly related to the normal operation of plant unit. However, with the increase of blade length and flow rate, non-linear effects such as finite deformation must be considered in strength computation to guarantee enough accuracy. Parallel computation is adopted to improve the efficiency of classical nonlinear finite element method and shorten the blade design period. So it is of extraordinary importance for engineering practice. In this paper, the dynamic partial differential equations and the finite element method forms for turbine blades under centrifugal load and flow load are given firstly. Then, according to the characteristics of turbine blade model, the classical method is optimized based on central processing unit + graphics processing unit heterogeneous parallel computation. Finally, the numerical experiment validations are performed. The computation speed of the algorithm proposed in this paper is compared with the speed of ANSYS. For the rectangle plate model with mesh number of 10 k to 4000 k, a maximum speed-up of 4.31 can be obtained. For the real blade-rim model with mesh number of 500 k, the speed-up of 4.54 times can be obtained.

  14. STUDY ON DYNAMIC CONSTITUTIVE RELATIONS FOR CONCRETE WITH FINITE DEFORMATION

    Institute of Scientific and Technical Information of China (English)

    陈书宇; 沈成康; 金吾根

    2004-01-01

    The differences between finite deformation and infinitesimal deformation are discussed. They are exercised on elasto-viscoplastic constitutive relations of concrete.Then, a rate-dependent mechanics model was presented on the basis of Ottosen' s fourparameter yield criterion, where different loading surface transferring laws were taken into account, when material was in hardening stage or in softening stage, respectively. The model is well established, so that it can be applied to simulate the response of concrete subject to impact loading. Green-Naghdi stress rate was introduced as objective stress rate.Appropriate hypothesis was postulated in accordance with many experimental results, which could reflect the mechanical behaviour of concrete with large deformation. Available thoughts as well as effective methods are also provided for the research on related engineering problems.

  15. Research on nonlinear constitutive relationship of permanent deformation in asphalt pavements

    Institute of Scientific and Technical Information of China (English)

    PENG; Miaojuan; XU; Zhihong

    2006-01-01

    To predict correctly the rut depths in asphalt pavements,a new nonlinear viscoelastic-elastoplastic constitutive model of permanent deformation in asphalt pavements is presented.The model combines a generalized Maxwell model with an elastoplastic one.Then from the creep theory,the linear and nonlinear constitutive equations of the generalized Maxwell model are obtained.From the nonlinear finite element method for the rutting of the asphalt pavement,the rut depths of 4 asphalt-aggregate mixtures are obtained.And the results are compared with the ones from the finite element method by SHRP and the experiments by SWK/UN.The results in this paper are better than the ones by SHRP,and agree with the ones of the experiment by SWK/UN.This shows that the nonlinear viscoelastic-elastoplastic constitutive model,which is presented in this paper for the rutting of the asphalt pavement,is effective.The properties,such as nonlinear elasticity,plasticity,viscoelasticity and nonlinear viscoelasticity,which affect the rutting of an asphalt pavement,can be shown in the model.And the characteristics of the permanent deformation of the asphalt pavement can be presented entirely in the model.

  16. Curved Displacement Transfer Functions for Geometric Nonlinear Large Deformation Structure Shape Predictions

    Science.gov (United States)

    Ko, William L.; Fleischer, Van Tran; Lung, Shun-Fat

    2017-01-01

    For shape predictions of structures under large geometrically nonlinear deformations, Curved Displacement Transfer Functions were formulated based on a curved displacement, traced by a material point from the undeformed position to deformed position. The embedded beam (depth-wise cross section of a structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution could be described with a piecewise linear or a piecewise nonlinear function. The discretization approach enabled piecewise integrations of the embedded-beam curvature equations to yield the Curved Displacement Transfer Functions, expressed in terms of embedded beam geometrical parameters and surface strains. By entering the surface strain data into the Displacement Transfer Functions, deflections along each embedded beam can be calculated at multiple points for mapping the overall structural deformed shapes. Finite-element linear and nonlinear analyses of a tapered cantilever tubular beam were performed to generate linear and nonlinear surface strains and the associated deflections to be used for validation. The shape prediction accuracies were then determined by comparing the theoretical deflections with the finiteelement- generated deflections. The results show that the newly developed Curved Displacement Transfer Functions are very accurate for shape predictions of structures under large geometrically nonlinear deformations.

  17. Plastic theory for the multi-crystal metals-From infinitesimal deformation to finite deformation

    Institute of Scientific and Technical Information of China (English)

    2003-01-01

    Multi-crystal metals have the property of volume conservation in the plastic state. In the infinitesimal deformation plasticity the strain tensor can be split into a deviator part and a volumetric part. The vanishing of the first variant of the strain tensor is equivalent to the volume conservation. Furthermore, the split of the strain into an elastic part and a plastic part is also adopted widely. The flow rule is thus established. These two splits are not confirmed in the finite deformation plasticity. The plasticity criterion and the flow rule are thus facing great challenge. There are various definitions of strain measures in the finite deformation theory. Though the choosing of strain measure is arbitrary in the elastic problem, it is strongly restricted in the plastic problem. By theoretical and experimental studies, it is shown that the logarithmic strain is the only suitable strain measure in the metal forming problem.

  18. The effect of large deformation and material nonlinearity on gel indentation

    Institute of Scientific and Technical Information of China (English)

    Zheng Duan; Yonghao An; Jiaping Zhang; Hanqing Jiang

    2012-01-01

    A gel,an aggregate of polymers with solvents,has dual attributes of solid and liquid as solvent migrates in and out of the polymer network.Indentation has recently been used to characterize the mechanical properties of gels.This paper evaluates the effects of large deformation and material nonlinearity on gel indentation through theoretical modeling and finite element analysis.It is found that large deformation significantly affects the interpretation of the experimental observations and the classical relation between indentation force and depth has limitations for large deformation.The material nonlinearity does not play a very important role on indentation experiment so that the poroelasticity is a good approximation.Based on these observations,this paper proposes an alternative approach to measure the mechanical properties of gels,namely,uniaxial compression experiment.

  19. Finite Element Analysis to Two-Dimensional Nonlinear Sloshing Problems

    Institute of Scientific and Technical Information of China (English)

    严承华; 王赤忠; 程尔升

    2001-01-01

    A two-dimensional nonlinear sloshing problem is analyzed by means of the fully nonlinear theory and time domainsecond order theory of water waves. Liquid sloshing in a rectangular container subjected to a horizontal excitation is sim-ulated by the finite element method. Comparisons between the two theories are made based on their numerical results. Itis found that good agreement is obtained for the case of small amplitude oscillation and obvious differences occur forlarge amplitude excitation. Even though, the second order solution can still exhibit typical nonlinear features ofnonlinear wave and can be used instead of the fully nonlinear theory.

  20. Nonlinear structural finite element model updating and uncertainty quantification

    Science.gov (United States)

    Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.

    2015-04-01

    This paper presents a framework for nonlinear finite element (FE) model updating, in which state-of-the-art nonlinear structural FE modeling and analysis techniques are combined with the maximum likelihood estimation method (MLE) to estimate time-invariant parameters governing the nonlinear hysteretic material constitutive models used in the FE model of the structure. The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem. A proof-of-concept example, consisting of a cantilever steel column representing a bridge pier, is provided to verify the proposed nonlinear FE model updating framework.

  1. Generalization of strain-gradient theory to finite elastic deformation for isotropic materials

    Science.gov (United States)

    Beheshti, Alireza

    2017-03-01

    This paper concerns finite deformation in the strain-gradient continuum. In order to take account of the geometric nonlinearity, the original strain-gradient theory which is based on the infinitesimal strain tensor is rewritten given the Green-Lagrange strain tensor. Following introducing the generalized isotropic Saint Venant-Kirchhoff material model for the strain-gradient elasticity, the boundary value problem is investigated in not only the material configuration but also the spatial configuration building upon the principle of virtual work for a three-dimensional solid. By presenting one example, the convergence of the strain-gradient and classical theories is studied.

  2. Biomechanical simulation of thorax deformation using finite element approach.

    Science.gov (United States)

    Zhang, Guangzhi; Chen, Xian; Ohgi, Junji; Miura, Toshiro; Nakamoto, Akira; Matsumura, Chikanori; Sugiura, Seiryo; Hisada, Toshiaki

    2016-02-06

    The biomechanical simulation of the human respiratory system is expected to be a useful tool for the diagnosis and treatment of respiratory diseases. Because the deformation of the thorax significantly influences airflow in the lungs, we focused on simulating the thorax deformation by introducing contraction of the intercostal muscles and diaphragm, which are the main muscles responsible for the thorax deformation during breathing. We constructed a finite element model of the thorax, including the rib cage, intercostal muscles, and diaphragm. To reproduce the muscle contractions, we introduced the Hill-type transversely isotropic hyperelastic continuum skeletal muscle model, which allows the intercostal muscles and diaphragm to contract along the direction of the fibres with clinically measurable muscle activation and active force-length relationship. The anatomical fibre orientations of the intercostal muscles and diaphragm were introduced. Thorax deformation consists of movements of the ribs and diaphragm. By activating muscles, we were able to reproduce the pump-handle and bucket-handle motions for the ribs and the clinically observed motion for the diaphragm. In order to confirm the effectiveness of this approach, we simulated the thorax deformation during normal quiet breathing and compared the results with four-dimensional computed tomography (4D-CT) images for verification. Thorax deformation can be simulated by modelling the respiratory muscles according to continuum mechanics and by introducing muscle contractions. The reproduction of representative motions of the ribs and diaphragm and the comparison of the thorax deformations during normal quiet breathing with 4D-CT images demonstrated the effectiveness of the proposed approach. This work may provide a platform for establishing a computational mechanics model of the human respiratory system.

  3. Finite element analysis on deformation of high embankment in heavy-haul railway subjected to freeze-thaw cycles

    Institute of Scientific and Technical Information of China (English)

    ChengYi Yu; Shuang Tian; Liang Tang; XianZhang Ling; GuoQing Zhou

    2015-01-01

    Finite element simulations are increasingly providing a versatile environment for this topic. In this study, a two-dimensional finite element analysis is conducted to predict the deformation of high embankment in Bazhun heavy-haul railway, China. A recently developed nonlinear softening-type constitutive model is utilized to model the be-havior of subgrade filling materials subjected to freeze-thaw cycles. For the convenience of practical application, the dynamic loading induced by a vehicle is treated as a quasi-static axle load. The deformation of this embankment with different moisture content under freeze-thaw cycles is compared. The results show that when subjected to the first freeze-thaw cycle, the embankment experienced significant deformation variations. Maximum deformation was usually achieved after the embankment with optimum moisture content experienced six freeze-thaw cycles, however, the em-bankment with moisture content of 8.0% and 9.5% deforms continuously even after experiencing almost ten freeze-thaw cycles. Overall, this study provides a simple nonlinear finite element approach for calculating the deformation of the embankment in changing climate conditions.

  4. Finite rotation and nonlinear beam kinematics

    Science.gov (United States)

    Hodges, Dewey H.

    1987-01-01

    Standard means of representing finite rotation in rigid-body kinematics, including orientation angles, Euler parameters, and Rodrigues parameters, are reviewed and compared. General kinematical relations for a beam theory that treats arbitrarily large rotation are then presented. The standard methods of representing finite rotations are applied to these kinematical expressions, and comparison is made among the standard methods and additional methods found in the literature, such as quasi-coordinates and linear combinations of projection angles. The method of Rodrigues parameters is shown to stand out for both its simplicity and generality when applied to beam kinematics, a result that is really missing from the literature.

  5. Non-bicolourable Finite Configurations of Rays and Their Deformations

    CERN Document Server

    Ruuge, Artur

    2009-01-01

    A new infinite family of examples of finite non-bicolorable configurations of rays in Hilbert space is described. Such configurations appear in the analysis of quantum mechanics in terms of Bell's inequalities and Kochen-Specker theorem and illustrate that there is no measurable space in the background of the probability model of a quantum system. The mentioned examples are naturally parametrized by a positive integer divisible by four and by several complex-valued parameters, whose number depends on this integer. In order to compare two configurations with the same number of rays, a notion of deformation of a configuration is introduced. The constructed examples are then interpreted as obtained by way of deformations.

  6. Adaptive Algorithms of Nonlinear Approximation with Finite Terms

    Institute of Scientific and Technical Information of China (English)

    Wen Bin WEI; Yue Sheng XU; Pei Xin YE

    2007-01-01

    This paper deals with realizable adaptive algorithms of the nonlinear approximation with finite terms based on wavelets. We present a concrete algorithm by which we may find the required index set Am for the greedy algorithm GPm(·,ψ). This makes the greedy algorithm realize the near best approximation in practice. Moreover, we study the efficiency of the finite-term approximation of another algorithm introduced by Birge and Massart.

  7. Finite deformations of an electroelastic circular cylindrical tube

    Science.gov (United States)

    Melnikov, Andrey; Ogden, Ray W.

    2016-12-01

    In this paper the theory of nonlinear electroelasticity is used to examine deformations of a pressurized thick-walled circular cylindrical tube of soft dielectric material with closed ends and compliant electrodes on its curved boundaries. Expressions for the dependence of the pressure and reduced axial load on the deformation and a potential difference between, or uniform surface charge distributions on, the electrodes are obtained in respect of a general isotropic electroelastic energy function. To illustrate the behaviour of the tube, specific forms of energy functions accounting for different mechanical properties coupled with a deformation independent quadratic dependence on the electric field are used for numerical purposes, for a given potential difference and separately for a given charge distribution. Numerical dependences of the non-dimensional pressure and reduced axial load on the deformation are obtained for the considered energy functions. Results are then given for the thin-walled approximation as a limiting case of a thick-walled cylindrical tube without restriction on the energy function. The theory described herein provides a general basis for the detailed analysis of the electroelastic response of tubular dielectric elastomer actuators, which is illustrated for a fixed axial load in the absence of internal pressure and fixed internal pressure in the absence of an applied axial load.

  8. High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

    Science.gov (United States)

    Fisher, Travis C.; Carpenter, Mark H.

    2013-01-01

    Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

  9. Nonlinear susceptibilities of finite conjugated organic polymers

    Science.gov (United States)

    Beratan, David N.; Onuchic, Jose Nelson; Perry, Joseph W.

    1987-01-01

    Tight-binding calculations of the length dependence of the third-order molecular hyperpolarizability for polyenes and polyynes are reported. The pi-electron wave functions were determined by exploiting the limited translational symmetry of the molecules. Perturbation theory was used to calculate the longitudinal component of the electronic nonresonant hyperpolarizability. This is the first two-'band' calculation of third-order hyperpolarizabilities on finite pi-electron systems of varying length. In contrast to the results of the one-'band' models, the hyperpolarizability densities increase rapidly and then, after about 10-15 repeating units, approach an asymptotic value.

  10. An Orthogonal Residual Procedure for Nonlinear Finite Element Equations

    DEFF Research Database (Denmark)

    Krenk, S.

    A general and robust solution procedure for nonlinear finite element equations with limit points is developed. At each equilibrium iteration the magnitude of the load is adjusted such that the residual force is orthogonal to the current displacement increment from the last equilibrium state...

  11. A Dual Orthogonality Procedure for Nonlinear Finite Element Equations

    DEFF Research Database (Denmark)

    Krenk, S.; Hededal, O.

    In the orthogonal residual procedure for solution of nonlinear finite element equations the load is adjusted in each equilibrium iteration to satisfy an orthogonality condition to the current displacement increment. It is here shown that the quasi-newton formulation of the orthogonal residual...

  12. Real-Time Nonlinear Finite Element Computations on GPU - Application to Neurosurgical Simulation.

    Science.gov (United States)

    Joldes, Grand Roman; Wittek, Adam; Miller, Karol

    2010-12-15

    Application of biomechanical modeling techniques in the area of medical image analysis and surgical simulation implies two conflicting requirements: accurate results and high solution speeds. Accurate results can be obtained only by using appropriate models and solution algorithms. In our previous papers we have presented algorithms and solution methods for performing accurate nonlinear finite element analysis of brain shift (which includes mixed mesh, different non-linear material models, finite deformations and brain-skull contacts) in less than a minute on a personal computer for models having up to 50.000 degrees of freedom. In this paper we present an implementation of our algorithms on a Graphics Processing Unit (GPU) using the new NVIDIA Compute Unified Device Architecture (CUDA) which leads to more than 20 times increase in the computation speed. This makes possible the use of meshes with more elements, which better represent the geometry, are easier to generate, and provide more accurate results.

  13. Finite lattice distortion patterns in plastically deformed zircon grains

    Directory of Open Access Journals (Sweden)

    E. Kovaleva

    2014-07-01

    Full Text Available This study examines finite deformation patterns of zircon grains from high-temperature natural shear zones. Various zircon-bearing rocks were collected in the Western Tauern Window, Eastern Alps, where they were deformed under amphibolite facies conditions, and in the Ivrea-Verbano Zone (IVZ, Southern Alps, where deformation is related with granulite-facies metamorphism. Among the sampled rocks are: granitic orthogneisses, meta-lamprophyres and paragneisses, all of which are highly deformed. The investigated zircon grains ranging from 10 to 50 microns were studied in situ using a combination of scanning electron microscope (SEM techniques, including secondary electron (SE, backscattered electron (BSE, forward scattered electron (FSE, cathodoluminescence (CL imaging, and crystallographic orientation mapping by electron backscatter diffraction analysis (EBSD, as well as micro-Raman spectroscopy. Energy-dispersive X-ray spectrometry (EDS was applied to host phases. Microstructural analysis of crystal-plastically deformed zircon grains was based on high-resolution EBSD maps. Three general types of finite lattice distortion patterns were detected: Type (I is defined by gradual bending of the zircon lattice with orientation changes of about 0.6° to 1.4° per μm without subgrain boundary formation. Type (II represents local gradual bending of the crystal lattice coupled with the formation of subgrain boundaries that have concentric semicircular shapes in 2-D sections. Cumulative grain-internal orientation variations range from 7° to 40° within single grains. Type (III is characterized by formation of subgrains separated by a well-defined subgrain boundary network, where subgrain boundaries show a characteristic angular closed contour in 2-D sections. The cumulative orientation variation within a single grain ranges from 3° to 10°. Types (I and (II predominate in granulite facies rocks, whereas type (III is restricted to the amphibolite facies

  14. Efficient inversion of three-dimensional finite element models of volcano deformation

    Science.gov (United States)

    Charco, M.; Galán del Sastre, P.

    2014-03-01

    Numerical techniques, as such as finite element method, allow for the inclusion of features, such as topography and/or mechanical heterogeneities, for the interpretation of volcanic deformation. However, models based on these numerical techniques usually are not suitable to be included in non-linear estimations of source parameters based on explorative optimization schemes because they require a calculation of the numerical approach for every evaluation of the misfit function. We present a procedure for finite element (FE) models that can be combined with explorative inversion schemes. The methodology is based on including a body force term representing an infinitesimal source in the model formulation that is responsible for pressure (volume) changes in the medium. This provides significant savings in both the time required for mesh generation and actual computational time of the numerical approach. Furthermore, we develop an inversion algorithm to estimate those parameters that characterize the changes in location and pressure (volume) of deformation sources. Both provide FE inversions in a single step, avoiding remeshing and assembly of the linear system of algebraic equations that define the numerical approach and/or the automatic mesh generation. After providing the theoretical basis for the model, the numerical approach and the algorithm for the inversions, we test the methodology using a synthetic example in a stratovolcano. Our results suggest that the FE inversion methodology can be considered suitable for efficiently save time in quantitative interpretations of volcano deformation.

  15. Probabilistic finite elements for transient analysis in nonlinear continua

    Science.gov (United States)

    Liu, W. K.; Belytschko, T.; Mani, A.

    1985-01-01

    The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

  16. Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles.

    Directory of Open Access Journals (Sweden)

    Olga Kononova

    2016-01-01

    Full Text Available The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams modeling the particle structure. The beams' deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F-deformation (X spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young's moduli for Hertzian and bending deformations, and the structural damage dependent beams' survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications.

  17. Analysis of acoustic resonator with shape deformation using finite element method

    Indian Academy of Sciences (India)

    G M Kalmse; Ajay Chaudhari; P B Patil

    2000-10-01

    An acoustic resonator with shape deformation has been analysed using the finite element method. The shape deformation issuch that the volume of the resonator remains constant. The effect of deformation on the resonant frequencies is studied. Deformation splits the degenerate frequencies.

  18. Nonlinear Finite Element Analysis of a Composite Non-Cylindrical Pressurized Aircraft Fuselage Structure

    Science.gov (United States)

    Przekop, Adam; Wu, Hsi-Yung T.; Shaw, Peter

    2014-01-01

    The Environmentally Responsible Aviation Project aims to develop aircraft technologies enabling significant fuel burn and community noise reductions. Small incremental changes to the conventional metallic alloy-based 'tube and wing' configuration are not sufficient to achieve the desired metrics. One of the airframe concepts that might dramatically improve aircraft performance is a composite-based hybrid wing body configuration. Such a concept, however, presents inherent challenges stemming from, among other factors, the necessity to transfer wing loads through the entire center fuselage section which accommodates a pressurized cabin confined by flat or nearly flat panels. This paper discusses a nonlinear finite element analysis of a large-scale test article being developed to demonstrate that the Pultruded Rod Stitched Efficient Unitized Structure concept can meet these challenging demands of the next generation airframes. There are specific reasons why geometrically nonlinear analysis may be warranted for the hybrid wing body flat panel structure. In general, for sufficiently high internal pressure and/or mechanical loading, energy related to the in-plane strain may become significant relative to the bending strain energy, particularly in thin-walled areas such as the minimum gage skin extensively used in the structure under analysis. To account for this effect, a geometrically nonlinear strain-displacement relationship is needed to properly couple large out-of-plane and in-plane deformations. Depending on the loading, this nonlinear coupling mechanism manifests itself in a distinct manner in compression- and tension-dominated sections of the structure. Under significant compression, nonlinear analysis is needed to accurately predict loss of stability and postbuckled deformation. Under significant tension, the nonlinear effects account for suppression of the out-of-plane deformation due to in-plane stretching. By comparing the present results with the previously

  19. Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles

    CERN Document Server

    Kononova, Olga; Marx, Kenneth A; Wuite, Gijs J L; Roos, Wouter H; Barsegov, Valeri

    2015-01-01

    We present a new theory for modeling forced indentation spectral lineshapes of biological particles, which considers non-linear Hertzian deformation due to an indenter-particle physical contact and bending deformations of curved beams modeling the particle structure. The bending of beams beyond the critical point triggers the particle dynamic transition to the collapsed state, an extreme event leading to the catastrophic force drop as observed in the force (F)-deformation (X) spectra. The theory interprets fine features of the spectra: the slope of the FX curves and the position of force-peak signal, in terms of mechanical characteristics --- the Young's moduli for Hertzian and bending deformations E_H and E_b, and the probability distribution of the maximum strength with the strength of the strongest beam F_b^* and the beams' failure rate m. The theory is applied to successfully characterize the $FX$ curves for spherical virus particles --- CCMV, TrV, and AdV.

  20. Computational aspects of an implicit finite element procedure for elasto-viscoplastic large deformation problems

    Science.gov (United States)

    Arif, Abul Fazal Muhammad

    1991-12-01

    The details of formulation, numerical implementation, and evaluation of an implicit finite element procedure for nonlinear problems involving large deformation and/or large rotations is presented. A two parameter family of incrementally objective integration schemes is proposed for the analysis of a hypoelastic model with a broad range of unified rate-dependent viscoplastic constitutive models in large deformation problems. These algorithms are a generalization of the mid-point integration rule. An important step in the solution of nonlinear deformation problems using a Newton-Raphson type of iterative scheme is the calculation of a tangent operator (the so-called Jacobian) by linearizing the involved field equations. Full linearization of the virtual work equation is performed in an updated Lagrangian framework together with a calculation of the consistent linearized material moduli. In general, the reference configuration is updated after each iteration to coincide instantaneously with the present guess of the unknown equilibrium configuration. Another approach is to use the previous equilibrium state as the reference configuration until the new equilibrium configuration at the end of the time step is found. The performance of the family of incrementally objective integration schemes and the two different Jacobians is explored with emphasis on their accuracy and convergence characteristics when large incremental steps are used. Some details of the finite element implementation are given for plane strain and axisymmetric problems and results for several numerical test and practical examples are presented and discussed. Finally, the above computational procedure is extended to problems where the theory of exact kinematics is considered and the hyperelastic approximation is used.

  1. Large nonlinear w$_{\\infty}$ algebras from nonlinear integrable deformations of self dual gravity

    CERN Document Server

    Castro, C

    1994-01-01

    A proposal for constructing a universal nonlinear {\\hat W}_{\\infty} algebra is made as the symmetry algebra of a rotational Killing-symmetry reduction of the nonlinear perturbations of Moyal-Integrable deformations of D=4 Self Dual Gravity (IDSDG). This is attained upon the construction of a nonlinear bracket based on nonlinear gauge theories associated with infinite dimensional Lie algebras. A Quantization and supersymmetrization program can also be carried out. The relevance to the Kadomtsev-Petviashvili hierarchy, 2D dilaton gravity, quantum gravity and black hole physics is discussed in the concluding remarks.

  2. Finite element treatment of soft elastohydrodynamic lubrication problems in the finite deformation regime

    Science.gov (United States)

    Stupkiewicz, Stanisław

    2009-10-01

    Soft elastohydrodynamic lubrication (EHL) problem is studied for a reciprocating elastomeric seal with full account of finite configuration changes. The fluid part is described by the Reynolds equation which is formulated on the deformed boundary of the seal treated as a hyperelastic body. The paper is concerned with the finite element (FE) treatment of this soft EHL problem. Displacement-based FE discretization is applied for the solid part. The Reynolds equation is discretized using the FE method or, alternatively, the discontinuous Galerkin method, both employing higher-order interpolation of pressure. The performance of both methods is assessed by studying convergence and stability of the solution for a benchmark problem of an O-ring seal. It is shown that the solution may exhibit spurious oscillations which occur in severe lubrication conditions. Mesh refinement results in reduction of these oscillations, while increasing the pressure interpolation order or application of the discontinuous Galerkin method does not help significantly.

  3. Finite element model calibration of a nonlinear perforated plate

    Science.gov (United States)

    Ehrhardt, David A.; Allen, Matthew S.; Beberniss, Timothy J.; Neild, Simon A.

    2017-03-01

    This paper presents a case study in which the finite element model for a curved circular plate is calibrated to reproduce both the linear and nonlinear dynamic response measured from two nominally identical samples. The linear dynamic response is described with the linear natural frequencies and mode shapes identified with a roving hammer test. Due to the uncertainty in the stiffness characteristics from the manufactured perforations, the linear natural frequencies are used to update the effective modulus of elasticity of the full order finite element model (FEM). The nonlinear dynamic response is described with nonlinear normal modes (NNMs) measured using force appropriation and high speed 3D digital image correlation (3D-DIC). The measured NNMs are used to update the boundary conditions of the full order FEM through comparison with NNMs calculated from a nonlinear reduced order model (NLROM). This comparison revealed that the nonlinear behavior could not be captured without accounting for the small curvature of the plate from manufacturing as confirmed in literature. So, 3D-DIC was also used to identify the initial static curvature of each plate and the resulting curvature was included in the full order FEM. The updated models are then used to understand how the stress distribution changes at large response amplitudes providing a possible explanation of failures observed during testing.

  4. NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

    Institute of Scientific and Technical Information of China (English)

    崔霞

    2002-01-01

    A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD,the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1- and L2-norm space estimates and the O((△t)2) estimate for time variable are obtained.

  5. Geometrically-linear and nonlinear analysis of linear viscoelastic composites using the finite element method

    Science.gov (United States)

    Hammerand, Daniel C.

    Over the past several decades, the use of composite materials has grown considerably. Typically, fiber-reinforced polymer-matrix composites are modeled as being linear elastic. However, it is well-known that polymers are viscoelastic in nature. Furthermore, the analysis of complex structures requires a numerical approach such as the finite element method. In the present work, a triangular flat shell element for linear elastic composites is extended to model linear viscoelastic composites. Although polymers are usually modeled as being incompressible, here they are modeled as compressible. Furthermore, the macroscopic constitutive properties for fiber-reinforced composites are assumed to be known and are not determined using the matrix and fiber properties along with the fiber volume fraction. Hygrothermo-rheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Both the temperature and moisture are taken to be prescribed. Hence, the heat energy generated by the viscoelastic deformations is not considered. When the deformations and rotations are small under an applied load history, the usual engineering stress and strain measures can be used and the time history of a viscoelastic deformation process is determined using the original geometry of the structure. If, however, sufficiently large loads are applied, the deflections and rotations will be large leading to changes in the structural stiffness characteristics and possibly the internal loads carried throughout the structure. Hence, in such a case, nonlinear effects must be taken into account and the appropriate stress and strain measures must be used. Although a geometrically-nonlinear finite element code could always be used to compute geometrically-linear deformation processes, it is inefficient to use such a code for small deformations, due to

  6. MODELING OF NONLINEAR DEFORMATION AND BUCKLING OF ELASTIC INHOMOGENEOUS SHELLS

    Directory of Open Access Journals (Sweden)

    Bazhenov V.A.

    2014-06-01

    Full Text Available The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and postbuckling behavior of thin thermoelastic inhomogeneous shells with complex-shaped mid-surface, geometrical features throughout the thickness, and multilayer structure under complex thermomechanical loading. The method is based on the geometrically nonlinear equations of three-dimensional thermoelasticity and the moment finiteelement scheme. The method is justified numerically. Comparing solutions with those obtained by other authors and by software LIRA and SCAD is conducted.

  7. Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure. I - Theory

    Science.gov (United States)

    Padovan, Joe

    1987-01-01

    In a three-part series of papers, a generalized finite element analysis scheme is developed to handle the steady and transient response of moving/rolling nonlinear viscoelastic structure. This paper considers the development of the moving/rolling element strategy, including the effects of large deformation kinematics and viscoelasticity modeled by fractional integrodifferential operators. To improve the solution strategy, a special hierarchical constraint procedure is developed for the case of steady rolling/translating, as well as a transient scheme involving the use of a Grunwaldian representation of the fractional operator.

  8. A nonlinear truss finite element with varying stiffness

    Directory of Open Access Journals (Sweden)

    Ďuriš R.

    2007-11-01

    Full Text Available This contribution deals with a new truss element with varying stiffness intended to geometric and physically nonlinear analysis of composite structures. We present a two-node straight composite truss finite element derived by new nonincremental full geometric nonlinear approach. Stiffness matrix of this composite truss contains transfer constants, which accurately describe the polynomial longitudinal variation of cross-section area and material properties. These variations could be caused by nonhomogenous temperature field or by varying components volume fractions of the composite or/and functionally graded materials (FGM´s. Numerical examples were solved to verify the established relations. The accuracy of the new proposed finite truss element are compared and discused.

  9. Arc-length technique for nonlinear finite element analysis

    Institute of Scientific and Technical Information of China (English)

    MEMON Bashir-Ahmed; SU Xiao-zu(苏小卒)

    2004-01-01

    Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, Received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.

  10. Finite Element Analysis for Effect of Roll Radius on Metal Deformation of Hot Rolling Plate

    Institute of Scientific and Technical Information of China (English)

    LUO De-xing; CHEN Qi-an; LIU Li-wen

    2005-01-01

    The deformation of rolling piece in hot rolling by flat roll with different radii is analyzed with three-dimensional large deformation thermo-mechanical coupling finite element method. The distribution laws of stress, strain and strain energy density in deformation zone with rolls of different radii were studied. The result indicated that under the same condition, the larger the roll radius is, the more vigorous the deformation in deformation zone is.

  11. Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Q.; Sprague, M. A.; Jonkman, J.; Johnson, N.

    2014-01-01

    This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context of LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.

  12. Nonlinear Deformation Processes and Damage Modes of Super Carbon Nanotubes with Armchair-Armchair Topology

    Institute of Scientific and Technical Information of China (English)

    CHEN Yu-Li; LIU Bin; YIN Ya-Jun; HUANG Yong-Gang; HWUANG Keh-Chih

    2008-01-01

    The tensile deformations and fractures of super carbon nanotubes (SCNTs) with armchair-armchair topology are investigated by using the atomic-scale finite element method. SCNTs generated from carbon nanotubes (CNTs) with different characteristic aspect ratios are found to have different nonlinear behaviours under uniaxiai tensions. Specifically, an SCNT with higher aspect ratio has three distinct stages: rotation, stretch and rupture, while an SCNT with lower aspect ratio has only two stages. This information may compensate for previous work and enrich our knowledge about Y-branched CNTs and SCNTs.

  13. Coupling nonlinear Stokes and Darcy flow using mortar finite elements

    KAUST Repository

    Ervin, Vincent J.

    2011-11-01

    We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions. © 2010 Published by Elsevier B.V. on behalf of IMACS.

  14. A comparison of numerical methods used for finite element modelling of soft tissue deformation

    KAUST Repository

    Pathmanathan, P

    2009-05-01

    Soft tissue deformation is often modelled using incompressible non-linear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. The effect of these choices on the accuracy of the computed solution is investigated, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. Model problems are set up with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). It was found that the choice of pressure basis functions is vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general it is important to take the expected regularity of the solution into account when choosing a numerical scheme. © IMechE 2009.

  15. Variation of hydraulic gradient in nonlinear finite strain consolidation

    Institute of Scientific and Technical Information of China (English)

    谢新宇; 黄杰卿; 王文军; 李金柱

    2014-01-01

    In the research field of ground water, hydraulic gradient is studied for decades. In the consolidation field, hydraulic gradient is yet to be investigated as an important hydraulic variable. So, the variation of hydraulic gradient in nonlinear finite strain consolidation was focused on in this work. Based on lab tests, the nonlinear compressibility and nonlinear permeability of Ningbo soft clay were obtained. Then, a strongly nonlinear governing equation was derived and it was solved with the finite element method. Afterwards, the numerical analysis was performed and it was verified with the existing experiment for Hong Kong marine clay. It can be found that the variation of hydraulic gradient is closely related to the magnitude of external load and the depth in soils. It is interesting that the absolute value of hydraulic gradient (AVHG) increases rapidly first and then decreases gradually after reaching the maximum at different depths of soils. Furthermore, the changing curves of AVHG can be roughly divided into five phases. This five-phase model can be employed to study the migration of pore water during consolidation.

  16. Domain decomposition solvers for nonlinear multiharmonic finite element equations

    KAUST Repository

    Copeland, D. M.

    2010-01-01

    In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.

  17. Nonlinear Finite Element Analysis of Nanoindentation of Viral Capsids

    CERN Document Server

    Gibbons, M M; Gibbons, Melissa M.; Klug, William S.

    2006-01-01

    Recent Atomic Force Microscope (AFM) nanoindentation experiments measuring mechanical response of the protein shells of viruses have provided a quantitative description of their strength and elasticity. To better understand and interpret these measurements, and to elucidate the underlying mechanisms, this paper adopts a course-grained modeling approach within the framework of three-dimensional nonlinear continuum elasticity. Homogeneous, isotropic, elastic, thick shell models are proposed for two capsids: the spherical Cowpea Chlorotic Mottle Virus (CCMV), and the ellipsocylindrical bacteriophage $\\phi 29$. As analyzed by the finite element method, these models enable parametric characterization of the effects of AFM tip geometry, capsid dimensions, and capsid constitutive descriptions. The generally nonlinear force response of capsids to indentation is shown to be insensitive to constitutive details, and greatly influenced by geometry. Nonlinear stiffening and softening of the force response is dependent on ...

  18. Finite Element Model and Validation of Nasal Tip Deformation.

    Science.gov (United States)

    Manuel, Cyrus T; Harb, Rani; Badran, Alan; Ho, David; Wong, Brian J F

    2017-03-01

    Nasal tip mechanical stability is important for functional and cosmetic nasal airway surgery. Palpation of the nasal tip provides information on tip strength to the surgeon, though it is a purely subjective assessment. Providing a means to simulate nasal tip deformation with a validated model can offer a more objective approach in understanding the mechanics and nuances of the nasal tip support and eventual nasal mechanics as a whole. Herein we present validation of a finite element (FE) model of the nose using physical measurements recorded using an ABS plastic-silicone nasal phantom. Three-dimensional photogrammetry was used to capture the geometry of the phantom at rest and while under steady state load. The silicone used to make the phantom was mechanically tested and characterized using a linear elastic constitutive model. Surface point clouds of the silicone and FE model were compared for both the loaded and unloaded state. The average Hausdorff distance between actual measurements and FE simulations across the nose were 0.39 ± 1.04 mm and deviated up to 2 mm at the outermost boundaries of the model. FE simulation and measurements were in near complete agreement in the immediate vicinity of the nasal tip with millimeter accuracy. We have demonstrated validation of a two-component nasal FE model, which could be used to model more complex modes of deformation where direct measurement may be challenging. This is the first step in developing a nasal model to simulate nasal mechanics and ultimately the interaction between geometry and airflow.

  19. Capacity of a Nonlinear Optical Channel with Finite Memory

    CERN Document Server

    Agrell, Erik; Durisi, Giuseppe; Karlsson, Magnus

    2014-01-01

    The channel capacity of a nonlinear, dispersive fiber-optic link is revisited. To this end, the popular Gaussian noise (GN) model is extended with a parameter to account for the finite memory of realistic fiber channels. This finite-memory model is harder to analyze mathematically but, in contrast to previous models, it is valid also for nonstationary or heavy-tailed input signals. For uncoded transmission and standard modulation formats, the new model gives the same results as the regular GN model when the memory of the channel is about 10 symbols or more. These results confirm previous results that the GN model is accurate for uncoded transmission. However, when coding is considered, the results obtained using the finite-memory model are very different from those obtained by previous models, even when the channel memory is large. In particular, the peaky behavior of the channel capacity, which has been reported for numerous nonlinear channel models, appears to be an artifact of applying models derived for i...

  20. Finite Volume Evolution Galerkin Methods for Nonlinear Hyperbolic Systems

    Science.gov (United States)

    Lukáčová-Medvid'ová, M.; Saibertová, J.; Warnecke, G.

    2002-12-01

    We present new truly multidimensional schemes of higher order within the frame- work of finite volume evolution Galerkin (FVEG) methods for systems of nonlinear hyperbolic conservation laws. These methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of the multidimensional hyperbolic system, such that all of the infinitely many directions of wave propagation are taken into account. Following our previous results for the wave equation system, we derive approximate evolution operators for the linearized Euler equations. The integrals along the Mach cone and along the cell interfaces are evaluated exactly, as well as by means of numerical quadratures. The influence of these numerical quadratures will be discussed. Second-order resolution is obtained using a conservative piecewise bilinear recovery and the midpoint rule approximation for time integration. We prove error estimates for the finite volume evolution Galerkin scheme for linear systems with constant coefficients. Several numerical experiments for the nonlinear. Euler equations, which confirm the accuracy and good multidimensional behavior of the FVEG schemes, are presented as well.

  1. Study of non-linear deformation of vocal folds in simulations of human phonation

    Science.gov (United States)

    Saurabh, Shakti; Bodony, Daniel

    2014-11-01

    Direct numerical simulation is performed on a two-dimensional compressible, viscous fluid interacting with a non-linear, viscoelastic solid as a model for the generation of the human voice. The vocal fold (VF) tissues are modeled as multi-layered with varying stiffness in each layer and using a finite-strain Standard Linear Solid (SLS) constitutive model implemented in a quadratic finite element code and coupled to a high-order compressible Navier-Stokes solver through a boundary-fitted fluid-solid interface. The large non-linear mesh deformation is handled using an elliptic/poisson smoothening technique. Supra-glottal flow shows asymmetry in the flow, which in turn has a coupling effect on the motion of the VF. The fully compressible simulations gives direct insight into the sound produced as pressure distributions and the vocal fold deformation helps study the unsteady vortical flow resulting from the fluid-structure interaction along the full phonation cycle. Supported by the National Science Foundation (CAREER Award Number 1150439).

  2. ANALYSIS OF A MIXED FINITE ELEMENT METHOD FOR A PHASE FIELD BENDING ELASTICITY MODEL OF VESICLE MEMBRANE DEFORMATION

    Institute of Scientific and Technical Information of China (English)

    Qiang Du; Liyong Zhu

    2006-01-01

    In this paper, we study numerical approximations of a recently proposed phase field model for the vesicle membrane deformation governed by the variation of the elastic bending energy. To overcome the challenges of high order nonlinear differential systems and the nonlinear constraints associated with the problem, we present the phase field bending elasticity model in a nested saddle point formulation. A mixed finite element method is then employed to compute the equilibrium configuration of a vesicle membrane with prescribed volume and surface area. Coupling the approximation results for a related linearized problem and the general theory of Brezzi-Rappaz-Raviart, optimal order error estimates for the finite element approximations of the phase field model are obtained. Numerical results areprovided to substantiate the derived estimates.

  3. A mixed finite element method for nonlinear diffusion equations

    KAUST Repository

    Burger, Martin

    2010-01-01

    We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.

  4. Nonlinear Micromorphic Continuum Mechanics and Finite Strain Elastoplasticity

    Science.gov (United States)

    2010-11-01

    equations for finite element nonlinear solution . Such numerical time integration... equation 211 in Box 1, and in Box 4 for the numerical integration. For ∇(χn+1 − χn) and ∇χn+1 in Box 4, because χ is a nodal DOF in a FE solution and...ρ′f ′ kdv ′ (27) ρakdv def = ∫ dv ρ′a′ kdv ′ (28) 15 From equation 25 and equations 26–28, there results ∫ ∂B σlknlda+ ∫ B ρ(fk − ak)dv = 0 (29) ∫

  5. Prediction of Human Vertebral Compressive Strength Using Quantitative Computed Tomography Based Nonlinear Finite Element Method

    Directory of Open Access Journals (Sweden)

    Ahad Zeinali

    2007-12-01

    Full Text Available Introduction: Because of the importance of vertebral compressive fracture (VCF role in increasing the patients’ death rate and reducing their quality of life, many studies have been conducted for a noninvasive prediction of vertebral compressive strength based on bone mineral density (BMD determination and recently finite element analysis. In this study, QCT-voxel based nonlinear finite element method is used for predicting vertebral compressive strength. Material and Methods: Four thoracolumbar vertebrae were excised from 3 cadavers with an average age of 42 years. They were then put in a water phantom and were scanned using the QCT. Using a computer program prepared in MATLAB, detailed voxel based geometry and mechanical characteristics of the vertebra were extracted from the CT images. The three dimensional finite element models of the samples were created using ANSYS computer program. The compressive strength of each vertebra body was calculated based on a linearly elastic-linearly plastic model and large deformation analysis in ANSYS and was compared to the value measured experimentally for that sample. Results: Based on the obtained results the QCT-voxel based nonlinear finite element method (FEM can predict vertebral compressive strength more effectively and accurately than the common QCT-voxel based linear FEM. The difference between the predicted strength values using this method and the measured ones was less than 1 kN for all the samples. Discussion and Conclusion: It seems that the QCT-voxel based nonlinear FEM used in this study can predict more effectively and accurately the vertebral strengths based on every vertebrae specification by considering their detailed geometric and densitometric characteristics.

  6. Nonlinear Finite Element Modelling of Railway Turnout System considering Bearer/Sleeper-Ballast Interaction

    Directory of Open Access Journals (Sweden)

    James Sae Siew

    2015-01-01

    Full Text Available Rail turnouts are built to enable flexibility in the rail network as they allow for vehicles to switch between various tracks, therefore maximizing the utilisation of existing rail infrastructure. In general, railway turnouts are a safety-critical and expensive feature to a rail system as they suffer aggressive operational loads, in comparison to a plain rail track, and thus require frequent monitoring and maintenance. In practice, great consideration is given to the dynamic interaction between the turnouts components as a failed component may have adverse effects on the performance of neighbouring components. This paper presents a nonlinear 3D finite element (FE model, taking into account the nonlinearities of materials, in order to evaluate the interaction and behaviour of turnout components. Using ABAQUS, the finite element model was developed to simulate standard concrete bearers with 60 kg/m rail and with a tangential turnout radius of 250 m. The turnout structure is supported by a ballast layer, which is represented by a nonlinearly deformable tensionless solid. The numerical studies firstly demonstrate the importance of load transfer mechanisms in the failure modes of the turnout components. The outcome will lead to a better design and maintenance of railway turnouts, improving public safety and operational reliability.

  7. Mapping deformation method and its application to nonlinear equations

    Institute of Scientific and Technical Information of China (English)

    李画眉

    2002-01-01

    An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinearpartial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraicmapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein-Gordon equation. This isapplied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained,including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions.

  8. Hierarchical Non-linear Image Registration Integrating Deformable Segmentation

    Institute of Scientific and Technical Information of China (English)

    RAN Xin; QI Fei-hu

    2005-01-01

    A hierarchical non-linear method for image registration was presented, which integrates image segmentation and registration under a variational framework. An improved deformable model is used to simultaneously segment and register feature from multiple images. The objects in the image pair are segmented by evolving a single contour and meanwhile the parameters of affine registration transformation are found out. After that, a contour-constrained elastic registration is applied to register the images correctly. The experimental results indicate that the proposed approach is effective to segment and register medical images.

  9. Deformation analysis of optical flat surface with finite element method

    Science.gov (United States)

    Fu, Pengqiang; Ren, Boyuan; Wang, Yiwen; Zhang, Dewei; Zhang, Longjiang; Su, Xing

    2016-10-01

    Proposing a new method for testing the ultra-precision aerostatic spindle motion accuracy based on analyzing the online real-time dynamic interference image. Optical flat crystal as the testing standard will be installed at the end of the ultra precision aerostatic spindle and will motion along with the spindle. On the other end of the spindle, the tool will be installed for online processing. The image data of optical flat crystal collected by the high-precision dynamic interferometer will be processed for analyzing the spindle error. For collecting higher accuracy image data, the installation way of optical flat crystal is one of the key technologies. Base on this, the effects of the clamping means on the surface accuracy of optical flat crystal is studied. At first, the finite element model of the optical flat crystal`s clamping structure were established. Secondly, the influence of the material of the supporting annulus, preload lateral clamping and spindle speed on the surface accuracy of optical flat crystal had been analyzed. At last, the improved and optimized structure of the optical flat crystal has been presented. As the analysis results shown, the RMS value of reference surface is 9.47nm and the deformation values of the central region is 0.17nm which satisfies the requirement of surface accuracy and installation of optical flat crystal. It has a very important theoretical and practical significance to establish spindle online testing system and research rotary error generating mechanism of ultra-precision spindle to improve surface accuracy of ultra-precision machining.

  10. Assessment of the non-linear behaviour of plastic ankle foot orthoses by the finite element method.

    Science.gov (United States)

    Syngellakis, S; Arnold, M A; Rassoulian, H

    2000-01-01

    The stiffness characteristics of plastic ankle foot orthoses (AFOs) are studied through finite element modelling and stress analysis. Particular attention is given to the modelling and prediction of non-linear AFO behaviour, which has been frequently observed in previous experimental studies but not fully addressed analytically. Both large deformation effects and material non-linearity are included in the formulation and their individual influence on results assessed. The finite element program is subsequently applied to the simulation of a series of tests designed to investigate the relation between AFO trimline location and stiffness for moderate and large rotations. Through careful consideration and identification of key modelling parameters, the developed finite element solution proves to be a reliable and effective alternative means of assessing variations of a typical plastic AFO design so that particular patient requirements could be met, in the long term.

  11. Numerical modeling of nonlinear deformation and buckling of composite plate-shell structures under pulsed loading

    Science.gov (United States)

    Abrosimov, N. A.

    1999-11-01

    Nonlinear three-dimensional problems of dynamic deformation, buckling, and posteritical behavior of composite shell structures under pulsed loads are analyzed. The structure is assumed to be made of rigidly joined plates and shells of revolution along the lines coinciding with the coordinate directions of the joined elements. Individual structural elements can be made of both composite and conventional isotropic materials. The kinematic model of deformation of the structural elements is based on Timoshenko-type hypotheses. This approach is oriented to the calculation of nonstationary deformation processes in composite structures under small deformations but large displacements and rotation angles, and is implemented in the context of a simplified version of the geometrically nonlinear theory of shells. The physical relations in the composite structural elements are based on the theory of effective moduli for individual layers or for the package as a whole, whereas in the metallic elements this is done in the framework of the theory of plastic flow. The equations of motion of a composite shell structure are derived based on the principle of virtual displacements with some additional conditions allowing for the joint operation of structural elements. To solve the initial boundary-value problem formulated, an efficient numerical method is developed based on the finite-difference discretization of variational equations of motion in space variables and an explicit second-order time-integration scheme. The permissible time-integration step is determined using Neumann's spectral criterion. The above method is especially efficient in calculating thin-walled shells, as well as in the case of local loads acting on the structural element, when the discretization grid has to be condensed in the zones of rapidly changing solutions in space variables. The results of analyzing the nonstationary deformation processes and critical loads are presented for composite and isotropic

  12. On modelling large deformations of heterogeneous biological tissues using a mixed finite element formulation.

    Science.gov (United States)

    Wu, Tim; Hung, Alice P-L; Hunter, Peter; Mithraratne, Kumar

    2015-01-01

    This study addresses the issue of modelling material heterogeneity of incompressible bodies. It is seen that when using a mixed (displacement-pressure) finite element formulation, the basis functions used for pressure field may not be able to capture the nonlinearity of material parameters, resulting in pseudo-residual stresses. This problem can be resolved by modifying the constitutive relation using Flory's decomposition of the deformation gradient. A two-parameter Mooney-Rivlin constitutive relation is used to demonstrate the methodology. It is shown that for incompressible materials, the modification does not alter the mechanical behaviour described by the original constitutive model. In fact, the modified constitutive equation shows a better predictability when compared against analytical solutions. Two strategies of describing the material variation (i.e. linear and step change) are explained, and their solutions are evaluated for an ideal two-material interfacing problem. When compared with the standard tied coupling approach, the step change method exhibited a much better agreement because of its ability to capture abrupt changes of the material properties. The modified equation in conjunction with integration point-based material heterogeneity is then used to simulate the deformations of heterogeneous biological structures to illustrate its applications.

  13. Fully coupled heat conduction and deformation analyses of nonlinear viscoelastic composites

    KAUST Repository

    Khan, Kamran

    2012-05-01

    This study presents an integrated micromechanical model-finite element framework for analyzing coupled heat conduction and deformations of particle-reinforced composite structures. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermomechanical properties and micro-macro field variables due to coupled heat conduction and nonlinear thermoviscoelastic deformation of a particulate composite that takes into account the dissipation of energy from the viscoelastic constituents. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic homogeneous materials is developed. The algorithm is then integrated to the proposed micromechanical model. A significant temperature generation due to the dissipation effect in the viscoelastic matrix was observed when the composite body is subjected to cyclic mechanical loadings. Heat conduction due to the dissipation of the energy cannot be ignored in predicting the factual temperature and deformation fields within the composite structure, subjected to cyclic loading for a long period. A higher creep resistant matrix material or adding elastic particles can lower the temperature generation. Our analyses suggest that using particulate composites and functionally graded materials can reduce the heat generation due to energy dissipation. © 2012 Elsevier Ltd.

  14. Finite-element formulations for problems of large elastic-plastic deformation

    Science.gov (United States)

    Mcmeeking, R. M.; Rice, J. R.

    1975-01-01

    An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is ideally suited to isotropically hardening Prandtl-Reuss materials. Further, the formulation is given in a manner which allows any conventional finite element program, for 'small strain' elastic-plastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. The paper closes with a unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures. Further, a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain, and the inadequacies of some of these are commented upon.

  15. Finite element formulations for problems of large elastic-plastic deformation

    Science.gov (United States)

    Mcmeeking, R. M.; Rice, J. R.

    1974-01-01

    An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is suited to isotropically hardening Prandtl-Reuss materials. The formulation is given in a manner which allows any conventional finite element program, for "small strain" elasticplastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. A unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures, and a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain.

  16. Propagation, reflection, and transmission of SH-waves in slightly compressible, finitely deformed elastic media

    Institute of Scientific and Technical Information of China (English)

    M. CHATTERJEE; A. CHATTOPADHYAY

    2015-01-01

    The propagation, reflection, and transmission of SH waves in slightly com-pressible, finitely deformed elastic media are considered in this paper. The dispersion relation for SH-wave propagation in slightly compressible, finitely deformed layer over-lying a slightly compressible, finitely deformed half-space is derived. The present paper also deals with the reflection and refraction (transmission) phenomena due to the SH wave incident at the plane interface between two distinct slightly compressible, finitely deformed elastic media. The closed form expressions for the amplitude ratios of reflection and refraction coefficients of the reflected and refracted SH waves are obtained from suit-able boundary conditions. For the numerical discussions, we consider the Neo-Hookean form of a strain energy function. The phase speed curves, the variations of reflection, and transmission coefficients with the angle of incidence, and the plots of the slowness sections are presented by means of graphs.

  17. Analysis of nonlinear deformations and damage in CFRP textile laminates

    Science.gov (United States)

    Ullah, H.; Harland, A. R.; Lucas, T.; Price, D.; Silberschmidt, V. V.

    2011-07-01

    Carbon fibre-reinforced polymer (CFRP) textile composites are widely used in aerospace, automotive and construction components and structures thanks to their relatively low production costs, higher delamination and impact strength. They can also be used in various products in sports industry. These products are usually exposed to different in-service conditions such as large bending deformation and multiple impacts. Composite materials usually demonstrate multiple modes of damage and fracture due to their heterogeneity and microstructure, in contrast to more traditional homogeneous structural materials like metals and alloys. Damage evolution affects both their in-service properties and performance that can deteriorate with time. These damage modes need adequate means of analysis and investigation, the major approaches being experimental characterisation, numerical simulations and microtomography analysis. This research deals with a deformation behaviour and damage in composite laminates linked to their quasi-static bending. Experimental tests are carried out to characterise the behaviour of woven CFRP material under large-deflection bending. Two-dimensional finite element (FE) models are implemented in the commercial code Abaqus/Explicit to study the deformation behaviour and damage in woven CFRP laminates. Multiple layers of bilinear cohesive-zone elements are employed to model the onset and progression of inter-ply delamination process. X-ray Micro-Computed Tomography (MicroCT) analysis is carried out to investigate internal damage mechanisms such as cracking and delaminations. The obtained results of simulations are in agreement with experimental data and MicroCT scans.

  18. Nonlinear explicit transient finite element analysis on the Intel Delta

    Energy Technology Data Exchange (ETDEWEB)

    Plaskacz, E.J. [Argonne National Lab., IL (United States); Ramirez, M.R.; Gupta, S. [Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Civil Engineering

    1993-03-01

    Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.

  19. Nonlinear explicit transient finite element analysis on the Intel Delta

    Energy Technology Data Exchange (ETDEWEB)

    Plaskacz, E.J. (Argonne National Lab., IL (United States)); Ramirez, M.R.; Gupta, S. (Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Civil Engineering)

    1993-01-01

    Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.

  20. Demonstration of finite element simulations in MOOSE using crystallographic models of irradiation hardening and plastic deformation

    Energy Technology Data Exchange (ETDEWEB)

    Patra, Anirban [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Wen, Wei [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Martinez Saez, Enrique [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Tome, Carlos [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2016-05-31

    This report describes the implementation of a crystal plasticity framework (VPSC) for irradiation hardening and plastic deformation in the finite element code, MOOSE. Constitutive models for irradiation hardening and the crystal plasticity framework are described in a previous report [1]. Here we describe these models briefly and then describe an algorithm for interfacing VPSC with finite elements. Example applications of tensile deformation of a dog bone specimen and a 3D pre-irradiated bar specimen performed using MOOSE are demonstrated.

  1. Non linear bend instability theory and finite amplitude evolution of bed deformations in meandering rivers

    Science.gov (United States)

    Bolla Pittaluga, M.; Nobile, G.; Seminara, G.

    2007-12-01

    We develop a three dimensional non linear asymptotic theory for flow and bed topography in meandering channels able to describe finite amplitude perturbations of bottom topography. The model extends a previous analysis on the equilibrium finite bed deformations, accounting here for arbitrary, yet slow, variations of channel curvature. This approach then allows us to formulate a non-linear bend instability theory, which predicts several characteristic features of the actual meandering process and extends results obtained by classical linear bend theories. In agreement with previous weakly non linear findings and consistently with field observations, the bend growth rate turns out to have a peak at some value of the meander wavenumber, typically larger than the resonant value of linear stability theory. Moreover, a feature typical of non linear waves arises: the selected wavenumber depends on the amplitude of the initial perturbation and, in particular, larger wavelengths are associated with larger amplitudes. The picture offered by results obtained through the present theory seems fully satisfactory and consistent with field observations as well as previous theoretical findings. Further substantiation of the model has been achieved by comparing predictions obtained for a test case (a reach of the Cecina river, Italy) with field observations. Finally the model is also extended to follow the evolution of bed deformations in time in order to investigate the morphological response of the river to a sequence of flood events characterized by a slow temporal variation of flow and sediment supply. Such an investigation would possibly provide a rational interpretation of the as yet loosely defined notion of formative discharge of an alluvial river.

  2. A nonlinear small-deformation theory for transient droplet electrohydrodynamics

    CERN Document Server

    Das, Debasish

    2016-01-01

    The deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher-Taylor leaky dielectric model. The main assumption of the model is that any net charge in the system is concentrated on the interface between the two liquids as a result of the jump in Ohmic currents from the bulk. Upon application of the field, the drop can either attain a steady prolate or oblate shape with toroidal circulating flows both inside and outside arising from tangential stresses on the interface due to action of the field on the surface charge distribution. Since the pioneering work of \\cite{taylor1966}, there have been numerous computational and theoretical studies to predict the deformations measured in experiments. Most existing theoretical models, however, have either neglected transient charge relaxation or nonlinear charge convection by the interfacial flow. In this work, we develop a novel small-deformation theor...

  3. Computational procedures for finite deformation rate-independent plasticity and viscoplasticity based on overstress

    Science.gov (United States)

    Gomaa, Said Taha Khalil

    2000-10-01

    This thesis is dedicated to developing the computational procedures required in implementing the finite element method for finite deformation, rate-independent plasticity and finite deformation viscoplasticity theory based on overstress. The classical rate-independent, von Mises plasticity is formulated using both hypoelastic-plastic model and hyperelastic-plastic model. In the hypoelastic-plastic model, a relationship between an objective rate of Kirchhoff stress, based on a new recently proposed logarithmic spin [13], and the elastic part of rate of deformation tensor is postulated. In the hyperelastic-plastic model, the deformation gradient is decomposed into elastic and plastic deformations, a relationship between Kirchhoff stress and the logarithm of the elastic left stretch tensor is used. Numerical procedures for the integration of both models are developed. The isotropic, viscoplasticity theory based on overstress consisting of a flow law and two tensor valued and one scalar valued stress-like state variables is extended to finite deformation. To this end the Cauchy stress rate and the rates of the two tensor-valued state variables are interpreted as Eulerian tensors. The rate of deformation is equal to the sum of the elastic (the rate form of Hooke's law) and the inelastic rate of deformation, which depends on the overstress. The model does not contain a strain like quantity. Two integration schemes are considered: (i) a one step time integration scheme based on the forward gradient approximation and (ii) unconditionally stable implicit integration scheme based on backward Euler. The finite deformation, anisotropic, viscoplasticity theory based on overstress is formulated. A hypoelastic relation between the Lagrangian, rotated, logarithmic Cauchy stress rate and the rotated rate of deformation is used. The deformation induced anisotropy is modeled using a compliance tensor that allowed to grow according to Armstrong-Frederick law for fourth order tensors

  4. Generalized multiscale finite element methods. nonlinear elliptic equations

    KAUST Repository

    Efendiev, Yalchin R.

    2013-01-01

    In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.

  5. Non-linear rotation-free shell finite-element models for aortic heart valves.

    Science.gov (United States)

    Gilmanov, Anvar; Stolarski, Henryk; Sotiropoulos, Fotis

    2017-01-04

    Hyperelastic material models have been incorporated in the rotation-free, large deformation, shell finite element (FE) formulation of (Stolarski et al., 2013) and applied to dynamic simulations of aortic heart valve. Two models used in the past in analysis of such problem i.e. the Saint-Venant and May-Newmann-Yin (MNY) material models have been considered and compared. Uniaxial tests for those constitutive equations were performed to verify the formulation and implementation of the models. The issue of leaflets interactions during the closing of the heart valve at the end of systole is considered. The critical role of using non-linear anisotropic model for proper dynamic response of the heart valve especially during the closing phase is demonstrated quantitatively. This work contributes an efficient FE framework for simulating biological tissues and paves the way for high-fidelity flow structure interaction simulations of native and bioprosthetic aortic heart valves. Copyright © 2016. Published by Elsevier Ltd.

  6. Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure. Part 1: Theory

    Science.gov (United States)

    Padovan, Joe

    1986-01-01

    In a three part series of papers, a generalized finite element analysis scheme is developed to handle the steady and transient response of moving/rolling nonlinear viscoelastic structure. This paper considers the development of the moving/rolling element strategy, including the effects of large deformation kinematics and viscoelasticity modelled by fractional integro-differential operators. To improve the solution strategy, a special hierarchical constraint procedure is developed for the case of steady rolling/translating as well as a transient scheme involving the use of a Grunwaldian representation of the fractional operator. In the second and third parts of the paper, 3-D extensions are developed along with transient contact strategies enabling the handling of impacts with obstructions. Overall, the various developments are benchmarked via comprehensive 2- and 3-D simulations. These are correlated with experimental data to define modelling capabilities.

  7. Finite element modelling of manufacturing processes for plastic deformation

    Directory of Open Access Journals (Sweden)

    Fernando Mejía Umaña

    2010-04-01

    Full Text Available The object of the Mechanical and Electrical Engineering Departament's computational mechanics of solids section is to offer industry solutions to problems requiring deeper knowledge regarding the mechanincs of solids and how they can be numerically modelled. This article summarises the foundations of plastic deformation, together with the results obtained during the experimental phase and from modelling two applications of plastic deformation processes being studied as part of mechanical engineering students' undergraduate projects.

  8. Deformation Control of Deep Excavation Pit and Numerical Simulation with Finite Element Method

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    The authors firstly introduce deformation control of deep excavation pit in detail, and then put forward new conceptions such as: effective coefficient of excavation pit, effective area, ineffective area and critical line, and also put forward the referential criteria of deformation control. The System of Optimization Design with Deformation Control of Deep Excavation Pit and Numerical Simulation with Finite Element Method (SDCDEFEM) is also briefly introduced. Factors influencing deformation of excavation pit are analyzed by the system. The measured and simulated data of maximum deformations (settlement, displacement and upheaval) and their positions are analyzed and discussed. The statistic formula estimating maximum deformations and their positions was gained, and economical-effective measures of deformation control were brought forward.

  9. ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL-Ⅱ: FINITE ELEMENT MODELING AND APPLICATION

    Institute of Scientific and Technical Information of China (English)

    Xingzhe Wang; Xiaojing Zheng

    2009-01-01

    Based on the generalized variational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established (see, Analyses on nonlinear coupling of magneto-thermo-elasticity of ferromagnetic thin shell-Ⅰ), the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.

  10. Polymorphism of iron at high pressure: A 3D phase-field model for displacive transitions with finite elastoplastic deformations

    Science.gov (United States)

    Vattré, A.; Denoual, C.

    2016-07-01

    A thermodynamically consistent framework for combining nonlinear elastoplasticity and multivariant phase-field theory is formulated at large strains. In accordance with the Clausius-Duhem inequality, the Helmholtz free energy and time-dependent constitutive relations give rise to displacive driving forces for pressure-induced martensitic phase transitions in materials. Inelastic forces are obtained by using a representation of the energy landscape that involves the concept of reaction pathways with respect to the point group symmetry operations of crystal lattices. On the other hand, additional elastic forces are derived for the most general case of large strains and rotations, as well as nonlinear, anisotropic, and different elastic pressure-dependent properties of phases. The phase-field formalism coupled with finite elastoplastic deformations is implemented into a three-dimensional Lagrangian finite element approach and is applied to analyze the iron body-centered cubic (α-Fe) into hexagonal close-packed (ɛ-Fe) phase transitions under high hydrostatic compression. The simulations exhibit the major role played by the plastic deformation in the morphological and microstructure evolution processes. Due to the strong long-range elastic interactions between variants without plasticity, a forward α → ɛ transition is energetically unfavorable and remains incomplete. However, plastic dissipation releases considerably the stored strain energy, leading to the α ↔ ɛ ↔α‧ (forward and reverse) polymorphic phase transformations with an unexpected selection of variants.

  11. Adaptive Finite-Time Stabilization of High-Order Nonlinear Systems with Dynamic and Parametric Uncertainties

    Directory of Open Access Journals (Sweden)

    Meng-Meng Jiang

    2016-01-01

    Full Text Available Under the weaker assumption on nonlinear functions, the adaptive finite-time stabilization of more general high-order nonlinear systems with dynamic and parametric uncertainties is solved in this paper. To solve this problem, finite-time input-to-state stability (FTISS is used to characterize the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, backstepping, and finite-time input-to-state stability approaches, an adaptive state feedback controller is designed to guarantee high-order nonlinear systems are globally finite-time stable.

  12. Estimation of Young's modulus and Poisson's ratio of soft tissue from indentation using two different-sized indentors: finite element analysis of the finite deformation effect.

    Science.gov (United States)

    Choi, A P C; Zheng, Y P

    2005-03-01

    Young's modulus and Poisson's ratio of a tissue can be simultaneously obtained using two indentation tests with two different sized indentors in two indentations. Owing to the assumption of infinitesimal deformation of the indentation, the finite deformation effect of indentation on the calculated material parameters was not fully understood in the double indentation approach. However, indentation tests with infinitesimal deformation are not practical for the measurement of real tissues. Accordingly, finite element models were developed to simulate the indentation with different indentor diameters and different deformation ratios to investigate the finite deformation effect of indentation. The results indicated that Young's modulus E increased with the increase in the indentation deformation w, if the finite deformation effect of indentation was not considered. This phenomenon became obvious when Poisson's ratio v approached 0.5 and/or the ratio of indentor radius and tissue thickness a/h increased. The calculated Young's modulus could be different by 23% at 10% deformation in comparison with its real value. The results also demonstrated that the finite deformation effect to indentation on the calculation of Poisson's ratio v was much smaller. After the finite deformation effect of indentation was considered, the error of the calculated Young's modulus could be controlled within 5% (a/h = 1) and 2% (a/h = 2) for deformation up to 10%.

  13. Efficient Realization of the Mixed Finite Element Discretization for nonlinear Problems

    OpenAIRE

    Knabner, Peter; Summ, Gerhard

    2016-01-01

    We consider implementational aspects of the mixed finite element method for a special class of nonlinear problems. We establish the equivalence of the hybridized formulation of the mixed finite element method to a nonconforming finite element method with augmented Crouzeix-Raviart ansatz space. We discuss the reduction of unknowns by static condensation and propose Newton's method for the solution of local and global systems. Finally, we show, how such a nonlinear problem arises from the mixe...

  14. An implicit three-dimensional model for describing the inelastic response of solids undergoing finite deformation

    Science.gov (United States)

    Rajagopal, K. R.; Srinivasa, A. R.

    2016-08-01

    The aim of this paper is to develop a new unified class of 3D nonlinear anisotropic finite deformation inelasticity model that (1) exhibits rate-independent or dependent hysteretic response (i.e., response wherein reversal of the external stimuli does not cause reversal of the path in state space) with or without yield surfaces. The hysteresis persists with quasistatic loading. (2) Encompasses a wide range of different types of inelasticity models (such as Mullins effect in rubber, rock and soil mechanics, traditional metal plasticity, hysteretic behavior of shape memory materials) into a simple unified framework that is relatively easy to implement in computational schemes and (3) does not require any a priori particular notion of plastic strain or yield function. The core idea behind the approach is the development of an system of implicit rate equations that allow for the continuity of the response but with different rates along different directions. The theory, which is in purely mechanical setting, subsumes and generalizes many commonly used approaches for hypoelasticity and rate-independent plasticity. We illustrate its capability by modeling the Mullins effect which is the inelastic behavior of certain rubbery materials. We are able to simulate the entire cyclic response without the use of additional internal variables, i.e., the entire response is modeled by using an implicit function of stress and strain measures and their rates.

  15. Viscoelasticity behavior for finite deformations, using a consistent hypoelastic model based on Rivlin materials

    Science.gov (United States)

    Altmeyer, Guillaume; Panicaud, Benoit; Rouhaud, Emmanuelle; Wang, Mingchuan; Roos, Arjen; Kerner, Richard

    2016-11-01

    When constructing viscoelastic models, rate-form relations appear naturally to relate strain and stress tensors. One has to ensure that these tensors and their rates are indifferent with respect to the change of observers and to the superposition with rigid body motions. Objective transports are commonly accepted to ensure this invariance. However, the large number of transport operators developed makes the choice often difficult for the user and may lead to physically inconsistent formulation of hypoelasticity. In this paper, a methodology based on the use of the Lie derivative is proposed to model consistent hypoelasticity as an equivalent incremental formulation of hyperelasticity. Both models are shown to be reversible and completely equivalent. Extension to viscoelasticity is then proposed from this consistent model by associating consistent hypoelastic models with viscous behavior. As an illustration, Mooney-Rivlin nonlinear elasticity is coupled with Newton viscosity and a Maxwell-like material is investigated. Numerical solutions are then presented to illustrate a viscoelastic material subjected to finite deformations for a large range of strain rates.

  16. A perturbation approach for geometrically nonlinear structural analysis using a general purpose finite element code

    NARCIS (Netherlands)

    Rahman, T.

    2009-01-01

    In this thesis, a finite element based perturbation approach is presented for geometrically nonlinear analysis of thin-walled structures. Geometrically nonlinear static and dynamic analyses are essential for this class of structures. Nowadays nonlinear analysis of thin-walled shell structures is oft

  17. GLOBAL FINITE ELEMENT NONLINEAR GALERKIN METHOD FOR THE PENALIZED NAVIER-STOKES EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Yin-nian He; Yan-ren Hou; Li-quan Mei

    2001-01-01

    A global finite element nonlinear Galerkin method for the penalized Navier-Stokes equations is presented. This method is based on two finite element spaces XH and Xh,defined respectively on one coarse grid with grid size H and one fine grid with grid size h << H. Comparison is also made with the finite element Galerkin method. If we choose H = O(ε-1/4h1/2), ε> 0 being the penalty parameter, then two methods are of the same order of approximation. However, the global finite element nonlinear Galerkin method is much cheaper than the standard finite element Galerkin method. In fact, in the finite element Galerkin method the nonlinearity is treated on the fine grid finite element space Xh and while in the global finite element nonlinear Galerkin method the similar nonlinearity is treated on the coarse grid finite element space XH and only the linearity needs to be treated on the fine grid increment finite element space Wh. Finally, we provide numerical test which shows above results stated.

  18. Solving geometrically nonlinear tasks of the statics of hinged-rod systems basing on finite element method in the form of classical mixed method

    Directory of Open Access Journals (Sweden)

    Ignat’ev Aleksandr Vladimirovich

    2016-02-01

    Full Text Available The most widely used numerical method used in linear calculation of building structures is finite element method in traditional form of displacements. Different software is developed on its basis. Though it is only possible to check the certainty of these numerical solutions, especially of non-linear tasks of engineering structures’ deformation by the coincidence of the results obtained by two different methods. The authors solved geometrically nonlinear task of the static deformation of a flat hinged-rod system consisting of five linear elastic rods undergoing great tension-compression strains. The solution was obtained basing on the finite element method in the form of classical mixed method developed by the authors. The set of all equilibrium states of the system, both stable and unstable, and all the limit points were found. The certainty of the solution was approved by the coincidence of the results obtained by other authors basing on traditional finite element method in displacements.

  19. A finite deformation theory of higher-order gradient crystal plasticity

    DEFF Research Database (Denmark)

    Kuroda, Mitsutoshi; Tvergaard, Viggo

    2008-01-01

    crystal plasticity that is based on an assumption of the existence of higher-order stresses. Furthermore, a boundary-value problem for simple shear of a constrained thin strip is studied numerically, and some characteristic features of finite deformation are demonstrated through a comparison to a solution......For higher-order gradient crystal plasticity, a finite deformation formulation is presented. The theory does not deviate much from the conventional crystal plasticity theory. Only a back stress effect and additional differential equations for evolution of the geometrically necessary dislocation...... (GND) densities supplement the conventional theory within a non-work-conjugate framework in which there is no need to introduce higher-order microscopic stresses that would be work-conjugate to slip rate gradients. We discuss its connection to a work-conjugate type of finite deformation gradient...

  20. Finite strain analyses of deformations in polymer specimens

    DEFF Research Database (Denmark)

    Tvergaard, Viggo

    2016-01-01

    Analyses of the stress and strain state in test specimens or structural components made of polymer are discussed. This includes the Izod impact test, based on full 3D transient analyses. Also a long thin polymer tube under internal pressure has been studied, where instabilities develop...... viscoplastic flow on the indentation response. Also, the ability of the simpler expanding spherical cavity model to reproduce the trends from the 3D finite element solutions has been assessed....

  1. Finite strip analysis of anisotropic laminated composite plates using higher-order shear deformation theory

    Science.gov (United States)

    Akhras, G.; Cheung, M. S.; Li, W.

    1994-08-01

    In the present study, a finite strip method for the elastic analysis of anisotropic laminated composite plates is developed according to higher-order shear deformation theory. This theory accounts for the parabolic distribution of the transverse shear strains through the thickness of the plate and for zero transverse shear stresses on the plate surfaces. In comparison with the finite strip method based on first-order shear deformation theory, the present method gives improved results while using approximately the same number of degrees of freedom. It also eliminates the need for shear correction factors in calculating the transverse shear stiffness.

  2. Finite Element Surface Layer Inheritable Condition Residual Stresses Model in Surface Plastic Deformation Processes

    Science.gov (United States)

    Mahalov, M. S.; Blumenstein, V. Yu

    2016-04-01

    The residual stresses (RS) research and computational algorithms creation in complex types of loading on the product lifecycle stages relevance is shown. The RS forming finite element model at surface plastic deformation strengthening machining, including technological inheritance effect, is presented. A model feature is the production previous stages obtained transformation properties consideration, as well as these properties evolution during metal particles displacement through the deformation space in the present loading step.

  3. Finite-time Consensus for Nonlinear Multi-agent Systems with Fixed Topologies

    CERN Document Server

    Shang, Yilun

    2009-01-01

    In this paper, we study finite-time state consensus problems for continuous nonlinear multi-agent systems. Building on the theory of finite-time Lyapunov stability, we propose sufficient criteria which guarantee the system to reach a consensus in finite time, provided that the underlying directed network contains a spanning tree. Novel finite-time consensus protocols are introduced as examples for applying the criteria. Simulations are also presented to illustrate our theoretical results.

  4. Finite Deformation of Materials with an Ensemble of Defects

    Energy Technology Data Exchange (ETDEWEB)

    J.K. Dienes

    2003-01-01

    The theory of large deformations developed here is closely related to continuum mechanics but it differs in several major respects, especially in considering the deformation associated with various types of physical behavior, making it possible to synthesize a general approach to formulating constitutive laws. One goal is to derive general concepts of strain, strain rate, stress, and stress rate that are somewhat more physics-based than in most standard works on continuum mechanics, and to demonstrate some new relations between these quantities. With these concepts it is possible to develop a generalized principle of superposition of strain rates (GSSR) that accounts for damage as well as plastic flow. The traditional superposition of strain rates allows for addition of elastic and plastic strain rates and is commonly thought to be valid only for small strains. The GSSR allows us to compute deformations involving plastic flow and, in addition, brittle failure, fragmentation, high-pressure effects and other types of behavior as necessary, and the theory is valid for arbitrarily large deformations. In fact, GSSR is derived from more basic ideas and has broader application than the standard superposition of strain rates. The physical basis for calculations of complex material response is developed in a separate report. The implementation into the SCRAM computer program is documented separately. The polar decomposition theorem is taken as a starting point for the theory of large deformation, an approach somewhat different from that usually taken in continuum mechanics. Two sets of orthogonal axes are distinguished, space axes that are fixed in ambient space, and polar axes that are related to material deformation. This clarifies several concepts; for example, it is shown that the Signorini and Green-St. Venant strains are actually measures of the same physical entity, one in space axes and the other in polar axes. It follows that they are not competing measures, as is

  5. Finite Deformation of Materials with an Ensemble of Defects

    Energy Technology Data Exchange (ETDEWEB)

    J.K. Dienes

    2003-01-01

    The theory of large deformations developed here is closely related to continuum mechanics but it differs in several major respects, especially in considering the deformation associated with various types of physical behavior, making it possible to synthesize a general approach to formulating constitutive laws. One goal is to derive general concepts of strain, strain rate, stress, and stress rate that are somewhat more physics-based than in most standard works on continuum mechanics, and to demonstrate some new relations between these quantities. With these concepts it is possible to develop a generalized principle of superposition of strain rates (GSSR) that accounts for damage as well as plastic flow. The traditional superposition of strain rates allows for addition of elastic and plastic strain rates and is commonly thought to be valid only for small strains. The GSSR allows us to compute deformations involving plastic flow and, in addition, brittle failure, fragmentation, high-pressure effects and other types of behavior as necessary, and the theory is valid for arbitrarily large deformations. In fact, GSSR is derived from more basic ideas and has broader application than the standard superposition of strain rates. The physical basis for calculations of complex material response is developed in a separate report. The implementation into the SCRAM computer program is documented separately. The polar decomposition theorem is taken as a starting point for the theory of large deformation, an approach somewhat different from that usually taken in continuum mechanics. Two sets of orthogonal axes are distinguished, space axes that are fixed in ambient space, and polar axes that are related to material deformation. This clarifies several concepts; for example, it is shown that the Signorini and Green-St. Venant strains are actually measures of the same physical entity, one in space axes and the other in polar axes. It follows that they are not competing measures, as is

  6. Neurosurgery Simulation Using Non-linear Finite Element Modeling and Haptic Interaction.

    Science.gov (United States)

    Lee, Huai-Ping; Audette, Michel; Joldes, Grand Roman; Enquobahrie, Andinet

    2012-02-23

    Real-time surgical simulation is becoming an important component of surgical training. To meet the real-time requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary element method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.

  7. Neurosurgery simulation using non-linear finite element modeling and haptic interaction

    Science.gov (United States)

    Lee, Huai-Ping; Audette, Michel; Joldes, Grand R.; Enquobahrie, Andinet

    2012-02-01

    Real-time surgical simulation is becoming an important component of surgical training. To meet the realtime requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary element method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.

  8. RANDOM MICROSTRUCTURE FINITE ELEMENT METHOD FOR EFFECTIVE NONLINEAR PROPERTIES OF COMPOSITE MATERIALS

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    Some theoretical methods have been reported to deal with nonlinear problems of composite materials but the accuracy is not so good. In the meantime, a lot of nonlinear problems are difficult to be managed by the theoretical methods. The present study aims to use the developed method, the random microstructure finite element method, to deal with these nonlinear problems. In this paper, the random microstructure finite element method is used to deal with all three kinds of nonlinear property problems of composite materials. The analyzed results suggest that the influences of the nonlinear phenomena on the effective properties of composite materials are significant and the random microstructure finite element method is an efficient tool to investigate the nonlinear problems.

  9. Harmonic response of a class of finite extensibility nonlinear oscillators

    Science.gov (United States)

    Febbo, M.

    2011-06-01

    Finite extensibility oscillators are widely used to simulate those systems that cannot be extended to infinity. For example, they are used when modelling the bonds between molecules in a polymer or DNA molecule or when simulating filaments of non-Newtonian liquids. In this paper, the dynamic behavior of a harmonically driven finite extensibility oscillator is presented and studied. To this end, the harmonic balance method is applied to determine the amplitude-frequency and amplitude-phase equations. The distinguishable feature in this case is the bending of the amplitude-frequency curve to the frequency axis, making it asymptotically approach the limit of maximum elongation of the oscillator, which physically represents the impossibility of the system reaching this limit. Also, the stability condition that defines stable and unstable steady-state solutions is derived. The study of the effect of the system parameters on the response reveals that a decreasing value of the damping coefficient or an increasing value of the excitation amplitude leads to the appearance of a multi-valued response and to the existence of a jump phenomenon. In this sense, the critical amplitude of the excitation, which means here a certain value of external excitation that results in the occurrence of jump phenomena, is also derived. Numerical experiments to observe the effects of system parameters on the frequency-amplitude response are performed and compared with analytical calculations. At a low value of the damping coefficient or at a high value of excitation amplitude, the agreement is poor for low frequencies but good for high frequencies. It is demonstrated that the disagreement is caused by the neglect of higher-order harmonics in the analytical formulation. These higher-order harmonics, which appear as distinguishable peaks at certain values in the frequency response curves, are possible to calculate considering not the linearized frequency of the oscillator but its actual

  10. 考虑剪切效应有限变形粘弹性板的动力稳定性%Dynamic Stability of Viscoelastic Plates with Finite Deformation and Shear Effects

    Institute of Scientific and Technical Information of China (English)

    李晶晶; 程昌钧; 张能辉

    2002-01-01

    Based on Reddy' s theory of plates with higher-order shear deformations and the Boltzmann superposition principles, thegoverning equations were established for dynamic stability of viscoelastic plates with finite deformations taking account of shear ef-fects. The Galerkin method was applied to simplify the set of equations. The numerical methods in nonlinear dynamics were used tosolve the simplified system. It could be seen that there are plenty of dynamic properties for this kind of viscoelastic plates under trans-verse harmonic loads. The influences of the transverse shear deformations and material parameter on the dynamic behavior of nonlin-ear viscoelastic plates were investigated.

  11. A comparison of boundary element and finite element methods for modeling axisymmetric polymeric drop deformation

    NARCIS (Netherlands)

    Hooper, Russell; Toose, E.M.; Macosko, Christopher W.; Derby, Jeffrey J.

    2001-01-01

    A modified boundary element method (BEM) and the DEVSS-G finite element method (FEM) are applied to model the deformation of a polymeric drop suspended in another fluid subjected to start-up uniaxial extensional flow. The effects of viscoelasticity, via the Oldroyd-B differential model, are

  12. Steen-Ermakov-Pinney equation and integrable nonlinear deformation of one-dimensional Dirac equation

    OpenAIRE

    Prykarpatskyy, Yarema

    2017-01-01

    The paper deals with nonlinear one-dimensional Dirac equation. We describe its invariants set by means of the deformed linear Dirac equation, using the fact that two ordinary differential equations are equivalent if their sets of invariants coincide.

  13. LEAST-SQUARES MIXED FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    Dan-ping Yang

    2002-01-01

    Two least-squares mixed finite element schemes are formulated to solve the initialboundary value problem of a nonlinear parabolic partial differential equation and the convergence of these schemes are analyzed.

  14. A FINITE DIFFERENCE SCHEME FOR THE GENERALIZED NONLINEAR SCHRODINGER EQUATION WITH VARIABLE COEFFICIENTS

    Institute of Scientific and Technical Information of China (English)

    Wei-zhong Dai; Raja Nassar

    2000-01-01

    A finite difference scheme for the generalized nonlinear Schrodinger equation with variable coefficients is developed. The scheme is shown to satisfy two conser vation laws. Numerical results show that the scheme is accurate and efficient.

  15. The Full—Discrete Mixed Finite Element Methods for Nonlinear Hyperbolic Equations

    Institute of Scientific and Technical Information of China (English)

    YanpingCHEN; YunqingHUANG

    1998-01-01

    This article treats mixed finite element methods for second order nonlinear hyperbolic equations.A fully discrete scheme is presented and improved L2-error estimates are established.The convergence of both the function value andthe flux is demonstrated.

  16. TEST AND CHARACTERIZATION FOR THE INCOMPRESSIBLE HYPERELASTIC PROPERTIES OF CONDITIONED RUBBERS UNDER MODERATE FINITE DEFORMATION

    Institute of Scientific and Technical Information of China (English)

    XiaYong; LiWei; XiaYuanming

    2004-01-01

    In this paper, the automated grid method is applied to test for the mechanical properties of conditioned rubbers under the moderate finite deformation (not exceeding 100%).More accurate stress-strain curves of conditioned rubber specimens under different conditioned strains are obtained. Test results show differences between these curves. Based on an analysis of the classical constitutive models, a new modified eight-chain model is proposed, which take saccount of both the locking stretch of chains and the interaction effect in the network. Fitting test data shows that the modified model well characterizes the incompressible hyperelastic mechanical behavior of conditioned rubbers under the moderate finite deformation as well as under the large deformation.

  17. A Model for Estimating Nonlinear Deformation and Damage in Ceramic Matrix Composites (Preprint)

    Science.gov (United States)

    2011-07-01

    AFRL-RX-WP-TP-2011-4232 A MODEL FOR ESTIMATING NONLINEAR DEFORMATION AND DAMAGE IN CERAMIC MATRIX COMPOSITES (PREPRINT) Unni Santhosh and...5a. CONTRACT NUMBER In-house 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62102F 6. AUTHOR(S) Unni Santhosh and Jalees Ahmad 5d. PROJECT...Composite Materials, 2010 A Model for Estimating Nonlinear Deformation and Damage in Ceramic Matrix Composites Unni Santhosh and Jalees Ahmad Research

  18. Finite-time Lyapunov exponents in time-delayed nonlinear dynamical systems.

    Science.gov (United States)

    Kanno, Kazutaka; Uchida, Atsushi

    2014-03-01

    We introduce a method for the calculation of finite-time Lyapunov exponents in time-delayed nonlinear dynamical systems. We apply the method to the Mackey-Glass model with time-delayed feedback. We investigate the standard deviation of the probability distribution of the finite-time Lyapunov exponents when the finite time or the delay time is changed. It is found that the standard deviation decreases in a power-law scaling with the exponent ∼0.5 as the finite time or the delay time is increased. Similar results are obtained for the finite-time Lyapunov spectrum.

  19. On the accuracy and efficiency of finite difference solutions for nonlinear waves

    DEFF Research Database (Denmark)

    Bingham, Harry B.

    2006-01-01

    We consider the relative accuracy and efficiency of low- and high-order finite difference discretizations of the exact potential flow problem for nonlinear water waves. The continuous differential operators are replaced by arbitrary order finite difference schemes on a structured but non...

  20. Non-smooth finite-time stabilization for a class of nonlinear systems

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    In this paper, global finite-time stabilization problem for a large class of nonlinear control systems is considered. An iterative design approach is given based on Lyapunov function. The finite time stabilizing control laws are constructed in the form of continuous but non-smooth time-invariant feedback.

  1. Defmod - Parallel multiphysics finite element code for modeling crustal deformation during the earthquake/rifting cycle

    CERN Document Server

    Ali, S Tabrez

    2014-01-01

    In this article, we present Defmod, a fully unstructured, two or three dimensional, parallel finite element code for modeling crustal deformation over time scales ranging from milliseconds to thousands of years. Defmod can simulate deformation due to all major processes that make up the earthquake/rifting cycle, in non-homogeneous media. Specifically, it can be used to model deformation due to dynamic and quasistatic processes such as co-seismic slip or dike intrusion(s), poroelastic rebound due to fluid flow and post-seismic or post-rifting viscoelastic relaxation. It can also be used to model deformation due to processes such as post-glacial rebound, hydrological (un)loading, injection and/or withdrawal of compressible or incompressible fluids from subsurface reservoirs etc. Defmod is written in Fortran 95 and uses PETSc's parallel sparse data structures and implicit solvers. Problems can be solved using (stabilized) linear triangular, quadrilateral, tetrahedral or hexahedral elements on shared or distribut...

  2. Finite element simulations of deformation behavior in equal channel angular pressing using a rotated die

    Institute of Scientific and Technical Information of China (English)

    Yixuan TAN; Saiyi LI

    2012-01-01

    A new die design for equal channel angular pressing (ECAP) of square cross-section billet was proposed by a 45° rotation of the inlet and outlet channels around the channel axes.ECAP utilizing the rotated and conventional dies was simulated in three dimensions using the finite element method.Conditions with different material properties and friction coefficients were studied.The billet deformation behavior was evaluated in terms of the spatial distribution of equivalent plastic strain,plastic deformation zone and load history.The results show that the rotated die appears to produce billets with a smaller deformation inhomogeneity over the entire crosssection and a greater average of equivalent plastic strain at the cost of a slightly larger working load.The billet deformation enters into a steady state earlier in the case of the rotated die than the conventional die under the condition of a relatively large friction coefficient.

  3. The influence of storms on finite amplitude sand wave dynamics: an idealized nonlinear model

    NARCIS (Netherlands)

    Campmans, G.H.P.; Roos, P.C.; de Vriend, H.J.; Hulscher, S.J.M.H.

    2017-01-01

    We investigate the effects of storms on finite amplitude sand wave growth using a new idealized nonlinear morphodynamic model. We find that the growth speed initially linearly increases with sand wave amplitude, after which nonlinear effects cause the growth to decrease. This finally leads to an

  4. The finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model

    OpenAIRE

    Balog, Janos(Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, MTA Lendület Holographic QFT Group, 1525, Budapest 114, P.O.B. 49, Hungary); Hegedus, Arpad

    2009-01-01

    Nonlinear integral equations are proposed for the description of the full finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model in a periodic box. Numerical results for the energy eigenvalues are compared to the rotator spectrum and perturbation theory for small volumes and with the recently proposed generalized Luscher formulas at large volumes.

  5. Non-linear finite element analysis in structural mechanics

    CERN Document Server

    Rust, Wilhelm

    2015-01-01

    This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.

  6. A Coupling Model of the Discontinuous Deformation Analysis Method and the Finite Element Method

    Institute of Scientific and Technical Information of China (English)

    ZHANG Ming; YANG Heqing; LI Zhongkui

    2005-01-01

    Neither the finite element method nor the discontinuous deformation analysis method can solve problems very well in rock mechanics and engineering due to their extreme complexities. A coupling method combining both of them should have wider applicability. Such a model coupling the discontinuous deformation analysis method and the finite element method is proposed in this paper. In the model, so-called line blocks are introduced to deal with the interaction via the common interfacial boundary of the discontinuous deformation analysis domain with the finite element domain. The interfacial conditions during the incremental iteration process are satisfied by means of the line blocks. The requirement of gradual small displacements in each incremental step of this coupling method is met through a displacement control procedure. The model is simple in concept and is easy in numerical implementation. A numerical example is given. The displacement obtained by the coupling method agrees well with those obtained by the finite element method, which shows the rationality of this model and the validity of the implementation scheme.

  7. Defects in Nonlinear Elastic Crystals: Differential Geometry, Finite Kinematics, and Second-Order Analytical Solutions

    Science.gov (United States)

    2015-04-01

    of dislocations in anisotropic crystals, Int. J. Eng. Sci. 5, 171–190 (1967). [92] A. Yavari and A. Goriely, Riemann -Cartan geometry of nonlinear...distributed point defects, Proc. R. Soc. Lond. A 468, 3902–3922 (2012). [94] A. Yavari and A. Goriely, Riemann -Cartan geometry of nonlinear disclination...ARL-RP-0522 ● APR 2015 US Army Research Laboratory Defects in Nonlinear Elastic Crystals: Differential Geometry , Finite

  8. Evaluation of the capacity of communication lines with nonlinear finite memory

    Science.gov (United States)

    Shapiro, E. G.; Shapiro, D. A.

    2016-12-01

    We propose a method for calculating the capacity of a finite-memory channel up to the square of the nonlinear memory parameter. A comparison with a regular Gaussian model is performed, in which the Kerr nonlinearity is considered as an additional Gaussian noise. The estimate by the regular Gaussian model is shown to yield a greater capacity as compared with the estimate obtained by the nonlinear memory model. The optimal signal powers, providing the maximum mutual information, are found to be equal.

  9. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics

    CERN Document Server

    Wu, Shen R

    2012-01-01

    A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit FiniteElement Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in master

  10. Finite-time stabilization for a class of stochastic nonlinear systems via output feedback.

    Science.gov (United States)

    Zha, Wenting; Zhai, Junyong; Fei, Shumin; Wang, Yunji

    2014-05-01

    This paper investigates the problem of global finite-time stabilization in probability for a class of stochastic nonlinear systems. The drift and diffusion terms satisfy lower-triangular or upper-triangular homogeneous growth conditions. By adding one power integrator technique, an output feedback controller is first designed for the nominal system without perturbing nonlinearities. Based on homogeneous domination approach and stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system will converge to the origin in finite time and stay at the origin thereafter with probability one. Two simulation examples are presented to illustrate the effectiveness of the proposed design procedure.

  11. Domain decomposition based iterative methods for nonlinear elliptic finite element problems

    Energy Technology Data Exchange (ETDEWEB)

    Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)

    1994-12-31

    The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.

  12. Comparative Analysis of Bulge Deformation between 2D and 3D Finite Element Models

    Directory of Open Access Journals (Sweden)

    Qin Qin

    2014-02-01

    Full Text Available Bulge deformation of the slab is one of the main factors that affect slab quality in continuous casting. This paper describes an investigation into bulge deformation using ABAQUS to model the solidification process. A three-dimensional finite element analysis model of the slab solidification process has been first established because the bulge deformation is closely related to slab temperature distributions. Based on slab temperature distributions, a three-dimensional thermomechanical coupling model including the slab, the rollers, and the dynamic contact between them has also been constructed and applied to a case study. The thermomechanical coupling model produces outputs such as the rules of bulge deformation. Moreover, the three-dimensional model has been compared with a two-dimensional model to discuss the differences between the two models in calculating the bulge deformation. The results show that the platform zone exists in the wide side of the slab and the bulge deformation is affected strongly by the ratio of width-to-thickness. The indications are also that the difference of the bulge deformation for the two modeling ways is little when the ratio of width-to-thickness is larger than six.

  13. DEFORMATION ANALYSIS OF SHEET METAL SINGLE-POINT INCREMENTAL FORMING BY FINITE ELEMENT METHOD SIMULATION

    Institute of Scientific and Technical Information of China (English)

    MA Linwei; MO Jianhua

    2008-01-01

    Single-point incremental forming (SPIF) is an innovational sheet metal forming method without dedicated dies, which belongs to rapid prototyping technology. In generalizing the SPIF of sheet metal, the deformation analysis on forming process becomes an important and useful method for the planning of shell products, the choice of material, the design of the forming process and the planning of the forming tool. Using solid brick elements, the finite element method(FEM) model of truncated pyramid was established. Based on the theory of anisotropy and assumed strain formulation, the SPIF processes with different parameters were simulated. The resulted comparison between the simulations and the experiments shows that the FEM model is feasible and effective. Then, according to the simulated forming process, the deformation pattern of SPIF can be summarized as the combination of plane-stretching deformation and bending deformation. And the study about the process parameters' impact on deformation shows that the process parameter of interlayer spacing is a dominant factor on the deformation. Decreasing interlayer spacing, the strain of one step decreases and the formability of blank will be improved. With bigger interlayer spacing, the plastic deformation zone increases and the forming force will be bigger.

  14. Nonlinear dynamics of planetary gears using analytical and finite element models

    Science.gov (United States)

    Ambarisha, Vijaya Kumar; Parker, Robert G.

    2007-05-01

    Vibration-induced gear noise and dynamic loads remain key concerns in many transmission applications that use planetary gears. Tooth separations at large vibrations introduce nonlinearity in geared systems. The present work examines the complex, nonlinear dynamic behavior of spur planetary gears using two models: (i) a lumped-parameter model, and (ii) a finite element model. The two-dimensional (2D) lumped-parameter model represents the gears as lumped inertias, the gear meshes as nonlinear springs with tooth contact loss and periodically varying stiffness due to changing tooth contact conditions, and the supports as linear springs. The 2D finite element model is developed from a unique finite element-contact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the finite element analysis. The dynamics of planetary gears show a rich spectrum of nonlinear phenomena. Nonlinear jumps, chaotic motions, and period-doubling bifurcations occur when the mesh frequency or any of its higher harmonics are near a natural frequency of the system. Responses from the dynamic analysis using analytical and finite element models are successfully compared qualitatively and quantitatively. These comparisons validate the effectiveness of the lumped-parameter model to simulate the dynamics of planetary gears. Mesh phasing rules to suppress rotational and translational vibrations in planetary gears are valid even when nonlinearity from tooth contact loss occurs. These mesh phasing rules, however, are not valid in the chaotic and period-doubling regions.

  15. Influence of load capacity on hydrostatic journal support deformation in finite element calculation

    Institute of Scientific and Technical Information of China (English)

    邵俊鹏; 张艳芹; 李永海; 于晓东; 姜辉

    2008-01-01

    Based on the application of the four-oil-pad radial hydrostatic bearing in heavy equipments, the deformation of the four-oil-pad radial hydrostatic bearing was calculated by using the finite element method. The formula of film stiffness, film thickness and carrying capacity were established; the influence of the main parameters, such as load, load area and deformation on the supportability was analyzed; and the capacity of the two kinds of bearings was compared. The result shows that the carrying capacity of typeⅠ is prior to that of type Ⅱ . Calculations provide a theoretical basis for the bearing choosing and structure designing in the actual project.

  16. Finite-time H∞ filtering for non-linear stochastic systems

    Science.gov (United States)

    Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

    2016-09-01

    This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

  17. Nonlinear effects of the finite amplitude ultrasound wave in biological tissues

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    Nonlinear effects will occur during the transmission of the finite amplitude wave in biological tissues.The theoretical prediction and experimental demonstration of the nonlinear effects on the propagation of the finite amplitude wave at the range of biomedical ultrasound frequency and intensity are studied.Results show that the efficiency factor and effective propagation distance will decrease while the attenuation coefficient increases due to the existence of nonlinear effects.The experimental results coincided quite well with the theory.This shows that the effective propagation distance and efficiency factor can be used to describe quantitatively the influence of nonlinear effects on the propagation of the finite amplitude sound wave in biological tissues.

  18. Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

    Directory of Open Access Journals (Sweden)

    Minsong Zhang

    2014-01-01

    Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.

  19. PRINCIPAL COMPONENT DECOMPOSITION BASED FINITE ELEMENT MODEL UPDATING FOR STRAIN-RATE-DEPENDENCE NONLINEAR DYNAMIC PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    GUO Qintao; ZHANG Lingmi; TAO Zheng

    2008-01-01

    Thin wall component is utilized to absorb impact energy of a structure. However, the dynamic behavior of such thin-walled structure is highly non-linear with material, geometry and boundary non-linearity. A model updating and validation procedure is proposed to build accurate finite element model of a frame structure with a non-linear thin-walled component for dynamic analysis. Design of experiments (DOE) and principal component decomposition (PCD) approach are applied to extract dynamic feature from nonlinear impact response for correlation of impact test result and FE model of the non-linear structure. A strain-rate-dependent non-linear model updating method is then developed to build accurate FE model of the structure. Computer simulation and a real frame structure with a highly non-linear thin-walled component are employed to demonstrate the feasibility and effectiveness of the proposed approach.

  20. NONLINEAR EVOLUTION ANALYSIS OF T-S DISTURBANCE WAVE AT FINITE AMPLITUDE IN NONPARALLEL BOUNDARY LAYERS

    Institute of Scientific and Technical Information of China (English)

    唐登斌; 夏浩

    2002-01-01

    The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, which is very effective, was used to study the nonlinear evolution of T-S disturbance wave at finite amplitudes. Solving nonlinear equations of different modes by using predictor-corrector and iterative approach, which is uncoupled between modes, improving computational accuracy by using high order compact differential scheme, satisfying normalization condition, determining tables of nonlinear terms at different modes, and implementing stably the spatial marching, were included in this method. With different initial amplitudes, the nonlinear evolution of T-S wave was studied. The nonlinear nonparallel results of examples compare with data of direct numerical simulations (DNS) using full Navier- Stokes equations.

  1. A finite element formulation for modeling dynamic wetting on flexible substrates and in deformable porous media.

    Energy Technology Data Exchange (ETDEWEB)

    Schunk, Peter Randall; Cairncross, Richard A. (Drexel University, Philadelphia, PA); Madasu, S. (Drexel University, Philadelphia, PA)

    2004-03-01

    This report summarizes research advances pursued with award funding issued by the DOE to Drexel University through the Presidential Early Career Award (PECASE) program. Professor Rich Cairncross was the recipient of this award in 1997. With it he pursued two related research topics under Sandia's guidance that address the outstanding issue of fluid-structural interactions of liquids with deformable solid materials, focusing mainly on the ubiquitous dynamic wetting problem. The project focus in the first four years was aimed at deriving a predictive numerical modeling approach for the motion of the dynamic contact line on a deformable substrate. A formulation of physical model equations was derived in the context of the Galerkin finite element method in an arbitrary Lagrangian/Eulerian (ALE) frame of reference. The formulation was successfully integrated in Sandia's Goma finite element code and tested on several technologically important thin-film coating problems. The model equations, the finite-element implementation, and results from several applications are given in this report. In the last year of the five-year project the same physical concepts were extended towards the problem of capillary imbibition in deformable porous media. A synopsis of this preliminary modeling and experimental effort is also discussed.

  2. Validation and application of three-dimensional discontinuous deformation analysis with tetrahedron finite element meshed block

    Institute of Scientific and Technical Information of China (English)

    Jun Liu; Zheng Nan; Ping Yi

    2012-01-01

    In the last decade,three dimensional discontinuous deformation analyses (3D DDA) has attracted more and more attention of researchers and geotechnical engineers worldwide.The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation,which would cause block expansion under rigid body rotation and thus limit its capability to model block deformation.In this paper,3D DDA is coupled with tetrahedron finite elements to tackle these two problems.Tetrahedron is the simplest in the 3D domain and makes it easy to implement automatic discretization,even for complex topology shape.Furthermore,element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly.The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested.Validation is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes,i.e.,wedge failure.Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases.Finally,a complex rockslide example demonstrates the robustness and versatility of the coupled method.

  3. Modeling viscoelastic deformation of the earth due to surface loading by commercial finite element package - ABAQUS

    Science.gov (United States)

    Kit Wong, Ching; Wu, Patrick

    2017-04-01

    Wu (2004) developed a transformation scheme to model viscoelatic deformation due to glacial loading by commercial finite element package - ABAQUS. Benchmark tests confirmed that this method works extremely well on incompressible earth model. Bangtsson & Lund (2008),however, showed that the transformation scheme would lead to incorrect results if compressible material parameters are used. Their study implies that Wu's method of stress transformation is inadequate to model the load induced deformation of a compressible earth under the framework of ABAQUS. In light of this, numerical experiments are carried out to find if there exist other methods that serve this purpose. All the tested methods are not satisfying as the results failed to converge through iterations, except at the elastic limit. Those tested methods will be outlined and the results will be presented. Possible reasons of failure will also be discussed. Bängtsson, E., & Lund, B. (2008). A comparison between two solution techniques to solve the equations of glacially induced deformation of an elastic Earth. International journal for numerical methods in engineering, 75(4), 479-502. Wu, P. (2004). Using commercial finite element packages for the study of earth deformations, sea levels and the state of stress. Geophysical Journal International, 158(2), 401-408.

  4. New Algorithm Model for Processing Generalized Dynamic Nonlinear Data Derived from Deformation Monitoring Network

    Institute of Scientific and Technical Information of China (English)

    LIN Xiangguo; LIANG Yong

    2005-01-01

    The processing of nonlinear data was one of hot topics in surveying and mapping field in recent years.As a result, many linear methods and nonlinear methods have been developed.But the methods for processing generalized nonlinear surveying and mapping data, especially for different data types and including unknown parameters with random or nonrandom, are seldom noticed.A new algorithm model is presented in this paper for processing nonlinear dynamic multiple-period and multiple-accuracy data derived from deformation monitoring network.

  5. Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code

    Science.gov (United States)

    Bartels, Robert E.

    2005-01-01

    A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.

  6. THIRD ORDER SHEAR DEFORMATION MODEL FOR LAMINATED SHELLS WITH FINITE ROTATIONS:FORMULATION AND CONSISTENT LINEARIZATION

    Institute of Scientific and Technical Information of China (English)

    Mohamed BALAH; Hamdan Naser AL-GHAMEDY

    2004-01-01

    The paper presents an approach for the formulation of general laminated shells based on a third order shear deformation theory. These shells undergo finite (unlimited in size) rotations and large overall motions but with small strains. A singularity-free parametrization of the rotation field is adopted. The constitutive equations, derived with respect to laminate curvilinear coordinates,are applicable to shell elements with an arbitrary number of orthotropic layers and where the material principal axes can vary from layer to layer. A careful consideration of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations leads to symmetric tangent stiffness matrices. The matrix formulation adopted here makes it possible to implement the present formulation within the framework of the finite element method as a straightforward task.

  7. Finite element modeling of nanotube structures linear and non-linear models

    CERN Document Server

    Awang, Mokhtar; Muhammad, Ibrahim Dauda

    2016-01-01

    This book presents a new approach to modeling carbon structures such as graphene and carbon nanotubes using finite element methods, and addresses the latest advances in numerical studies for these materials. Based on the available findings, the book develops an effective finite element approach for modeling the structure and the deformation of grapheme-based materials. Further, modeling processing for single-walled and multi-walled carbon nanotubes is demonstrated in detail.

  8. Elastic-viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative deformation gradient.

    Science.gov (United States)

    Weickenmeier, J; Jabareen, M

    2014-11-01

    The characteristic highly nonlinear, time-dependent, and often inelastic material response of soft biological tissues can be expressed in a set of elastic-viscoplastic constitutive equations. The specific elastic-viscoplastic model for soft tissues proposed by Rubin and Bodner (2002) is generalized with respect to the constitutive equations for the scalar quantity of the rate of inelasticity and the hardening parameter in order to represent a general framework for elastic-viscoplastic models. A strongly objective integration scheme and a new mixed finite element formulation were developed based on the introduction of the relative deformation gradient-the deformation mapping between the last converged and current configurations. The numerical implementation of both the generalized framework and the specific Rubin and Bodner model is presented. As an example of a challenging application of the new model equations, the mechanical response of facial skin tissue is characterized through an experimental campaign based on the suction method. The measurement data are used for the identification of a suitable set of model parameters that well represents the experimentally observed tissue behavior. Two different measurement protocols were defined to address specific tissue properties with respect to the instantaneous tissue response, inelasticity, and tissue recovery.

  9. A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulation

    Energy Technology Data Exchange (ETDEWEB)

    Nachbagauer, Karin, E-mail: karin.nachbagauer@jku.at; Pechstein, Astrid S., E-mail: astrid.pechstein@jku.at; Irschik, Hans, E-mail: hans.irschik@jku.at [Johannes Kepler University Linz, Institute of Technical Mechanics (Austria); Gerstmayr, Johannes, E-mail: johannes.gerstmayr@lcm.at [Linz Center of Mechatronics GmbH (Austria)

    2011-10-15

    Many widely used beam finite element formulations are based either on Reissner's classical nonlinear rod theory or the absolute nodal coordinate formulation (ANCF). Advantages of the second method have been pointed out by several authors; among the benefits are the constant mass matrix of ANCF elements, the isoparametric approach and the existence of a consistent displacement field along the whole cross section. Consistency of the displacement field allows simpler, alternative formulations for contact problems or inelastic materials. Despite conceptional differences of the two formulations, the two models are unified in the present paper.In many applications, a nonlinear large deformation beam element with bending, axial and shear deformation properties is needed. In the present paper, linear and quadratic ANCF shear deformable beam finite elements are presented. A new locking-free continuum mechanics based formulation is compared to the classical Simo and Vu-Quoc formulation based on Reissner's virtual work of internal forces. Additionally, the introduced linear and quadratic ANCF elements are compared to a fully parameterized ANCF element from the literature. The performance of the respective elements is evaluated through analysis of conventional static and dynamic example problems. The investigation shows that the obtained linear and quadratic ANCF elements are advantageous compared to the original fully parameterized ANCF element.

  10. Quantifying the size-dependent effect of the residual surface stress on the resonant frequencies of silicon nanowires if finite deformation kinematics are considered.

    Science.gov (United States)

    Park, Harold S

    2009-03-18

    There are two major objectives to the present work. The first objective is to demonstrate that, in contrast to predictions from linear surface elastic theory, when nonlinear, finite deformation kinematics are considered, the residual surface stress does impact the resonant frequencies of silicon nanowires. The second objective of this work is to delineate, as a function of nanowire size, the relative contributions of both the residual (strain-independent) and the surface elastic (strain-dependent) parts of the surface stress to the nanowire resonant frequencies. Both goals are accomplished by using the recently developed surface Cauchy-Born model, which accounts for nanoscale surface stresses through a nonlinear, finite deformation continuum mechanics model that leads to the solution of a standard finite element eigenvalue problem for the nanowire resonant frequencies. In addition to demonstrating that the residual surface stress does impact the resonant frequencies of silicon nanowires, we further show that there is a strong size dependence to its effect; in particular, we find that consideration of the residual surface stress alone leads to significant errors in predictions of the nanowire resonant frequency, with an increase in error with decreasing nanowire size. Correspondingly, the strain-dependent part of the surface stress is found to have an increasingly important effect on the resonant frequencies of the nanowires with decreasing nanowire size.

  11. Implementation of a strain energy-based nonlinear finite element in the object-oriented environment

    Science.gov (United States)

    Wegner, Tadeusz; Pęczak, Andrzej

    2010-03-01

    The objective of the paper is to describe a novel finite element computational method based on a strain energy density function and to implement it in the object-oriented environment. The original energy-based finite element was put into the known standard framework of classes and handled in a different manner. The nonlinear properties of material are defined with a modified strain energy density function. The local relaxation procedure proposed as a method used to resolve a nonlinear problem is implemented in C++ language. The hexahedral element with eight nodes as well as the adaptation of the nonlinear finite element is introduced. The chosen numerical model is made of nearly incompressible hyperelastic material. The application of the proposed element is shown on the example of a rectangular parallelepiped with a hollow port.

  12. An approach to design semi-global finite-time observers for a class of nonlinear systems

    Institute of Scientific and Technical Information of China (English)

    DENG XiuCheng; SHEN YanJun

    2009-01-01

    In this paper, the problem of designing semi-global finite-time observers for a class of nonlinear systems is investigated. Based on the theories of finite-time stability, an approach to designing semi-global finite-time observers for the nonlinear systems is presented. It has been shown that, after the finite time, the designed finite-time observer realizes the accurate reconstruction of the states of the nonlinear system. A numerical example is given to illustrate the effectiveness and validity of the method.

  13. A non-linear elastic constitutive framework for replicating plastic deformation in solids.

    Energy Technology Data Exchange (ETDEWEB)

    Roberts, Scott Alan; Schunk, Peter Randall

    2014-02-01

    Ductile metals and other materials typically deform plastically under large applied loads; a behavior most often modeled using plastic deformation constitutive models. However, it is possible to capture some of the key behaviors of plastic deformation using only the framework for nonlinear elastic mechanics. In this paper, we develop a phenomenological, hysteretic, nonlinear elastic constitutive model that captures many of the features expected of a plastic deformation model. This model is based on calculating a secant modulus directly from a materials stress-strain curve. Scalar stress and strain values are obtained in three dimensions by using the von Mises invariants. Hysteresis is incorporated by tracking an additional history variable and assuming an elastic unloading response. This model is demonstrated in both single- and multi-element simulations under varying strain conditions.

  14. Finite time control for MIMO nonlinear system based on higher-order sliding mode.

    Science.gov (United States)

    Liu, Xiangjie; Han, Yaozhen

    2014-11-01

    Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm.

  15. Nonlinear Finite Element Analysis of Reinforced Concrete Shells

    Directory of Open Access Journals (Sweden)

    Mustafa K. Ahmed

    2013-05-01

    Full Text Available This investigation is to develop a numerical model suitable for nonlinear analysis of reinforced concrete shells. A nine-node Lagrangian element Figure (1 with enhanced shear interpolation will be used in this study. Table (1 describes shape functions and their derivatives of this element.An assumed transverse shear strain is used in the formulation of this element to overcome shear locking. Degenerated quadratic thick plate elements employing a layered discrelization through the thickness will be adopted. Different numbers of layers for different thickness can be used per element. A number of layers between (6 and 10 have proved to be appropriate to represent the nonlinear material behavior in structures. In this research 8 layers will be adequate. Material nonlinearities due to cracking of concrete, plastic flow or crushing of concrete in compression and yield condition of reinforcing steel are considered. The maximum tensile strength is used as a criterion for crack initiation. Attention is given to the tension stiffening phenomenon and the degrading effect of cracking on the compressive and shear strength of concrete. Perfect bond between concrete and steel is assumed. Attention is given also to geometric nonlinearities. An example have been chosen in order to demonstrate the suitability of the models by comparing the predicted behaviour with the experimental results for shell exhibiting various modes of failure.

  16. MO-F-BRA-04: Voxel-Based Statistical Analysis of Deformable Image Registration Error via a Finite Element Method.

    Science.gov (United States)

    Li, S; Lu, M; Kim, J; Glide-Hurst, C; Chetty, I; Zhong, H

    2012-06-01

    Purpose Clinical implementation of adaptive treatment planning is limited by the lack of quantitative tools to assess deformable image registration errors (R-ERR). The purpose of this study was to develop a method, using finite element modeling (FEM), to estimate registration errors based on mechanical changes resulting from them. Methods An experimental platform to quantify the correlation between registration errors and their mechanical consequences was developed as follows: diaphragm deformation was simulated on the CT images in patients with lung cancer using a finite element method (FEM). The simulated displacement vector fields (F-DVF) were used to warp each CT image to generate a FEM image. B-Spline based (Elastix) registrations were performed from reference to FEM images to generate a registration DVF (R-DVF). The F- DVF was subtracted from R-DVF. The magnitude of the difference vector was defined as the registration error, which is a consequence of mechanically unbalanced energy (UE), computed using 'in-house-developed' FEM software. A nonlinear regression model was used based on imaging voxel data and the analysis considered clustered voxel data within images. Results A regression model analysis showed that UE was significantly correlated with registration error, DVF and the product of registration error and DVF respectively with R̂2=0.73 (R=0.854). The association was verified independently using 40 tracked landmarks. A linear function between the means of UE values and R- DVF*R-ERR has been established. The mean registration error (N=8) was 0.9 mm. 85.4% of voxels fit this model within one standard deviation. Conclusions An encouraging relationship between UE and registration error has been found. These experimental results suggest the feasibility of UE as a valuable tool for evaluating registration errors, thus supporting 4D and adaptive radiotherapy. The research was supported by NIH/NCI R01CA140341. © 2012 American Association of Physicists in

  17. Structural analysis of composite wind turbine blades nonlinear mechanics and finite element models with material damping

    CERN Document Server

    Chortis, Dimitris I

    2013-01-01

    This book concerns the development of novel finite elements for the structural analysis of composite beams and blades. The introduction of material damping is also an important aspect of composite structures and it is presented here in terms of their static and dynamic behavior. The book thoroughly presents a new shear beam finite element, which entails new blade section mechanics, capable of predicting structural blade coupling due to composite coupling and/or internal section geometry. Theoretical background is further expanded towards the inclusion of nonlinear structural blade models and damping mechanics for composite structures. The models effectively include geometrically nonlinear terms due to large displacements and rotations, improve the modeling accuracy of very large flexible blades, and enable the modeling of rotational stiffening and buckling, as well as, nonlinear structural coupling. Validation simulations on specimen level study the geometric nonlinearities effect on the modal frequencies and...

  18. Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics

    Science.gov (United States)

    Atluri, S. N.; Nakagaki, M.; Kathiresan, K.

    1980-01-01

    In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.

  19. Finite-time Consensus of Heterogeneous Multi-agent Systems with Linear and Nonlinear Dynamics

    Institute of Scientific and Technical Information of China (English)

    ZHU Ya-Kun; GUAN Xin-Ping; LUO Xiao-Yuan

    2014-01-01

    In this paper, the finite-time consensus problems of heterogeneous multi-agent systems composed of both linear and nonlinear dynamics agents are investigated. Nonlinear consensus protocols are proposed for the heterogeneous multi-agent systems. Some sufficient conditions for the finite-time consensus are established in the leaderless and leader-following cases. The results are also extended to the case where the communication topology is directed and satisfies a detailed balance condition on coupling weights. At last, some simulation results are given to illustrate the effectiveness of the obtained theoretical results.

  20. Finite time extinction for nonlinear fractional evolution equations and related properties.

    OpenAIRE

    Jesus Ildefonso Diaz; Teresa Pierantozzi; Luis Vazquez

    2016-01-01

    The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly,...

  1. AN ANISOTROPIC NONCONFORMING FINITE ELEMENT METHOD FOR APPROXIMATING A CLASS OF NONLINEAR SOBOLEV EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Dongyang Shi; Haihong Wang; Yuepeng Du

    2009-01-01

    An anisotropic nonconforming finite element method is presented for a class of nonlinear Sobolev equations. The optimal error estimates and supercloseness are obtained for both semi-discrete and fully-discrete approximate schemes, which are the same as the traditional finite element methods. In addition, the global superconvergence is derived through the postprocessing technique. Numerical experiments are included to illustrate the feasibility of the proposed method.

  2. Validation of Finite Element Solutions of Nonlinear, Periodic Eddy Current Problems

    Directory of Open Access Journals (Sweden)

    Plasser René

    2014-12-01

    Full Text Available An industrial application is presented to validate a finite element analysis of 3-dimensional, nonlinear eddy-current problems with periodic excitation. The harmonic- balance method and the fixed-point technique are applied to get the steady state solution using the finite element method. The losses occurring in steel reinforcements underneath a reactor due to induced eddy-currents are computed and compared to measurements.

  3. Implementation of Lumped Plasticity Models and Developments in an Object Oriented Nonlinear Finite Element Code

    Science.gov (United States)

    Segura, Christopher L.

    Numerical simulation tools capable of modeling nonlinear material and geometric behavior are important to structural engineers concerned with approximating the strength and deformation capacity of a structure. While structures are typically designed to behave linear elastic when subjected to building code design loads, exceedance of the linear elastic range is often an important consideration, especially with regards to structural response during hazard level events (i.e. earthquakes, hurricanes, floods), where collapse prevention is the primary goal. This thesis addresses developments made to Mercury, a nonlinear finite element program developed in MATLAB for numerical simulation and in C++ for real time hybrid simulation. Developments include the addition of three new constitutive models to extend Mercury's lumped plasticity modeling capabilities, a constitutive driver tool for testing and implementing Mercury constitutive models, and Mercury pre and post-processing tools. Mercury has been developed as a tool for transient analysis of distributed plasticity models, offering accurate nonlinear results on the material level, element level, and structural level. When only structural level response is desired (collapse prevention), obtaining material level results leads to unnecessarily lengthy computational time. To address this issue in Mercury, lumped plasticity capabilities are developed by implementing two lumped plasticity flexural response constitutive models and a column shear failure constitutive model. The models are chosen for implementation to address two critical issues evident in structural testing: column shear failure and strength and stiffness degradation under reverse cyclic loading. These tools make it possible to model post-peak behavior, capture strength and stiffness degradation, and predict global collapse. During the implementation process, a need was identified to create a simple program, separate from Mercury, to simplify the process of

  4. Optimum Control for Nonlinear Dynamic Radial Deformation of Turbine Casing with Time-Varying LSSVM

    Directory of Open Access Journals (Sweden)

    Cheng-Wei Fei

    2015-01-01

    Full Text Available With the development of the high performance and high reliability of aeroengine, the blade-tip radial running clearance (BTRRC of high pressure turbine seriously influences the reliability and performance of aeroengine, wherein the radial deformation control of turbine casing has to be concerned in BTRRC design. To improve BTRRC design, the optimum control-based probabilistic optimization of turbine casing radial deformation was implemented using time-varying least square support vector machine (T-LSSVM by considering nonlinear material properties and dynamic thermal load. First the T-LSSVM method was proposed and its mathematical model was established. And then the nonlinear dynamic optimal control model of casing radial deformation was constructed with T-LSSVM. Thirdly, through the numerical experiments, the T-LSSVM method is demonstrated to be a promising approach in reducing additional design samples and improving computational efficiency with acceptable computational precision. Through the optimum control-based probabilistic optimization for nonlinear dynamic radial turbine casing deformation, the optimum radial deformation is 7.865 × 10−4 m with acceptable reliability degree 0.995 6, which is reduced by 7.86 × 10−5 m relative to that before optimization. These results validate the effectiveness and feasibility of the proposed T-LSSVM method, which provides a useful insight into casing radial deformation, BTRRC control, and the development of gas turbine with high performance and high reliability.

  5. Material nonlinear analysis via mixed-iterative finite element method

    Science.gov (United States)

    Sutjahjo, Edhi; Chamis, Christos C.

    1992-01-01

    The performance of elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors are tested using 4-node quadrilateral finite elements. The membrane result is excellent, which indicates the implementation of elastic-plastic mixed-iterative analysis is appropriate. On the other hand, further research to improve bending performance of the method seems to be warranted.

  6. High-speed nonlinear finite element analysis for surgical simulation using graphics processing units.

    Science.gov (United States)

    Taylor, Z A; Cheng, M; Ourselin, S

    2008-05-01

    The use of biomechanical modelling, especially in conjunction with finite element analysis, has become common in many areas of medical image analysis and surgical simulation. Clinical employment of such techniques is hindered by conflicting requirements for high fidelity in the modelling approach, and fast solution speeds. We report the development of techniques for high-speed nonlinear finite element analysis for surgical simulation. We use a fully nonlinear total Lagrangian explicit finite element formulation which offers significant computational advantages for soft tissue simulation. However, the key contribution of the work is the presentation of a fast graphics processing unit (GPU) solution scheme for the finite element equations. To the best of our knowledge, this represents the first GPU implementation of a nonlinear finite element solver. We show that the present explicit finite element scheme is well suited to solution via highly parallel graphics hardware, and that even a midrange GPU allows significant solution speed gains (up to 16.8 x) compared with equivalent CPU implementations. For the models tested the scheme allows real-time solution of models with up to 16,000 tetrahedral elements. The use of GPUs for such purposes offers a cost-effective high-performance alternative to expensive multi-CPU machines, and may have important applications in medical image analysis and surgical simulation.

  7. Accurate nonlinear modeling for flexible manipulators using mixed finite element formulation in order to obtain maximum allowable load

    Energy Technology Data Exchange (ETDEWEB)

    Esfandiar, Habib; KoraYem, Moharam Habibnejad [Islamic Azad University, Tehran (Iran, Islamic Republic of)

    2015-09-15

    In this study, the researchers try to examine nonlinear dynamic analysis and determine Dynamic load carrying capacity (DLCC) in flexible manipulators. Manipulator modeling is based on Timoshenko beam theory (TBT) considering the effects of shear and rotational inertia. To get rid of the risk of shear locking, a new procedure is presented based on mixed finite element formulation. In the method proposed, shear deformation is free from the risk of shear locking and independent of the number of integration points along the element axis. Dynamic modeling of manipulators will be done by taking into account small and large deformation models and using extended Hamilton method. System motion equations are obtained by using nonlinear relationship between displacements-strain and 2nd PiolaKirchoff stress tensor. In addition, a comprehensive formulation will be developed to calculate DLCC of the flexible manipulators during the path determined considering the constraints end effector accuracy, maximum torque in motors and maximum stress in manipulators. Simulation studies are conducted to evaluate the efficiency of the method proposed taking two-link flexible and fixed base manipulators for linear and circular paths into consideration. Experimental results are also provided to validate the theoretical model. The findings represent the efficiency and appropriate performance of the method proposed.

  8. Two-Dimensional Large Deformation Finite Element Analysis for the Pulling-up of Plate Anchor

    Institute of Scientific and Technical Information of China (English)

    WANG Dong; HU Yu-xia; JIN Xia

    2006-01-01

    Based on mesh regeneration and stress interpolation from an old mesh to a new one, a large deformation finite element model is developed for the study of the behaviour of circular plate anchors subjected to uplift loading. For the determination of the distributions of stress components across a clay foundation, the Recovery by Equilibrium in Patches is extended to plastic analyses. ABAQUS, a commercial finite element package, is customized and linked into our program so as to keep automatic and efficient running of large deformation calculation. The quality of stress interpolation is testified by evaluations of Tresca stress and nodal reaction forces. The complete pulling-up processes of plate anchors buried in homogeneous clay are simulated, and typical pulling force-displacement responses of a deep anchor and a shallow anchor are compared. Different from the results of previous studies, large deformation analysis is of the capability of estimating the breakaway between the anchor bottom and soils. For deep anchors, the variation of mobilized uplift resistance with anchor settlement is composed of three stages, and the initial buried depths of anchors affect the separation embedment slightly. The uplift bearing capacity of deep anchors is usually higher than that of shallow anchors.

  9. Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

    Directory of Open Access Journals (Sweden)

    Humberto Breves Coda

    2009-01-01

    Full Text Available This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples.

  10. Finite Time Control for Fractional Order Nonlinear Hydroturbine Governing System via Frequency Distributed Model

    Directory of Open Access Journals (Sweden)

    Bin Wang

    2016-01-01

    Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.

  11. Finite Temperature Induced Fermion Number In The Nonlinear sigma Model In (2+1) Dimensions

    CERN Document Server

    Dunne, G V; Rao, K; Dunne, Gerald V.; Lopez-Sarrion, Justo; Rao, Kumar

    2002-01-01

    We compute the finite temperature induced fermion number for fermions coupled to a static nonlinear sigma model background in (2+1) dimensions, in the derivative expansion limit. While the zero temperature induced fermion number is well known to be topological (it is the winding number of the background), at finite temperature there is a temperature dependent correction that is nontopological -- this finite T correction is sensitive to the detailed shape of the background. At low temperature we resum the derivative expansion to all orders, and we consider explicit forms of the background as a CP^1 instanton or as a baby skyrmion.

  12. Finite-dimensional even and odd nonlinear pair coherent states and their some nonclassical properties

    Institute of Scientific and Technical Information of China (English)

    Meng Xiang-Guo; Wang Ji-Suo; Liu Tang-Kun

    2008-01-01

    In this paper a new class of finite-dimensional even and odd nonlinear pair coherent states(EONLPCSs),which can be realized via operating the superposed evolution operators D±(τ)on the state |q,0),is constructed,then their orthonormalized property,completeness relations and some nonclassical properties are discussed.It is shown that the finite-dimensional EONLPCSs possess normalization and completeness relations.Moreover,the finite-dimensional EONLPCSs exhibit remarkably different sub-Poissonian distributions and phase probability distributions for different values of parameters q,η and ξ.

  13. Finite-Time Stabilization for a Class of Nonlinear Differential-Algebraic Systems Subject to Disturbance

    Directory of Open Access Journals (Sweden)

    Xiaohui Mo

    2017-01-01

    Full Text Available In this paper, finite-time stabilization problem for a class of nonlinear differential-algebraic systems (NDASs subject to external disturbance is investigated via a composite control manner. A composite finite-time controller (CFTC is proposed with a three-stage design procedure. Firstly, based on the adding a power integrator technique, a finite-time control (FTC law is explicitly designed for the nominal NDAS by only using differential variables. Then, by using homogeneous system theory, a continuous finite-time disturbance observer (CFTDO is constructed to estimate the disturbance generated by an exogenous system. Finally, a composite controller which consists of a feedforward compensation part based on CFTDO and the obtained FTC law is proposed. Rigorous analysis demonstrates that not only the proposed composite controller can stabilize the NDAS in finite time, but also the proposed control scheme exhibits nominal performance recovery property. Simulation examples are provided to illustrate the effectiveness of the proposed control approach.

  14. Nonlinear Finite Element Analysis of Pull-Out Test

    DEFF Research Database (Denmark)

    Saabye Ottesen, N

    1981-01-01

    A specific pull-out test used to determine in-situ concrete compressive strength is analyzed. This test consists of a steel disc that is extracted from the structure. The finite element analysis considers cracking as well as strain hardening and softening in the pre- and post-failure region......, respectively. The aim is to attain a clear insight into structural behavior. Special attention is given to the failure mode. Severe cracking occurs and the stress distribution is very inhomogeneous. However, large compressive forces run from the disc in a rather narrow band towards the support...

  15. High-order finite difference solution for 3D nonlinear wave-structure interaction

    DEFF Research Database (Denmark)

    Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter;

    2010-01-01

    This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme...... OceanWave3D presented in [1, 2]. A nonlinear decomposition of the solution into incident and scattered fields is used to increase the efficiency of the wave-structure interaction problem resolution. Application of the method to the diffraction of nonlinear waves around a fixed, bottom mounted circular...

  16. Study on high order perturbation-based nonlinear stochastic finite element method for dynamic problems

    Science.gov (United States)

    Wang, Qing; Yao, Jing-Zheng

    2010-12-01

    Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorithms and a framework related to SFEM based on the stochastic virtual work principle were studied. To prove the validity and practicality of the algorithms and framework, numerical examples for nonlinear dynamic problems with large variations were calculated and compared with the Monte-Carlo Simulation method. This comparison shows that the proposed approaches are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.

  17. Finite-Length Soliton Solutions of the Local Homogeneous Nonlinear Schrödinger Equation

    CERN Document Server

    Caparelli, E C; Mizrahi, S S

    1998-01-01

    We found a new kind of soliton solutions for the 5-parameter family of the potential-free Stenflo-Sabatier-Doebner-Goldin nonlinear modifications of the Schrödinger equation. In contradistinction to the "usual'' solitons like are nonanalytical functions with continuous first derivatives, which are different from zero only inside some finite regions of space. The simplest one-dimensional example is the function which is equal to identically equal to zero for |x-kt|>\\pi/(2g). The FLS exist even in the case of a weak nonlinearity, whereas the ``usual'' solitons exist provided the nonlinearity parameters surpass some critical values.

  18. Simulation of 3D parachute fluid-structure interaction based on nonlinear finite element method and preconditioning finite volume method

    Institute of Scientific and Technical Information of China (English)

    Fan Yuxin; Xia Jian

    2014-01-01

    A fluid–structure interaction method combining a nonlinear finite element algorithm with a preconditioning finite volume method is proposed in this paper to simulate parachute tran-sient dynamics. This method uses a three-dimensional membrane–cable fabric model to represent a parachute system at a highly folded configuration. The large shape change during parachute infla-tion is computed by the nonlinear Newton–Raphson iteration and the linear system equation is solved by the generalized minimal residual (GMRES) method. A membrane wrinkling algorithm is also utilized to evaluate the special uniaxial tension state of membrane elements on the parachute canopy. In order to avoid large time expenses during structural nonlinear iteration, the implicit Hil-ber–Hughes–Taylor (HHT) time integration method is employed. For the fluid dynamic simula-tions, the Roe and HLLC (Harten–Lax–van Leer contact) scheme has been modified and extended to compute flow problems at all speeds. The lower–upper symmetric Gauss–Seidel (LU-SGS) approximate factorization is applied to accelerate the numerical convergence speed. Finally, the test model of a highly folded C-9 parachute is simulated at a prescribed speed and the results show similar characteristics compared with experimental results and previous literature.

  19. Simulation of 3D parachute fluid–structure interaction based on nonlinear finite element method and preconditioning finite volume method

    Directory of Open Access Journals (Sweden)

    Fan Yuxin

    2014-12-01

    Full Text Available A fluid–structure interaction method combining a nonlinear finite element algorithm with a preconditioning finite volume method is proposed in this paper to simulate parachute transient dynamics. This method uses a three-dimensional membrane–cable fabric model to represent a parachute system at a highly folded configuration. The large shape change during parachute inflation is computed by the nonlinear Newton–Raphson iteration and the linear system equation is solved by the generalized minimal residual (GMRES method. A membrane wrinkling algorithm is also utilized to evaluate the special uniaxial tension state of membrane elements on the parachute canopy. In order to avoid large time expenses during structural nonlinear iteration, the implicit Hilber–Hughes–Taylor (HHT time integration method is employed. For the fluid dynamic simulations, the Roe and HLLC (Harten–Lax–van Leer contact scheme has been modified and extended to compute flow problems at all speeds. The lower–upper symmetric Gauss–Seidel (LU-SGS approximate factorization is applied to accelerate the numerical convergence speed. Finally, the test model of a highly folded C-9 parachute is simulated at a prescribed speed and the results show similar characteristics compared with experimental results and previous literature.

  20. Finite element modeling of passive material influence on the deformation and force output of skeletal muscle.

    Science.gov (United States)

    Hodgson, John A; Chi, Sheng-Wei; Yang, Judy P; Chen, Jiun-Shyan; Edgerton, Victor R; Sinha, Shantanu

    2012-05-01

    The pattern of deformation of different structural components of a muscle-tendon complex when it is activated provides important information about the internal mechanics of the muscle. Recent experimental observations of deformations in contracting muscle have presented inconsistencies with current widely held assumption about muscle behavior. These include negative strain in aponeuroses, non-uniform strain changes in sarcomeres, even of individual muscle fibers and evidence that muscle fiber cross sectional deformations are asymmetrical suggesting a need to readjust current models of contracting muscle. We report here our use of finite element modeling techniques to simulate a simple muscle-tendon complex and investigate the influence of passive intramuscular material properties upon the deformation patterns under isometric and shortening conditions. While phenomenological force-displacement relationships described the muscle fiber properties, the material properties of the passive matrix were varied to simulate a hydrostatic model, compliant and stiff isotropically hyperelastic models and an anisotropic elastic model. The numerical results demonstrate that passive elastic material properties significantly influence the magnitude, heterogeneity and distribution pattern of many measures of deformation in a contracting muscle. Measures included aponeurosis strain, aponeurosis separation, muscle fiber strain and fiber cross-sectional deformation. The force output of our simulations was strongly influenced by passive material properties, changing by as much as ~80% under some conditions. The maximum output was accomplished by introducing anisotropy along axes which were not strained significantly during a muscle length change, suggesting that correct costamere orientation may be a critical factor in the optimal muscle function. Such a model not only fits known physiological data, but also maintains the relatively constant aponeurosis separation observed during in vivo

  1. Finite element analysis of deformation characteristics in cold helical rolling of bearing steel-balls

    Institute of Scientific and Technical Information of China (English)

    曹强; 华林; 钱东升

    2015-01-01

    Due to the complexity of investigating deformation mechanisms in helical rolling (HR) process with traditional analytical method, it is significant to develop a 3D finite element (FE) model of HR process. The key forming conditions of cold HR of bearing steel-balls were detailedly described. Then, by taking steel-ball rolling elements of the B7008C angular contact ball bearing as an example, a completed 3D elastic-plastic FE model of cold HR forming process was established under SIMUFACT software environment. Furthermore, the deformation characteristics in HR process were discovered, including the forming process, evolution and distribution laws of strain, stress and damage based on Lemaitre relative damage model. The results reveal that the central loosening and cavity defects in HR process may have a combined effect of large negative hydrostatic pressure (positive mean stress) caused by multi-dimensional tensile stresses, high level transverse tensile stress, and circular-alternating shear stress in cross section.

  2. A structurally based viscoelastic model for passive myocardium in finite deformation

    Science.gov (United States)

    Shen, Jing Jin

    2016-09-01

    This paper discusses the finite-deformation viscoelastic modeling for passive myocardium tissue. The formulations established can also be applied to model other fiber-reinforced soft tissue. Based on the morphological structure of the myocardium, a specific free-energy function is constructed to reflect its orthotropicity. After deriving the stress-strain relationships in the simple shear deformation, a genetic algorithm is used to optimally estimate the material parameters of the myocardial constitutive equation. The results show that the proposed myocardial model can well fit the shear experimental data. To validate the viscoelastic model, it is used to predict the creep and the dynamic responses of a cylindrical model of the left ventricle. Upon comparing the results calculated by the proven myocardial elastic model with those by the viscoelastic model, the merits of the latter are discussed.

  3. FINITE ELEMENT ANALYSIS OF SUBSTRATE LOCAL PLASTIC DEFORMATION INDUCED BY CRACKED THIN HARD FILM

    Institute of Scientific and Technical Information of China (English)

    Zhu Youli; Ro(z)niatowski K; Kurzydlowski K; Huang Yuanlin; Xu Binshi

    2004-01-01

    It has been postulated that, with tensile loading conditions, micro-cracks on thin hard film act as stress concentrators enhancing plastic deformation of the substrate material in their vicinity. Under favorable conditions the localized plastic flow near the cracks may turn into macroscopic plastic strain thus affects the plasticity behaviors of the substrate. This phenomenon is analyzed quantitatively with finite element method with special attention focused on the analysis and discussion of the effects of plastic work hardening rate, film thickness and crack depth on maximum plastic strain, critical loading stress and the size of the local plastic deformation zone. Results show that micro-cracks on thin hard film have unnegligible effects on the plasticity behaviors of the substrate material under tensile loading.

  4. Finite Amplitude Method for Charge-Changing Transitions in Axially-Deformed Nuclei

    CERN Document Server

    Mustonen, M T; Zenginerler, Z; Engel, J

    2014-01-01

    We describe and apply a version of the finite amplitude method for obtaining the charge-changing nuclear response in the quasiparticle random phase approximation. The method is suitable for calculating strength functions and beta-decay rates, both allowed and forbidden, in axially-deformed open-shell nuclei. We demonstrate the speed and versatility of the code through a preliminary examination of the effects of tensor terms in Skyrme functionals on beta decay in a set of spherical and deformed open-shell nuclei. Like the isoscalar pairing interaction, the tensor terms systematically increase allowed beta-decay rates. This finding generalizes previous work in semimagic nuclei and points to the need for a comprehensive study of time-odd terms in nuclear density functionals.

  5. Corneal Viscoelastic Properties from Finite-Element Analysis of In Vivo Air-Puff Deformation

    Science.gov (United States)

    Kling, Sabine; Bekesi, Nandor; Dorronsoro, Carlos; Pascual, Daniel; Marcos, Susana

    2014-01-01

    Biomechanical properties are an excellent health marker of biological tissues, however they are challenging to be measured in-vivo. Non-invasive approaches to assess tissue biomechanics have been suggested, but there is a clear need for more accurate techniques for diagnosis, surgical guidance and treatment evaluation. Recently air-puff systems have been developed to study the dynamic tissue response, nevertheless the experimental geometrical observations lack from an analysis that addresses specifically the inherent dynamic properties. In this study a viscoelastic finite element model was built that predicts the experimental corneal deformation response to an air-puff for different conditions. A sensitivity analysis reveals significant contributions to corneal deformation of intraocular pressure and corneal thickness, besides corneal biomechanical properties. The results show the capability of dynamic imaging to reveal inherent biomechanical properties in vivo. Estimates of corneal biomechanical parameters will contribute to the basic understanding of corneal structure, shape and integrity and increase the predictability of corneal surgery. PMID:25121496

  6. Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures

    Science.gov (United States)

    Mital, Subodh K.; Goldberg, Robert K.; Bonacuse, Peter J.

    2012-01-01

    A research program has been developed to quantify the effects of the microstructure of a woven ceramic matrix composite and its variability on the effective properties and response of the material. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, chemical vapor infiltrated (CVI) SiC/SiC composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents, from which two dimensional finite element models were generated which approximated the actual specimen section geometry. A simplified elastic-plastic model, wherein all stress above yield is redistributed to lower stress regions, is used to approximate the progressive damage behavior for each of the composite constituents. Finite element analyses under in-plane tensile loading were performed to examine how the variability in the local microstructure affected the macroscopic stress-strain response of the material as well as the local initiation and progression of damage. The macroscopic stress-strain response appeared to be minimally affected by the variation in local microstructure, but the locations where damage initiated and propagated appeared to be linked to specific aspects of the local microstructure.

  7. FEMSA: a finite element simulation tool for quasi-static seismic deformation modeling

    Directory of Open Access Journals (Sweden)

    A. Piersanti

    2007-06-01

    Full Text Available We set up a computational tool to numerically model static and quasi-static deformation generated by faulting sources embedded in plane or spherical domains. We use a Finite Element (FE approach to automatically implement arbitrary faulting sources and calculate displacement and stress fields induced by slip on the fault. The package makes use of the capabilities of CalculiX, a non commercial FE software designed to solve field problems (see for details, and is freely distributed by request.

  8. Numerical research orthotropic geometrically nonlinear shell stability using the mixed finite element method

    Science.gov (United States)

    Stupishin, L.; Nikitin, K.; Kolesnikov, A.

    2017-05-01

    A methodology for shell stability research and determining buckling load, based on the mixed finite element method are proposed. Axisymmetric geometrically nonlinear shallow shells made of orthotropic material are considered. The results of numerical research of stability by changing the shape of shells, ratio of elastic modulus of the material and parameters of the support contour are presented.

  9. A smart nonstandard finite difference scheme for second order nonlinear boundary value problems

    NARCIS (Netherlands)

    Erdogan, Utku; Ozis, Turgut

    2011-01-01

    A new kind of finite difference scheme is presented for special second order nonlinear two point boundary value problems. An artificial parameter is introduced in the scheme. Symbolic computation is proposed for the construction of the scheme. Local truncation error of the method is discussed. Numer

  10. A Taylor-Galerkin finite element algorithm for transient nonlinear thermal-structural analysis

    Science.gov (United States)

    Thornton, E. A.; Dechaumphai, P.

    1986-01-01

    A Taylor-Galerkin finite element method for solving large, nonlinear thermal-structural problems is presented. The algorithm is formulated for coupled transient and uncoupled quasistatic thermal-structural problems. Vectorizing strategies ensure computational efficiency. Two applications demonstrate the validity of the approach for analyzing transient and quasistatic thermal-structural problems.

  11. A smart nonstandard finite difference scheme for second order nonlinear boundary value problems

    NARCIS (Netherlands)

    Erdogan, Utku; Ozis, Turgut

    2011-01-01

    A new kind of finite difference scheme is presented for special second order nonlinear two point boundary value problems. An artificial parameter is introduced in the scheme. Symbolic computation is proposed for the construction of the scheme. Local truncation error of the method is discussed.

  12. Linear and nonlinear Stability analysis for finite difference discretizations of higher order Boussinesq equations

    DEFF Research Database (Denmark)

    Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.

    2004-01-01

    This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly nonlinear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann...

  13. Ultimate limit state design of sheet pile walls by finite elements and nonlinear programming

    DEFF Research Database (Denmark)

    Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven

    2005-01-01

    as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe....

  14. Ultimate Limit State Design Of Sheet Pile Walls By Finite Elements And Nonlinear Programming

    DEFF Research Database (Denmark)

    Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven

    2005-01-01

    as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe...

  15. THE FINITE ELEMENT METHODS FOR A CLASS OF NONLINEAR PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Error estimates are established for the finite dement methods to solve a class of second or der nonlinear parabolic equations. Optimal rates of convergence in L2-and H1-norms are derived. Meanwhile,the schenes are second order correct in time.

  16. THE EFFECT OF NUMERICAL INTEGRATION IN FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    N'guimbi; Germain

    2001-01-01

    Abstract. The effect of numerical integration in finite element methods applied to a class of nonlinear parabolic equations is considered and some sufficient conditions on the quadrature scheme to ensure that the order of convergence is unaltered in the presence of numerical integration are given. Optimal Lz and H1 estimates for the error and its time derivative are established.

  17. COYOTE: a finite-element computer program for nonlinear heat-conduction problems

    Energy Technology Data Exchange (ETDEWEB)

    Gartling, D.K.

    1982-10-01

    COYOTE is a finite element computer program designed for the solution of two-dimensional, nonlinear heat conduction problems. The theoretical and mathematical basis used to develop the code is described. Program capabilities and complete user instructions are presented. Several example problems are described in detail to demonstrate the use of the program.

  18. A finite element-based perturbation method for nonlinear free vibration analysis of composite cylindrical shells

    NARCIS (Netherlands)

    Rahman, T.; Jansen, E.L.; Tiso, P.

    2011-01-01

    In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation an

  19. Nonlinear finite-element analysis and biomechanical evaluation of the lumbar spine

    DEFF Research Database (Denmark)

    Wong, Christian; Gehrchen, P Martin; Darvann, Tron;

    2003-01-01

    A finite-element analysis (FEA) model of an intact lumbar disc-body unit was generated. The vertebral body of the FEA model consisted of a solid tetrahedral core of trabecular bone surrounded by a cortical shell. The disc consisted of an incompressible nucleus surrounded by nonlinear annulus fibers...

  20. A finite element-based perturbation method for nonlinear free vibration analysis of composite cylindrical shells

    NARCIS (Netherlands)

    Rahman, T.; Jansen, E.L.; Tiso, P.

    2011-01-01

    In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation

  1. Nonlinearity and Strain-Rate Dependence in the Deformation Response of Polymer Matrix Composites Modeled

    Science.gov (United States)

    Goldberg, Robert K.

    2000-01-01

    There has been no accurate procedure for modeling the high-speed impact of composite materials, but such an analytical capability will be required in designing reliable lightweight engine-containment systems. The majority of the models in use assume a linear elastic material response that does not vary with strain rate. However, for containment systems, polymer matrix composites incorporating ductile polymers are likely to be used. For such a material, the deformation response is likely to be nonlinear and to vary with strain rate. An analytical model has been developed at the NASA Glenn Research Center at Lewis Field that incorporates both of these features. A set of constitutive equations that was originally developed to analyze the viscoplastic deformation of metals (Ramaswamy-Stouffer equations) was modified to simulate the nonlinear, rate-dependent deformation of polymers. Specifically, the effects of hydrostatic stresses on the inelastic response, which can be significant in polymers, were accounted for by a modification of the definition of the effective stress. The constitutive equations were then incorporated into a composite micromechanics model based on the mechanics of materials theory. This theory predicts the deformation response of a composite material from the properties and behavior of the individual constituents. In this manner, the nonlinear, rate-dependent deformation response of a polymer matrix composite can be predicted.

  2. On the nonlinearity interpretation of q- and f-deformation and some applications

    CERN Document Server

    Man'ko, V I

    1998-01-01

    q-oscillators are associated to the simplest non-commutative example of Hopf algebra and may be considered to be the basic building blocks for the symmetry algebras of completely integrable theories. They may also be interpreted as a special type of spectral nonlinearity, which may be generalized to a wider class of f-oscillator algebras. In the framework of this nonlinear interpretation, we discuss the structure of the stochastic process associated to q-deformation, the role of the q-oscillator as a spectrum-generating algebra for fast growing point spectrum, the deformation of fermion operators in solid-state models and the charge-dependent mass of excitations in f-deformed relativistic quantum fields.

  3. Explicit finite-difference time domain for nonlinear analysis of waveguide modes

    Science.gov (United States)

    Barakat, N. M.; Shabat, M. M.; El-Azab, S.; Jaeger, Dieter

    2003-07-01

    The Finite Difference Time Domain Technique is at present the most widely used tool employed in the study of light propagation in various photonic waveguide structure. In this paper we derived an explicit finite-difference time-domain (FDTD) method for solving the wave equation in a four optical waveguiding rectangular structure. We derive the stability condition to achieve the stability in nonlinear media region, we also check that the wave equation used is consistence and convergent with the approximate finite difference equation. Our method is tested against some previous problems and we find a high degree of accuracy, moreover it is easy for programming. Numerical results are illustrated for a rectangular waveguide with four layers, where one of these layers is a nonlinear medium.

  4. Computational contact and impact mechanics fundamentals of modeling interfacial phenomena in nonlinear finite element analysis

    CERN Document Server

    Laursen, Tod A

    2003-01-01

    This book comprehensively treats the formulation and finite element approximation of contact and impact problems in nonlinear mechanics. Intended for students, researchers and practitioners interested in numerical solid and structural analysis, as well as for engineers and scientists dealing with technologies in which tribological response must be characterized, the book includes an introductory but detailed overview of nonlinear finite element formulations before dealing with contact and impact specifically. Topics encompassed include the continuum mechanics, mathematical structure, variational framework, and finite element implementations associated with contact/impact interaction. Additionally, important and currently emerging research topics in computational contact mechanics are introduced, encompassing such topics as tribological complexity, conservative treatment of inelastic impact interaction, and novel spatial discretization strategies.

  5. A Physics-driven Neural Networks-based Simulation System (PhyNNeSS) for multimodal interactive virtual environments involving nonlinear deformable objects.

    Science.gov (United States)

    De, Suvranu; Deo, Dhannanjay; Sankaranarayanan, Ganesh; Arikatla, Venkata S

    2011-08-01

    BACKGROUND: While an update rate of 30 Hz is considered adequate for real time graphics, a much higher update rate of about 1 kHz is necessary for haptics. Physics-based modeling of deformable objects, especially when large nonlinear deformations and complex nonlinear material properties are involved, at these very high rates is one of the most challenging tasks in the development of real time simulation systems. While some specialized solutions exist, there is no general solution for arbitrary nonlinearities. METHODS: In this work we present PhyNNeSS - a Physics-driven Neural Networks-based Simulation System - to address this long-standing technical challenge. The first step is an off-line pre-computation step in which a database is generated by applying carefully prescribed displacements to each node of the finite element models of the deformable objects. In the next step, the data is condensed into a set of coefficients describing neurons of a Radial Basis Function network (RBFN). During real-time computation, these neural networks are used to reconstruct the deformation fields as well as the interaction forces. RESULTS: We present realistic simulation examples from interactive surgical simulation with real time force feedback. As an example, we have developed a deformable human stomach model and a Penrose-drain model used in the Fundamentals of Laparoscopic Surgery (FLS) training tool box. CONCLUSIONS: A unique computational modeling system has been developed that is capable of simulating the response of nonlinear deformable objects in real time. The method distinguishes itself from previous efforts in that a systematic physics-based pre-computational step allows training of neural networks which may be used in real time simulations. We show, through careful error analysis, that the scheme is scalable, with the accuracy being controlled by the number of neurons used in the simulation. PhyNNeSS has been integrated into SoFMIS (Software Framework for Multimodal

  6. A novel strong tracking finite-difference extended Kalman filter for nonlinear eye tracking

    Institute of Scientific and Technical Information of China (English)

    ZHANG ZuTao; ZHANG JiaShu

    2009-01-01

    Non-Intrusive methods for eye tracking are Important for many applications of vision-based human computer interaction. However, due to the high nonlinearity of eye motion, how to ensure the robust-ness of external interference and accuracy of eye tracking poses the primary obstacle to the integration of eye movements into today's interfaces. In this paper, we present a strong tracking finite-difference extended Kalman filter algorithm, aiming to overcome the difficulty In modeling nonlinear eye tracking. In filtering calculation, strong tracking factor is introduced to modify a priori covariance matrix and im-prove the accuracy of the filter. The filter uses finite-difference method to calculate partial derivatives of nonlinear functions for eye tracking. The latest experimental results show the validity of our method for eye tracking under realistic conditions.

  7. Feedforward deformation control of a dielectric elastomer actuator based on a nonlinear dynamic model

    Science.gov (United States)

    Gu, Guo-Ying; Gupta, Ujjaval; Zhu, Jian; Zhu, Li-Min; Zhu, Xiang-Yang

    2015-07-01

    In the practical applications of actuators, the control of their deformation or driving force is a key issue. Most of recent studies on dielectric elastomer actuators (DEAs) focus on issues of mechanics, physics, and material science, whereas less importance is given to the control of these soft actuators. In this paper, we underline the importance of a nonlinear dynamic model as the basis for a feedforward deformation control approach of a rubber-based DEA. Experimental evidence shows the effectiveness of the feedforward controller. The present study confirms that a DEA's trajectory can be finely controlled with a solid nonlinear dynamic model despite the presence of material nonlinearities and electromechanical coupling. The effective control of DEAs may pave the way for extensive emerging applications to soft robots.

  8. Implementing a Matrix-free Analytical Jacobian to Handle Nonlinearities in Models of 3D Lithospheric Deformation

    Science.gov (United States)

    Kaus, B.; Popov, A.

    2015-12-01

    The analytical expression for the Jacobian is a key component to achieve fast and robust convergence of the nonlinear Newton-Raphson iterative solver. Accomplishing this task in practice often requires a significant algebraic effort. Therefore it is quite common to use a cheap alternative instead, for example by approximating the Jacobian with a finite difference estimation. Despite its simplicity it is a relatively fragile and unreliable technique that is sensitive to the scaling of the residual and unknowns, as well as to the perturbation parameter selection. Unfortunately no universal rule can be applied to provide both a robust scaling and a perturbation. The approach we use here is to derive the analytical Jacobian for the coupled set of momentum, mass, and energy conservation equations together with the elasto-visco-plastic rheology and a marker in cell/staggered finite difference method. The software project LaMEM (Lithosphere and Mantle Evolution Model) is primarily developed for the thermo-mechanically coupled modeling of the 3D lithospheric deformation. The code is based on a staggered grid finite difference discretization in space, and uses customized scalable solvers form PETSc library to efficiently run on the massively parallel machines (such as IBM Blue Gene/Q). Currently LaMEM relies on the Jacobian-Free Newton-Krylov (JFNK) nonlinear solver, which approximates the Jacobian-vector product using a simple finite difference formula. This approach never requires an assembled Jacobian matrix and uses only the residual computation routine. We use an approximate Jacobian (Picard) matrix to precondition the Krylov solver with the Galerkin geometric multigrid. Because of the inherent problems of the finite difference Jacobian estimation, this approach doesn't always result in stable convergence. In this work we present and discuss a matrix-free technique in which the Jacobian-vector product is replaced by analytically-derived expressions and compare results

  9. Two-grid method for characteristisc mixed finite-element solutions of nonlinear convection-diffusion equations

    Institute of Scientific and Technical Information of China (English)

    QIN Xinqiang; MA Yichen; GONG Chunqiong

    2004-01-01

    A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.

  10. A finite deformation viscoelastic-viscoplastic constitutive model for self-healing materials

    Science.gov (United States)

    Shahsavari, H.; Naghdabadi, R.; Baghani, M.; Sohrabpour, S.

    2016-12-01

    In this paper, employing the Hencky strain, viscoelastic-viscoplastic response of self-healing materials is investigated. Considering the irreversible thermodynamics and using the effective configuration in the Continuum Damage-Healing Mechanics (CDHM), a phenomenological finite strain viscoelastic-viscoplastic constitutive model is presented. Considering finite viscoelastic and viscoplastic deformations, total deformation gradient is multiplicatively decomposed into viscoelastic and viscoplastic parts. Due to mathematical advantages and physical meaning of Hencky strain, this measure of strain is employed in the constitutive model development. In this regard, defining the damage and healing variables and employing the strain equivalence hypothesis, the strain tensor is determined in the effective configuration. Satisfying the Clausius-Duhem inequality, the evolution equations are introduced for the viscoelastic and viscoplastic strains. The damage and healing variables also evolve according to two different prescribed functions. To employ the proposed model in different loading conditions, the model is discretized in the semi-implicit form. Material parameters of the model are identified employing experimental tests on asphalt mixes available in the literature. Finally, capability of the model is demonstrated comparing the model predictions in the creep-recovery and repeated creep-recovery with the experimental results available in the literature and a good agreement between predicted and test results is revealed.

  11. FEMSA: A Finite Element Simulation Tool for Quasi-static Seismic Deformation Modeling

    Science.gov (United States)

    Volpe, M.; Melini, D.; Piersanti, A.

    2006-12-01

    Modeling postseismic deformation is an increasingly valuable tool in earthquake seismology. In particular, the Finite Element (FE) numerical method allows accurate modeling of complex faulting geometry, inhomogeneous materials and realistic viscous flow, appearing an excellent tool to investigate a lot of specific phenomena related with earthquakes. We developed a FE simulation tool, FEMSA (Finite Element Modeling for Seismic Applications), to model quasi-static deformation generated by faulting sources. The approach allows to automatically implement arbitrary faulting sources and calculate displacement and stress fields induced by slip on the fault. The package makes use of the capabilities of CalculiX, a non commercial FE software designed to solve field problems, and is freely distributed. The main advantages of the method are: reliability, wide diffusion and flexibility, allowing geometrical and/or rheological heterogeneities to be included in a mechanical analysis. We carried out an optimization study on boundary conditions as well as a series of benchmark simulations on test cases and we also verified the capability of our approach to face the presence of 3D heterogeneities within the domain. Here, we present our package and show some simple examples of application.

  12. 3D Finite Element Modeling of the 2009 L'Aquila Earthquake Deformation Field

    Science.gov (United States)

    Volpe, M.; Casarotti, E.; Piersanti, A.

    2009-12-01

    The L'Aquila earthquake (Mw 6.3) occurred on April 6th at 01:32 UTC in the Central Appennines at a depth of about 9 km and was felt all over Central Italy. The main shock was preceded by a long seismic sequence started several months before and was followed by thousands of aftershocks, some of them with Mw>4. We built up a high resolution three-dimensional model, incorporating surface topography, which was discretized using 20-nodes brick elements. The element horizontal size is biased from 500 m to 2 km using the paving meshing algorithm in combination with an appropriate adaptive sizing function. A realistic rheology was introduced from a vp/vpvs travel time tomographic model. We computed the co-seismic deformation induced by the earthquake by means of a recently developed finite elements simulation tool, FEMSA (Finite Element Modeling for Seismic Applications). We used different seismic source models obtained from fault inversion of GPS measurements, joint inversion of strong motion and GPS data and from inversion of DInSAR displacements. The synthetic deformation patterns were compared with the experimental results in order to evaluate which source model better reconciles the data and quantify the trade off introduced by 1D simulations.

  13. Nonlinear incompressible finite element for simulating loading of cardiac tissue--Part II: Three dimensional formulation for thick ventricular wall segments.

    Science.gov (United States)

    Horowitz, A; Sheinman, I; Lanir, Y

    1988-02-01

    A three dimensional incompressible and geometrically as well as materially nonlinear finite element is formulated for future implementation in models of cardiac mechanics. The stress-strain relations in the finite element are derived from a recently proposed constitutive law which is based on the histological composition of the myocardium. The finite element is formulated for large deformations and considers incompressibility by introducing the hydrostatic pressure as an additional variable. The results of passive loading cases simulated by this element allow to analyze the mechanical properties of ventricular wall segments, the main of which are that the circumferential direction is stiffer than the longitudinal one, that its shear stiffness is considerably lower than its tensile and compressive stiffness and that, due to its mechanically prominent role, the collagenous matrix may affect the myocardial perfusion.

  14. A Simulation of crustal deformation around sourthwest Japan using 3D Finite Element Method

    Science.gov (United States)

    Oma, T.; Ito, T.; Sasajima, R.

    2015-12-01

    In southwest Japan, the Philippine Sea plate is subducting beneath the Amurian plate at the Nankai Trough. Megathrust earthquakes have been occurred with recurrence intervals of about 100-150 years. Previous studies have estimated co-seismic slip distribution at the 1944 Tokankai and the 1946 Nankai earthquakes and interplate plate coupling along the Nankai Trough. Many of previous studies employed a homogeneous elastic half space or elastic and viscoelastic layers structure. However, these assumptions as mentioned above are inadequate, since inhomogeneous structure is exceled in the real earth result from subducting plate. Therefore, in order to estimate the effect of inhomogeneous structure on the crustal deformation, we calculate crustal deformation due to Megathrust earthquake using 3-dimensional Finite Element Method (FEM). We use FEM software PyLith v2.1. In this study, we construct a finite element mesh with the region of 3000km(SW) × 2300km(NS) × 400km(depth) cover Japanese Islands, using Cubit 13.0. This mesh is considered topography, the Philippine Sea plate, the Pacific plate, Moho discontinuity, and curvature of the earth. In order to examine differences of surface displacement between inhomogeneous and homogeneous structures, we use co-seismic slip distribution of the 1944 and 1946 earthquakes estimated by Sagiya and Thatcher (1999). In result, surface elastic response under inhomogeneous structure becomes 30% larger than it's homogeneous structure at the Muroto cape. This difference indicates that co-seismic slip or plate coupling distribution estimated from Green's function under an assumption of homogeneous structure is overestimated. Then, we calculate viscoelastic response assuming Maxwell rheology model and viscosity as 1×1019. As a result, predicted horizontal velocity of viscoelastic response due to the events corresponds to 10 % of observed present deformation. It suggest that spatial pattern of plate coupling might be change when we

  15. Evaluating Topographic Effects on Ground Deformation: Insights from Finite Element Modeling

    Science.gov (United States)

    Ronchin, Erika; Geyer, Adelina; Martí, Joan

    2015-07-01

    Ground deformation has been demonstrated to be one of the most common signals of volcanic unrest. Although volcanoes are commonly associated with significant topographic relief, most analytical models assume the Earth's surface as flat. However, it has been confirmed that this approximation can lead to important misinterpretations of the recorded surface deformation data. Here we perform a systematic and quantitative analysis of how topography may influence ground deformation signals generated by a spherical pressure source embedded in an elastic homogeneous media and how these variations correlate with the different topographic parameters characterizing the terrain form (e.g., slope, aspect, curvature). For this, we bring together the results presented in previous published papers and complement them with new axisymmetric and 3D finite element (FE) model results. First, we study, in a parametric way, the influence of a volcanic edifice centered above the pressure source axis. Second, we carry out new 3D FE models simulating the real topography of three different volcanic areas representative of topographic scenarios common in volcanic regions: Rabaul caldera (Papua New Guinea) and the volcanic islands of Tenerife and El Hierro (Canary Islands). The calculated differences are then correlated with a series of topographic parameters. The final aim is to investigate the artifacts that might arise from the use of half-space models at volcanic areas due to diverse topographic features (e.g., collapse caldera structures, prominent central edifices, large landslide scars).

  16. Finite Element Analysis of Biot’s Consolidation with a Coupled Nonlinear Flow Model

    Directory of Open Access Journals (Sweden)

    Yue-bao Deng

    2016-01-01

    Full Text Available A nonlinear flow relationship, which assumes that the fluid flow in the soil skeleton obeys the Hansbo non-Darcian flow and that the coefficient of permeability changes with void ratio, was incorporated into Biot’s general consolidation theory for a consolidation simulation of normally consolidated soft ground with or without vertical drains. The governing equations with the coupled nonlinear flow model were presented first for the force equilibrium condition and then for the continuity condition. Based on the weighted residual method, the finite element (FE formulations were then derived, and an existing FE program was modified accordingly to take the nonlinear flow model into consideration. Comparative analyses using established theoretical solutions and numerical solutions were completed, and the results were satisfactory. On this basis, we investigated the effect of the coupled nonlinear flow on consolidation development.

  17. Phase field modeling of brittle fracture for enhanced assumed strain shells at large deformations: formulation and finite element implementation

    Science.gov (United States)

    Reinoso, J.; Paggi, M.; Linder, C.

    2017-02-01

    Fracture of technological thin-walled components can notably limit the performance of their corresponding engineering systems. With the aim of achieving reliable fracture predictions of thin structures, this work presents a new phase field model of brittle fracture for large deformation analysis of shells relying on a mixed enhanced assumed strain (EAS) formulation. The kinematic description of the shell body is constructed according to the solid shell concept. This enables the use of fully three-dimensional constitutive models for the material. The proposed phase field formulation integrates the use of the (EAS) method to alleviate locking pathologies, especially Poisson thickness and volumetric locking. This technique is further combined with the assumed natural strain method to efficiently derive a locking-free solid shell element. On the computational side, a fully coupled monolithic framework is consistently formulated. Specific details regarding the corresponding finite element formulation and the main aspects associated with its implementation in the general purpose packages FEAP and ABAQUS are addressed. Finally, the applicability of the current strategy is demonstrated through several numerical examples involving different loading conditions, and including linear and nonlinear hyperelastic constitutive models.

  18. An Immersed Boundary Finite-Element Solver for Flow-Induced Deformation of Soft Structures with Application in Cardiac Flows

    Science.gov (United States)

    Bhardwaj, Rajneesh; Mittal, Rajat

    2011-11-01

    The modeling of complex biological phenomena such as cardiac mechanics is challenging. It involves complex three dimensional geometries, moving structure boundaries inside the fluid domain and large flow-induced deformations of the structure. We present a fluid-structure interaction solver (FSI) which couples a sharp-interface immersed boundary method for flow simulation with a powerful finite-element based structure dynamics solver. An implicit partitioned (or segregated) approach is implemented to ensure the stability of the solver. We validate the FSI solver with published benchmark for a configuration which involves a thin elastic plate attached to a rigid cylinder. The frequency and amplitude of the oscillations of the plate are in good agreement with published results and non-linear dynamics of the plate and its coupling with the flow field are discussed. The FSI solver is used to understand left-ventricular hemodynamics and flow-induced dynamics of mitral leaflets during early diastolic filling and results from this study are presented.

  19. Phase field modeling of brittle fracture for enhanced assumed strain shells at large deformations: formulation and finite element implementation

    Science.gov (United States)

    Reinoso, J.; Paggi, M.; Linder, C.

    2017-06-01

    Fracture of technological thin-walled components can notably limit the performance of their corresponding engineering systems. With the aim of achieving reliable fracture predictions of thin structures, this work presents a new phase field model of brittle fracture for large deformation analysis of shells relying on a mixed enhanced assumed strain (EAS) formulation. The kinematic description of the shell body is constructed according to the solid shell concept. This enables the use of fully three-dimensional constitutive models for the material. The proposed phase field formulation integrates the use of the (EAS) method to alleviate locking pathologies, especially Poisson thickness and volumetric locking. This technique is further combined with the assumed natural strain method to efficiently derive a locking-free solid shell element. On the computational side, a fully coupled monolithic framework is consistently formulated. Specific details regarding the corresponding finite element formulation and the main aspects associated with its implementation in the general purpose packages FEAP and ABAQUS are addressed. Finally, the applicability of the current strategy is demonstrated through several numerical examples involving different loading conditions, and including linear and nonlinear hyperelastic constitutive models.

  20. Geometrically nonlinear deformation and the emergent behavior of polarons in soft matter.

    Science.gov (United States)

    Li, Xiaobao; Liu, Liping; Sharma, Pradeep

    2015-11-07

    Mechanical strain can alter the electronic structure of both bulk semiconductors as well as nanostructures such as quantum dots. This fact has been extensively researched and exploited for tailoring electronic properties. The strain mediated interaction between the charge carriers and the lattice is interpreted through the so-called deformation potential. In the case of soft materials or nanostructures, such as DNA, the deformation potential leads to the formation of polarons which largely determine the electronic characteristics of DNA and similar polymer entities. In addition, polarons are also speculated to be responsible for the mechanism of quantum actuation in carbon nanotubes. The deformation potential is usually taken to be a linear function of the lattice deformation (U ∼ αε) where α is the deformation potential "constant" that determines the coupling strength and ε is the mechanical strain. In this letter, by carefully accounting for nonlinear geometric deformation that has been hitherto ignored so far in this context, we show that the deformation potential constant is renormalized in a non-trivial manner and is hardly a constant. It varies spatially within the material and with the size of the material. This effect, while negligible for hard materials, is found to be important for soft materials and critically impacts the interpretation of quantities such as polaron size, binding energy, and accordingly, electronic behavior.

  1. Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications.

    Science.gov (United States)

    Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

    2014-05-01

    An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.

  2. Geometrical nonlinear deformation model and its experimental study on bimorph giant magnetostrictive thin film

    Institute of Scientific and Technical Information of China (English)

    Wei LIU; Zhenyuan JIA; Fuji WANG; Yongshun ZHANG; Dongming GUO

    2008-01-01

    The geometrical nonlinearity of a giant magne-tostrictive thin film (GMF) can be clearly detected under the magnetostriction effect. Thus, using geometrical linear elastic theory to describe the strain, stress, and constitutive relationship of GMF is inaccurate. According to nonlinear elastic theory, a nonlinear deformation model of the bimorph GMF is established based on assumptions that the magnetostriction effect is equivalent to the effect of body force loaded on the GMF. With Taylor series method, the numerical solution is deduced. Experiments on TbDyFe/Polyimide (PI)/SmFe and TbDyFe/Cu/SmFe are then conducted to verify the proposed model, respectively. Results indicate that the nonlinear deflection curve model is in good conformity with the experimental data.

  3. Coarse-grained molecular dynamics: Nonlinear finite elements and finite temperature

    Energy Technology Data Exchange (ETDEWEB)

    Rudd, R E; Broughton, J Q

    2005-05-30

    Coarse-grained molecular dynamics (CGMD) is a technique developed as a concurrent multiscale model that couples conventional molecular dynamics (MD) to a more coarse-grained description of the periphery. The coarse-grained regions are modeled on a mesh in a formulation that generalizes conventional finite element modeling (FEM) of continuum elasticity. CGMD is derived solely from the MD model, however, and has no continuum parameters. As a result, it provides a coupling that is smooth and provides control of errors that arise at the coupling between the atomistic and coarse-grained regions. In this article, we elaborate on the formulation of CGMD, describing in detail how CGMD is applied to anharmonic solids and finite temperature simulations. As tests of CGMD, we present in detail the calculation of the phonon spectra for solid argon and tantalum in 3D, demonstrating how CGMD provides a better description of the elastic waves than that provided by FEM. We also present elastic wave scattering calculations that show the elastic wave scattering is more benign in CGMD than FEM. We also discuss the dependence of scattering on the properties of the mesh. We introduce a rigid approximation to CGMD that eliminates internal relaxation, similar to the Quasicontinuum technique, and compare it to the full CGMD.

  4. Simulation of 3D tumor cell growth using nonlinear finite element method.

    Science.gov (United States)

    Dong, Shoubing; Yan, Yannan; Tang, Liqun; Meng, Junping; Jiang, Yi

    2016-01-01

    We propose a novel parallel computing framework for a nonlinear finite element method (FEM)-based cell model and apply it to simulate avascular tumor growth. We derive computation formulas to simplify the simulation and design the basic algorithms. With the increment of the proliferation generations of tumor cells, the FEM elements may become larger and more distorted. Then, we describe a remesh and refinement processing of the distorted or over large finite elements and the parallel implementation based on Message Passing Interface to improve the accuracy and efficiency of the simulation. We demonstrate the feasibility and effectiveness of the FEM model and the parallelization methods in simulations of early tumor growth.

  5. Non-linear spacecraft component parameters identification based on experimental results and finite element modelling

    Science.gov (United States)

    Vismara, S. O.; Ricci, S.; Bellini, M.; Trittoni, L.

    2016-06-01

    The objective of the present paper is to describe a procedure to identify and model the non-linear behaviour of structural elements. The procedure herein applied can be divided into two main steps: the system identification and the finite element model updating. The application of the restoring force surface method as a strategy to characterize and identify localized non-linearities has been investigated. This method, which works in the time domain, has been chosen because it has `built-in' characterization capabilities, it allows a direct non-parametric identification of non-linear single-degree-of-freedom systems and it can easily deal with sine-sweep excitations. Two different application examples are reported. At first, a numerical test case has been carried out to investigate the modelling techniques in the case of non-linear behaviour based on the presence of a free-play in the model. The second example concerns the flap of the Intermediate eXperimental Vehicle that successfully completed its 100-min mission on 11 February 2015. The flap was developed under the responsibility of Thales Alenia Space Italia, the prime contractor, which provided the experimental data needed to accomplish the investigation. The procedure here presented has been applied to the results of modal testing performed on the article. Once the non-linear parameters were identified, they were used to update the finite element model in order to prove its capability of predicting the flap behaviour for different load levels.

  6. Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation

    Energy Technology Data Exchange (ETDEWEB)

    Naei, Mohammad Hassan; Rastgoo, Abbas [University of Tehran, Tehran (Iran, Islamic Republic of); Ebrahimi, Farzad [Faculty of Engineering and Technology, lmam Khomeini International University, Qazvin (Iran, Islamic Republic of)

    2009-08-15

    A theoretical model for geometrically nonlinear vibration analysis of piezoelectrically actuated circular plates made of functionally grade material (FGM) is presented based on Kirchhoff's-Love hypothesis with von-Karman type geometrical large nonlinear deformations. To determine the initial stress state and pre-vibration deformations of the smart plate a nonlinear static problem is solved followed by adding an incremental dynamic state to the pre-vibration state. The derived governing equations of the structure are solved by exact series expansion method combined with perturbation approach. The material properties of the FGM core plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. Control of the FGM plate's nonlinear deflections and natural frequencies using high control voltages is studied and their nonlinear effects are evaluated. Numerical results for FG plates with various mixture of ceramic and metal are presented in dimensionless forms. In a parametric study the emphasis is placed on investigating the effect of varying the applied actuator voltage as well as gradient index of FGM plate on vibration characteristics of the smart structure

  7. An axisymmetrical non-linear finite element model for induction heating in injection molding tools

    DEFF Research Database (Denmark)

    Guerrier, Patrick; Nielsen, Kaspar Kirstein; Menotti, Stefano;

    2016-01-01

    To analyze the heating and cooling phase of an induction heated injection molding tool accurately, the temperature dependent magnetic properties, namely the non-linear B-H curves, need to be accounted for in an induction heating simulation. Hence, a finite element model has been developed...... in to the injection molding tool. The model shows very good agreement with the experimental temperature measurements. It is also shown that the non-linearity can be used without the temperature dependency in some cases, and a proposed method is presented of how to estimate an effective linear permeability to use...

  8. Slope Safety Factor Calculations With Non-Linear Yield Criterion Using Finite Elements

    DEFF Research Database (Denmark)

    Clausen, Johan; Damkilde, Lars

    2006-01-01

    The factor of safety for a slope is calculated with the finite element method using a non-linear yield criterion of the Hoek-Brown type. The parameters of the Hoek-Brown criterion are found from triaxial test data. Parameters of the linear Mohr-Coulomb criterion are calibrated to the same triaxial...... are carried out at much higher stress levels than present in a slope failure, this leads to the conclusion that the use of the non-linear criterion leads to a safer slope design...

  9. Slope Safety Factor Calculations With Non-Linear Yield Criterion Using Finite Elements

    DEFF Research Database (Denmark)

    Clausen, Johan Christian; Damkilde, Lars

    2006-01-01

    The factor of safety for a slope is calculated with the finite element method using a non-linear yield criterion of the Hoek-Brown type. The parameters of the Hoek-Brown criterion are found from triaxial test data. Parameters of the linear Mohr-Coulomb criterion are calibrated to the same triaxial...... are carried out at much higher stress levels than present in a slope failure, this leads to the conclusion that the use of the non-linear criterion leads to a safer slope design....

  10. A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations

    KAUST Repository

    Guermond, Jean-Luc

    2014-01-01

    © 2014 Society for Industrial and Applied Mathematics. This paper proposes an explicit, (at least) second-order, maximum principle satisfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Comput. Methods Appl. Mech. Engrg., 272 (2014), pp. 198-213], a high-order entropy viscosity method, and the Boris-Book-Zalesak flux correction technique. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The formal second-order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems.

  11. Slope Safety Factor Calculations With Non-Linear Yield Criterion Using Finite Elements

    DEFF Research Database (Denmark)

    Clausen, Johan Christian; Damkilde, Lars

    2006-01-01

    The factor of safety for a slope is calculated with the finite element method using a non-linear yield criterion of the Hoek-Brown type. The parameters of the Hoek-Brown criterion are found from triaxial test data. Parameters of the linear Mohr-Coulomb criterion are calibrated to the same triaxial...... are carried out at much higher stress levels than present in a slope failure, this leads to the conclusion that the use of the non-linear criterion leads to a safer slope design....

  12. Slope Safety Factor Calculations With Non-Linear Yield Criterion Using Finite Elements

    DEFF Research Database (Denmark)

    Clausen, Johan; Damkilde, Lars

    2006-01-01

    The factor of safety for a slope is calculated with the finite element method using a non-linear yield criterion of the Hoek-Brown type. The parameters of the Hoek-Brown criterion are found from triaxial test data. Parameters of the linear Mohr-Coulomb criterion are calibrated to the same triaxial...... are carried out at much higher stress levels than present in a slope failure, this leads to the conclusion that the use of the non-linear criterion leads to a safer slope design...

  13. A molecular mechanics approach for analyzing tensile nonlinear deformation behavior of single-walled carbon nanotubes

    Institute of Scientific and Technical Information of China (English)

    Yu Wang; Daining Fang; Ai Kah Soh; Bin Liu

    2007-01-01

    In this paper, by capturing the atomic informa-tion and reflecting the behaviour governed by the nonlin-ear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single-walled carbon nanotubes (SWCNT's) is established to describe the nonlinear stress-strain curve of SWCNT's and to predict both the elastic properties and breaking strain of SWCNT's during tensile deformation. An analysis based on the virtual internal bond (VIB) model proposed by P. Zhang et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an acceptable analytical method for analyzing the mechanical behavior of SWCNT's.

  14. Constrained hierarchical least square nonlinear equation solvers. [for indefinite stiffness and large structural deformations

    Science.gov (United States)

    Padovan, J.; Lackney, J.

    1986-01-01

    The current paper develops a constrained hierarchical least square nonlinear equation solver. The procedure can handle the response behavior of systems which possess indefinite tangent stiffness characteristics. Due to the generality of the scheme, this can be achieved at various hierarchical application levels. For instance, in the case of finite element simulations, various combinations of either degree of freedom, nodal, elemental, substructural, and global level iterations are possible. Overall, this enables a solution methodology which is highly stable and storage efficient. To demonstrate the capability of the constrained hierarchical least square methodology, benchmarking examples are presented which treat structure exhibiting highly nonlinear pre- and postbuckling behavior wherein several indefinite stiffness transitions occur.

  15. Finite deformation analysis of continuum structures with time dependent anisotropic elastic plastic material behavior (LWBR/AWBA Development Program)

    Energy Technology Data Exchange (ETDEWEB)

    Hutula, D.N.

    1980-03-01

    A finite element procedure is presented for finite deformation analysis of continuum structures with time-dependent anisotropic elastic-plastic material behavior. An updated Lagrangian formulation is used to describe the kinematics of deformation. Anisotropic constitutive relations are referred, at each material point, to a set of three mutually orthogonal axes which rotate as a unit with an angular velocity equal to the spin at the point. The time-history of the solution is generated by using a linear incremental procedure with residual force correction, along with an automatic time step control algorithm which chooses time step sizes to control the accuracy and numerical stability of the solution.

  16. Nonlinear tracking in a diffusion process with a Bayesian filter and the finite element method

    DEFF Research Database (Denmark)

    Pedersen, Martin Wæver; Thygesen, Uffe Høgsbro; Madsen, Henrik

    2011-01-01

    A new approach to nonlinear state estimation and object tracking from indirect observations of a continuous time process is examined. Stochastic differential equations (SDEs) are employed to model the dynamics of the unobservable state. Tracking problems in the plane subject to boundaries...... become complicated using SMC because Monte Carlo randomness is introduced. The finite element (FE) method solves the Kolmogorov equations of the SDE numerically on a triangular unstructured mesh for which boundary conditions to the state-space are simple to incorporate. The FE approach to nonlinear state...... estimation is suited for off-line data analysis because the computed smoothed state densities, maximum a posteriori parameter estimates and state sequence are deterministic conditional on the finite element mesh and the observations. The proposed method is conceptually similar to existing point...

  17. A Corotational Finite Element Method Combined with Floating Frame Method for Large Steady-State Deformation and Free Vibration Analysis of a Rotating-Inclined Beam

    Directory of Open Access Journals (Sweden)

    Ming Hsu Tsai

    2011-01-01

    Full Text Available A corotational finite element method combined with floating frame method and a numerical procedure is proposed to investigate large steady-state deformation and infinitesimal-free vibrationaround the steady-state deformation of a rotating-inclined Euler beam at constant angular velocity. The element nodal forces are derived using the consistent second-order linearization of the nonlinear beam theory, the d'Alembert principle, and the virtual work principle in a current inertia element coordinates, which is coincident with a rotating element coordinate system constructed at the current configuration of the beam element. The governing equations for linear vibration are obtained by the first-order Taylor series expansion of the equation of motion at the position of steady-state deformation. Numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method and to investigate the steady-state deformation and natural frequency of the rotating beam with different inclined angle, angular velocities, radius of the hub, and slenderness ratios.

  18. Non-linear shape functions over time in the space-time finite element method

    Directory of Open Access Journals (Sweden)

    Kacprzyk Zbigniew

    2017-01-01

    Full Text Available This work presents a generalisation of the space-time finite element method proposed by Kączkowski in his seminal of 1970’s and early 1980’s works. Kączkowski used linear shape functions in time. The recurrence formula obtained by Kączkowski was conditionally stable. In this paper, non-linear shape functions in time are proposed.

  19. Properties of finite difference models of non-linear conservative oscillators

    Science.gov (United States)

    Mickens, R. E.

    1988-01-01

    Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.

  20. Error estimations of mixed finite element methods for nonlinear problems of shallow shell theory

    Science.gov (United States)

    Karchevsky, M.

    2016-11-01

    The variational formulations of problems of equilibrium of a shallow shell in the framework of the geometrically and physically nonlinear theory by boundary conditions of different main types, including non-classical, are considered. Necessary and sufficient conditions for their solvability are derived. Mixed finite element methods for the approximate solutions to these problems based on the use of second derivatives of the bending as auxiliary variables are proposed. Estimations of accuracy of approximate solutions are established.

  1. MULTISTAGE ADAPTIVE HIGHER-ORDER NONLINEAR FINITE IMPULSE RESPONSE FILTERS FOR CHAOTIC TIME SERIES PREDICTIONS

    Institute of Scientific and Technical Information of China (English)

    ZHANG JIA-SHU; XIAO XIAN-CI

    2001-01-01

    A multistage adaptive higher-order nonlinear finite impulse response (MAHONFIR) filter is proposed to predict chaotic time series. Using this approach, we may readily derive the decoupled parallel algorithm for the adaptation of the coefficients of the MAHONFIR filter, to guarantee a more rapid convergence of the adaptive weights to their optimal values. Numerical simulation results show that the MAHONFIR filters proposed here illustrate a very good performance for making an adaptive prediction of chaotic time series.

  2. Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

    KAUST Repository

    Angela Mihai, L.

    2013-03-01

    Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects manifested by specific models. As the finite element method computes uniform deformations exactly, for simple shear deformation and pure shear stress, the Poynting effect is represented exactly, while for the generalised shear and simple torsion, where the deformation is non-uniform, the solution is approximated efficiently and guaranteed computational bounds on the magnitude of the Poynting effect are obtained. The numerical results further indicate that, for a given elastic material, the same sign effect occurs under different shearing mechanisms, showing the genericity of the Poynting effect under a variety of shearing loads. In order to derive numerical models that exhibit either the positive or the negative Poynting effect, the so-called generalised empirical inequalities, which are less restrictive than the usual empirical inequalities involving material parameters, are assumed. © 2012 Elsevier Ltd.

  3. Classes of f-Deformed Landau Operators: Nonlinear Noncommutative Coordinates from Algebraic Representations

    CERN Document Server

    Geloun, Joseph Ben; Hounkonnou, M N

    2008-01-01

    We consider, in a superspace, new operator dependent noncommutative (NC) geometries of the nonlinear quantum Hall limit related to classes of f-deformed Landau operators in the spherical harmonic well. Different NC coordinate algebras are determined using unitary representation spaces of Fock-Heisenberg tensored algebras and of the Schwinger-Fock realisation of the su(1,1) Lie algebra. A reduced model allowing an underlying N=2 superalgebra is also discussed.

  4. Nonlinear deformation and localized failure of bacterial streamers in creeping flows

    Science.gov (United States)

    Biswas, Ishita; Ghosh, Ranajay; Sadrzadeh, Mohtada; Kumar, Aloke

    2016-08-01

    We investigate the failure of bacterial floc mediated streamers in a microfluidic device in a creeping flow regime using both experimental observations and analytical modeling. The quantification of streamer deformation and failure behavior is possible due to the use of 200 nm fluorescent polystyrene beads which firmly embed in the extracellular polymeric substance (EPS) and act as tracers. The streamers, which form soon after the commencement of flow begin to deviate from an apparently quiescent fully formed state in spite of steady background flow and limited mass accretion indicating significant mechanical nonlinearity. This nonlinear behavior shows distinct phases of deformation with mutually different characteristic times and comes to an end with a distinct localized failure of the streamer far from the walls. We investigate this deformation and failure behavior for two separate bacterial strains and develop a simplified but nonlinear analytical model describing the experimentally observed instability phenomena assuming a necking route to instability. Our model leads to a power law relation between the critical strain at failure and the fluid velocity scale exhibiting excellent qualitative and quantitative agreeing with the experimental rupture behavior.

  5. Small-amplitude excitations in a deformable discrete nonlinear Schrödinger equation

    CERN Document Server

    Konotop, V V

    1996-01-01

    A detailed analysis of the small-amplitude solutions of a deformed discrete nonlinear Schrödinger equation is performed. For generic deformations the system possesses "singular" points which split the infinite chain in a number of independent segments. We show that small-amplitude dark solitons in the vicinity of the singular points are described by the Toda-lattice equation while away from the singular points are described by the Korteweg-de Vries equation. Depending on the value of the deformation parameter and of the background level several kinds of solutions are possible. In particular we delimit the regions in the parameter space in which dark solitons are stable in contrast with regions in which bright pulses on nonzero background are possible. On the boundaries of these regions we find that shock waves and rapidly spreading solutions may exist.

  6. Finite time extinction for nonlinear fractional evolution equations and related properties

    Directory of Open Access Journals (Sweden)

    Jesus Ildefonso Diaz

    2016-08-01

    Full Text Available The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time.

  7. Non-linear Vibrations of Deep Cylindrical Shells by the p-Version Finite Element Method

    Directory of Open Access Journals (Sweden)

    Pedro Ribeiro

    2010-01-01

    Full Text Available A p-version shell finite element based on the so-called shallow shell theory is for the first time employed to study vibrations of deep cylindrical shells. The finite element formulation for deep shells is presented and the linear natural frequencies of different shells, with various boundary conditions, are computed. These linear natural frequencies are compared with published results and with results obtained using a commercial software finite element package; good agreement is found. External forces are applied and the displacements in the geometrically non-linear regime computed with the p-model are found to be close to the ones computed using a commercial FE package. In all numerical tests the p-FE model requires far fewer degrees of freedom than the regular FE models. A numerical study on the dynamic behaviour of deep shells is finally carried out.

  8. Distributed robust finite-time nonlinear consensus protocols for multi-agent systems

    Science.gov (United States)

    Zuo, Zongyu; Tie, Lin

    2016-04-01

    This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.

  9. Nonlinear microrheology and molecular imaging to map microscale deformations of entangled DNA networks

    Science.gov (United States)

    Wu, Tsai-Chin; Anderson, Rae

    We use active microrheology coupled to single-molecule fluorescence imaging to elucidate the microscale dynamics of entangled DNA. DNA naturally exists in a wide range of lengths and topologies, and is often confined in cell nucleui, forming highly concentrated and entangled biopolymer networks. Thus, DNA is the model polymer for understanding entangled polymer dynamics as well as the crowded environment of cells. These networks display complex viscoelastic properties that are not well understood, especially at the molecular-level and in response to nonlinear perturbations. Specifically, how microscopic stresses and strains propagate through entangled networks, and what molecular deformations lead to the network stress responses are unknown. To answer these important questions, we optically drive a microsphere through entangled DNA, perturbing the system far from equilibrium, while measuring the resistive force the DNA exerts on the bead during and after bead motion. We simultaneously image single fluorescent-labeled DNA molecules throughout the network to directly link the microscale stress response to molecular deformations. We characterize the deformation of the network from the molecular-level to the mesoscale, and map the stress propagation throughout the network. We further study the impact of DNA length (11 - 115 kbp) and topology (linear vs ring DNA) on deformation and propagation dynamics, exploring key nonlinear features such as tube dilation and power-law relaxation.

  10. A Finite Element Modeling Study on the Fingertip Deformation under Pressure Stimulation

    Directory of Open Access Journals (Sweden)

    Chen Huiling

    2016-01-01

    Full Text Available Pressure stimulus causes skin deformation and tactile sensation on the fingertip. Both theoretical approach and experimental technique may be used to investigate the relationship between the deformation and the sensation. Building an appropriate skin model is the most important step for further theoretical and experimental analysis. In this paper, a two dimensional (2D fingertip biomechanical model employing finite element (FE method is proposed based on the physiological structure of skin. With biomechanical and electrophysiological simulations, the predicted distributions of the strain energy density (SED and the stress/strain are obtained. The relation between the predicted biomechanical responses of the subcutaneous tissue and the discharged rate reported in the literatures are investigated. The results show that the soft tissues of fingertips are very sensitive to the external stimulus, and the spatial distribution characteristics of SED within soft tissues can explain the evoked charging rate of mechanoreceptors effectively. The simulation data of the proposed FE model is highly consistent with the verified data.

  11. Understanding compressive deformation behavior of porous Ti using finite element analysis

    Energy Technology Data Exchange (ETDEWEB)

    Roy, Sandipan; Khutia, Niloy [Department of Aerospace Engineering and Applied Mechanics, Indian Institute of Engineering Science and Technology, Shibpur (India); Das, Debdulal [Department of Metallurgy and Materials Engineering, Indian Institute of Engineering Science and Technology, Shibpur (India); Das, Mitun, E-mail: mitun@cgcri.res.in [Bioceramics and Coating Division, CSIR-Central Glass and Ceramic Research Institute, Kolkata (India); Balla, Vamsi Krishna [Bioceramics and Coating Division, CSIR-Central Glass and Ceramic Research Institute, Kolkata (India); Bandyopadhyay, Amit [W. M. Keck Biomedical Materials Research Laboratory, School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164 (United States); Chowdhury, Amit Roy, E-mail: arcbesu@gmail.com [Department of Aerospace Engineering and Applied Mechanics, Indian Institute of Engineering Science and Technology, Shibpur (India)

    2016-07-01

    In the present study, porous commercially pure (CP) Ti samples with different volume fraction of porosities were fabricated using a commercial additive manufacturing technique namely laser engineered net shaping (LENS™). Mechanical behavior of solid and porous samples was evaluated at room temperature under quasi-static compressive loading. Fracture surfaces of the failed samples were analyzed to determine the failure modes. Finite Element (FE) analysis using representative volume element (RVE) model and micro-computed tomography (CT) based model have been performed to understand the deformation behavior of laser deposited solid and porous CP-Ti samples. In vitro cell culture on laser processed porous CP-Ti surfaces showed normal cell proliferation with time, and confirmed non-toxic nature of these samples. - Highlights: • Porous CP-Ti samples fabricated using additive manufacturing technique • Compressive deformation behavior of porous samples closely matches with micro-CT and RVE based analysis • In vitro studies showed better cell proliferation with time on porous CP-Ti surfaces.

  12. Partial Refactorization in Sparse Matrix Solution: A New Possibility for Faster Nonlinear Finite Element Analysis

    Directory of Open Access Journals (Sweden)

    Qi Song

    2013-01-01

    Full Text Available This paper proposes a partial refactorization for faster nonlinear analysis based on sparse matrix solution, which is nowadays the default solution choice in finite element analysis and can solve finite element models up to millions degrees of freedom. Among various fill-in’s reducing strategies for sparse matrix solution, the graph partition is in general the best in terms of resultant fill-ins and floating-point operations and furthermore produces a particular graph of sparse matrix that prevents local change of entries from wide spreading in factorization. Based on this feature, an explicit partial triangular refactorization with local change is efficiently constructed with limited additional storage requirement in row-sparse storage scheme. The partial refactorization of the changed stiffness matrix inherits a big percentage of the original factor and is carried out only on partial factor entries. The proposed method provides a new possibility for faster nonlinear analysis and is mainly suitable for material nonlinear problems and optimization problems. Compared to full factorization, it can significantly reduce the factorization time and can make nonlinear analysis more efficient.

  13. Linear and nonlinear Stability analysis for finite difference discretizations of higher order Boussinesq equations

    DEFF Research Database (Denmark)

    Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.;

    2004-01-01

    This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly nonlinear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann......) techniques with matrix-based methods for formulations in both one and two horizontal dimensions. The matrix-based method is also extended to show the local de-stabilizing effects of the nonlinear terms, as well as the stabilizing effects of numerical dissipation. A comparison of the relative stability...... moderately non-normal, suggesting that the eigenvalues are likely suitable for analysis purposes. Numerical experiments demonstrate excellent agreement with the linear analysis, and good qualitative agreement with the local nonlinear analysis. The various methods of analysis combine to provide significant...

  14. A SIMPLE FINITE ELEMENT FOR NON-LINEAR ANALYSIS OF COMPOSITE PLATES

    Directory of Open Access Journals (Sweden)

    V.B. Tungikar

    2011-06-01

    Full Text Available Finite Element Analysis for geometrically nonlinear behaviour of laminated composite plates is presented andcompared with the reported investigations. However structural non-linearity is encountered in certain cases andneeds attention. A higher order displacement field that accounts for transverse shear effects under geometricnonlinear condition is employed in the formulation of a four node, rectangular, element with thirteen degrees offreedom per node. First order Zigzag terms have been included in displacement field for improvement in theresponse. Von Karman strain approach is considered in the present analysis. Incremental Pica iterative scheme isused to solve resulting nonlinear equilibrium equations. The formulation demonstrates its excellence in theperformance for predicting response at various lay ups and plies conditions.

  15. Bounds on the recoverable deformations of polycrystalline SMAs at finite strain

    Directory of Open Access Journals (Sweden)

    Peigney Michaël

    2015-01-01

    Full Text Available This communication is concerned with the theoretical prediction of the recoverable strains (i.e. the strains that can be recovered by the shape memory effect in polycrystalline SMAs. The analysis is carried out in the finite strain setting, considering a nonlinear elasticity model of phase transformation. The main results are some rigorous upper bounds on the set of recoverable strains. Those bounds depend on the polycrystalline texture through the volume fractions of the different orientations. A two-orientation polycrystal of tetragonal martensite is studied as an illustration. In that case, analytical expressions of the upper bounds are derived and the results are compared with lower bounds obtained by considering laminate textures. The issue of applying the proposed method to complex polycrystalline textures is commented on.

  16. Crystal plasticity finite element analysis of deformation behaviour in SAC305 solder joint

    Science.gov (United States)

    Darbandi, Payam

    Due to the awareness of the potential health hazards associated with the toxicity of lead (Pb), actions have been taken to eliminate or reduce the use of Pb in consumer products. Among those, tin (Sn) solders have been used for the assembly of electronic systems. Anisotropy is of significant importance in all structural metals, but this characteristic is unusually strong in Sn, making Sn based solder joints one of the best examples of the influence of anisotropy. The effect of anisotropy arising from the crystal structure of tin and large grain microstructure on the microstructure and the evolution of constitutive responses of microscale SAC305 solder joints is investigated. Insights into the effects of key microstructural features and dominant plastic deformation mechanisms influencing the measured relative activity of slip systems in SAC305 are obtained from a combination of optical microscopy, orientation imaging microscopy (OIM), slip plane trace analysis and crystal plasticity finite element (CPFE) modeling. Package level SAC305 specimens were subjected to shear deformation in sequential steps and characterized using optical microscopy and OIM to identify the activity of slip systems. X-ray micro Laue diffraction and high energy monochromatic X-ray beam were employed to characterize the joint scale tensile samples to provide necessary information to be able to compare and validate the CPFE model. A CPFE model was developed that can account for relative ease of activating slip systems in SAC305 solder based upon the statistical estimation based on correlation between the critical resolved shear stress and the probability of activating various slip systems. The results from simulations show that the CPFE model developed using the statistical analysis of activity of slip system not only can satisfy the requirements associated with kinematic of plastic deformation in crystal coordinate systems (activity of slip systems) and global coordinate system (shape changes

  17. Non-linear mass-spring system for large soft tissue deformations modeling

    CERN Document Server

    Nikolaev, Sergei

    2014-01-01

    Implant placement under soft tissues operation is described. In this operation tissues can reach such deformations that nonlinear properties are appeared. A mass-spring model modification for modeling nonlinear tissue operation is developed. A method for creating elasticity module using splines is described. For Poisson ratio different stiffness for different types of springs in cubic grid is used. For stiffness finding an equation system that described material tension is solved. The model is verified with quadratic sample tension experiment. These tests show that sample tension under external forces is equal to defined nonlinear elasticity module. The accuracy of Poisson ratio modeling is thirty five percent that is better the results of available ratio modeling method.

  18. Extending geometric conservation law to cell-centered finite difference methods on moving and deforming grids

    Science.gov (United States)

    Liao, Fei; Ye, Zhengyin

    2015-12-01

    Despite significant progress in recent computational techniques, the accurate numerical simulations, such as direct-numerical simulation and large-eddy simulation, are still challenging. For accurate calculations, the high-order finite difference method (FDM) is usually adopted with coordinate transformation from body-fitted grid to Cartesian grid. But this transformation might lead to failure in freestream preservation with the geometric conservation law (GCL) violated, particularly in high-order computations. GCL identities, including surface conservation law (SCL) and volume conservation law (VCL), are very important in discretization of high-order FDM. To satisfy GCL, various efforts have been made. An early and successful approach was developed by Thomas and Lombard [6] who used the conservative form of metrics to cancel out metric terms to further satisfy SCL. Visbal and Gaitonde [7] adopted this conservative form of metrics for SCL identities and satisfied VCL identity through invoking VCL equation to acquire the derivative of Jacobian in computation on moving and deforming grids with central compact schemes derived by Lele [5]. Later, using the metric technique from Visbal and Gaitonde [7], Nonomura et al. [8] investigated the freestream and vortex preservation properties of high-order WENO and WCNS on stationary curvilinear grids. A conservative metric method (CMM) was further developed by Deng et al. [9] with stationary grids, and detailed discussion about the innermost difference operator of CMM was shown with proof and corresponding numerical test cases. Noticing that metrics of CMM is asymmetrical without coordinate-invariant property, Deng et al. proposed a symmetrical CMM (SCMM) [12] by using the symmetric forms of metrics derived by Vinokur and Yee [10] to further eliminate asymmetric metric errors with stationary grids considered only. The research from Abe et al. [11] presented new asymmetric and symmetric conservative forms of time metrics and

  19. A TVD-WAF-based hybrid finite volume and finite difference scheme for nonlinearly dispersive wave equations

    Directory of Open Access Journals (Sweden)

    Jing Yin

    2015-07-01

    Full Text Available A total variation diminishing-weighted average flux (TVD-WAF-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer (HLL Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourth-order monotone upstream-centered scheme for conservation laws (MUSCL. The time marching scheme based on the third-order TVD Runge-Kutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.

  20. Robust finite-time event-triggered H∞ boundedness for network-based Markovian jump nonlinear systems.

    Science.gov (United States)

    Zhang, Honglu; Cheng, Jun; Wang, Hailing; Chen, Yiping; Xiang, Huili

    2016-07-01

    This paper investigates the problem of finite-time event-triggered H∞ boundedness for network-based Markovian jump nonlinear system. An improved model is introduced in terms of network-induced delay. By synthesizing the newly event-triggering conditions, the finite-time H∞ boundedness for networked Markovian jump nonlinear systems are guaranteed. At last, a numerical example is given to illustrate the effectiveness of proposed theoretical results.

  1. Analysis of third harmonic generation and four wave mixing in gold nanostructures by nonlinear finite difference time domain.

    Science.gov (United States)

    Sasanpour, Pezhman; Shahmansouri, Afsaneh; Rashidian, Bizhan

    2010-11-01

    Third order nonlinear effects and its enhancement in gold nanostructures has been numerically studied. Analysis method is based on computationally solving nonlinear Maxwell's equations, considering dispersion behavior of permittivity described by Drude model and third order nonlinear susceptibility. Simulation is done by method of nonlinear finite difference time domain method, in which nonlinear equations of electric field are solved by Newton-Raphshon method. As the main outcomes of third order nonlinear susceptibility, four wave mixing and third harmonic generation terms are produced around gold nanostructures. Results of analysis on different geometries and structures show that third order nonlinearity products are more enhanced in places where electric field enhancement is occurred due to surface plasmons. Results indicates that enhancement of nonlinearities is strongly occurred in structures whose interface is dielectric. According to analysis results, nonlinear effects are highly concentrated in the vicinity of nanostructures. Hence this approach can be used in applications where localized ultraviolet light is required.

  2. A Fully-Coupled, Fully-Implicit, Finite Element Model for Solving Multiphase Fluid Flow, Heat Transport and Rock Deformation in Enhanced Geothermal Systems

    Science.gov (United States)

    Lu, C.; Deng, S.; Podgorney, R. K.; Huang, H.

    2011-12-01

    Reliable reservoir performance predictions of enhanced geothermal reservoir systems require accurate and robust modeling for the coupled thermal-hydrological-mechanical processes. Conventionally, in order to reduce computational cost, these types of problems are solved using operator splitting method, usually by sequentially coupling a subsurface flow and heat transport simulator with a solid mechanics simulator via input files. However, such operator splitting approaches are applicable only to loosely coupled problems and usually converge slowly. As in most enhanced geothermal systems (EGS), fluid flow, heat transport, and rock deformation are typically strongly nonlinearly coupled, an alternative is to solve the system of nonlinear partial differential equations that govern the system simultaneously using a fully coupled solution procedure for fluid flow, heat transport, and solid mechanics. This procedure solves for all solution variables (fluid pressure, temperature and rock displacement fields) simultaneously, which leads to one large nonlinear algebraic system that needs to be solved by a strongly convergent nonlinear solver. Development over the past 10 years in the area of physics-based conditioning, strongly convergent nonlinear solvers (such as Jacobian Free Newton methods) and efficient linear solvers (such as GMRES, AMG), makes such an approach competitive. In this presentation, we will introduce a continuum-scaled parallel physics-based, fully coupled, modeling tool for predicting the dynamics of fracture initiation and propagation, fluid flow, rock deformation, and heat transport in a single integrated code named FALCON (Fracturing And Liquid-steam CONvection). FALCON is built upon a parallel computing framework developed at Idaho National Laboratory (INL) for solving coupled systems of nonlinear equations with finite element method with unstructured and adaptively refined/coarsened grids. Currently, FALCON contains poro- and thermal- elastic models

  3. Experimental Validation of Two-dimensional Finite Element Method for Simulating Constitutive Response of Polycrystals During High Temperature Plastic Deformation

    Science.gov (United States)

    Agarwal, Sumit; Briant, Clyde L.; Krajewski, Paul E.; Bower, Allan F.; Taleff, Eric M.

    2007-04-01

    A finite element method was recently designed to model the mechanisms that cause superplastic deformation (A.F. Bower and E. Wininger, A Two-Dimensional Finite Element Method for Simulating the Constitutive Response and Microstructure of Polycrystals during High-Temperature Plastic Deformation, J. Mech. Phys. Solids, 2004, 52, p 1289-1317). The computations idealize the solid as a collection of two-dimensional grains, separated by sharp grain boundaries. The grains may deform plastically by thermally activated dislocation motion, which is modeled using a conventional crystal plasticity law. The solid may also deform by sliding on the grain boundaries, or by stress-driven diffusion of atoms along grain boundaries. The governing equations are solved using a finite element method, which includes a front-tracking procedure to monitor the evolution of the grain boundaries and surfaces in the solid. The goal of this article is to validate these computations by systematically comparing numerical predictions to experimental measurements of the elevated-temperature response of aluminum alloy AA5083 (M.-A. Kulas, W.P. Green, E.M. Taleff, P.E. Krajewski, and T.R. McNelley, Deformation Mechanisms in Superplastic AA5083 materials. Metall. Mater. Trans. A, 2005, 36(5), p 1249-1261). The experimental work revealed that a transition occurs from grain-boundary sliding to dislocation (solute-drag) creep at approximately 0.001/s for temperatures between 425 and 500 °C. In addition, increasing the grain size from 7 to 10 μm decreased the transition to significantly lower strain rates. Predictions from the finite element method accurately predict the effect of grain size on the transition in deformation mechanisms.

  4. Finite-dimensional constrained fuzzy control for a class of nonlinear distributed process systems.

    Science.gov (United States)

    Wu, Huai-Ning; Li, Han-Xiong

    2007-10-01

    This correspondence studies the problem of finite-dimensional constrained fuzzy control for a class of systems described by nonlinear parabolic partial differential equations (PDEs). Initially, Galerkin's method is applied to the PDE system to derive a nonlinear ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, a systematic modeling procedure is given to construct exactly a Takagi-Sugeno (T-S) fuzzy model for the finite-dimensional ODE system under state constraints. Then, based on the T-S fuzzy model, a sufficient condition for the existence of a stabilizing fuzzy controller is derived, which guarantees that the state constraints are satisfied and provides an upper bound on the quadratic performance function for the finite-dimensional slow system. The resulting fuzzy controllers can also guarantee the exponential stability of the closed-loop PDE system. Moreover, a local optimization algorithm based on the linear matrix inequalities is proposed to compute the feedback gain matrices of a suboptimal fuzzy controller in the sense of minimizing the quadratic performance bound. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.

  5. Direct method of solving finite difference nonlinear equations for multicomponent diffusion in a gas centrifuge

    Energy Technology Data Exchange (ETDEWEB)

    Potemki, Valeri G. [Moscow State Engineering Physics Institute (Technical University), Moscow (Russian Federation). Dept. of Automatics and Electronics; Borisevich, Valentine D.; Yupatov, Sergei V. [Moscow State Enineering Physics Institute (Technical University), Moscow (Russian Federation). Dept. of Technical Physics

    1996-12-31

    This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner`s basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker`s form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author) 7 refs., 10 figs.

  6. A Finite Mixture of Nonlinear Random Coefficient Models for Continuous Repeated Measures Data.

    Science.gov (United States)

    Kohli, Nidhi; Harring, Jeffrey R; Zopluoglu, Cengiz

    2016-09-01

    Nonlinear random coefficient models (NRCMs) for continuous longitudinal data are often used for examining individual behaviors that display nonlinear patterns of development (or growth) over time in measured variables. As an extension of this model, this study considers the finite mixture of NRCMs that combine features of NRCMs with the idea of finite mixture (or latent class) models. The efficacy of this model is that it allows the integration of intrinsically nonlinear functions where the data come from a mixture of two or more unobserved subpopulations, thus allowing the simultaneous investigation of intra-individual (within-person) variability, inter-individual (between-person) variability, and subpopulation heterogeneity. Effectiveness of this model to work under real data analytic conditions was examined by executing a Monte Carlo simulation study. The simulation study was carried out using an R routine specifically developed for the purpose of this study. The R routine used maximum likelihood with the expectation-maximization algorithm. The design of the study mimicked the output obtained from running a two-class mixture model on task completion data.

  7. A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis

    Science.gov (United States)

    Jokhio, G. A.; Izzuddin, B. A.

    2015-05-01

    This article presents a new domain decomposition method for nonlinear finite element analysis introducing the concept of dual partition super-elements. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realized by replacing one or more subdomains in a "parent system," each with a placeholder super-element, where the subdomains are processed separately as "child partitions," each wrapped by a dual super-element along the partition boundary. The analysis of the overall system, including the satisfaction of equilibrium and compatibility at all partition boundaries, is realized through direct communication between all pairs of placeholder and dual super-elements. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing finite element analysis programs to achieve parallelization on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of large-scale problems. Several examples are presented in this article which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.

  8. Ground Deformation At Uturuncu Volcano, Bolivia: Insights From Finite Element Analysis

    Science.gov (United States)

    Hickey, J.; Gottsmann, J.; del Potro, R.

    2011-12-01

    This study focuses on a Finite Element Analysis of large-scale ground deformation at Uturuncu volcano in the Altiplano-Puna region of southern Bolivia, for the period 19th May 1996 to 24th December 2000. The amplitude of the line-of-sight displacement from InSAR is 7.4 cm, with a wavelength of around 80 km for that period. We present a series of forward models that explain the observed ground displacement using COMSOL Multiphysics and accounting for both homogeneous and heterogeneous crustal mechanics. The source geometry is approximated using spherical, prolate and oblate source shapes. Crustal heterogeneity is constrained by published seismic velocity profiles that indicate the presence of a large low-velocity body at depths of 17 km below the surface. We deduce that the observed uplift is best explained by a single prolate source, in an heterogeneous medium, centred between 16.1 and 18.9 km below local elevation, with a semi-major axis of 5.2 - 9.8 km, semi-minor axes of 2.9 - 5.5 km and a uniform pressure change of between 5.6 and 29.1 MPa, as determined by bootstrapping of the best-fitting models at 90% confidence. This model can be interpreted to reflect pressurisation, at very modest levels, of a magma chamber within the Altiplano-Puna Magma Body. Further efforts to explore the sensitivity of the model fits to the required source excess pressures are obtained by first-order approximations of varying Poisson ratio with depth, host rock viscoelasticity and source multiplicity. We find that such mechanisms play a primary role in explaining the observed deformation at Uturuncu. However, to further constrain the most likely causative source parameters the full three-dimensional displacement field is required.

  9. Neural Network Based Finite-Time Stabilization for Discrete-Time Markov Jump Nonlinear Systems with Time Delays

    Directory of Open Access Journals (Sweden)

    Fei Chen

    2013-01-01

    Full Text Available This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.

  10. Extension of non-linear beam models with deformable cross sections

    Science.gov (United States)

    Sokolov, I.; Krylov, S.; Harari, I.

    2015-12-01

    Geometrically exact beam theory is extended to allow distortion of the cross section. We present an appropriate set of cross-section basis functions and provide physical insight to the cross-sectional distortion from linear elastostatics. The beam formulation in terms of material (back-rotated) beam internal force resultants and work-conjugate kinematic quantities emerges naturally from the material description of virtual work of constrained finite elasticity. The inclusion of cross-sectional deformation allows straightforward application of three-dimensional constitutive laws in the beam formulation. Beam counterparts of applied loads are expressed in terms of the original three-dimensional data. Special attention is paid to the treatment of the applied stress, keeping in mind applications such as hydrogel actuators under environmental stimuli or devices made of electroactive polymers. Numerical comparisons show the ability of the beam model to reproduce finite elasticity results with good efficiency.

  11. Finite-time synchronization for second-order nonlinear multi-agent system via pinning exponent sliding mode control.

    Science.gov (United States)

    Hou, Huazhou; Zhang, Qingling

    2016-11-01

    In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method.

  12. Finite element analysis of planar twist channel angular extrusion (PTCAE) as a novel severe plastic deformation method

    Energy Technology Data Exchange (ETDEWEB)

    Shokuhfar, Ali; Shamsborhan, Mahmoud [K. N. Toosi University of Technology, Tehran (Iran, Islamic Republic of)

    2014-05-15

    A new severe plastic deformation (SPD) method based on equal channel angular pressing (ECAP) is introduced for producing ultrafine grains in bulk alloys, entitled as 'Planar twist channel angular extrusion (PTCAE)'. In PTCAE method, there is additional angle, α, (plus φ and ψ angles in ECAP method) which represents angle associated with the lateral reversal arc of curvature in deformation zone. Three dimensional finite element method (FEM) simulations of both ECAP and PTCAE processes were performed in order to investigate the plastic deformation state of processed samples and, moreover, the effect of different die geometry (in terms of variation of planar twist angle) on plastic strain distribution and magnitude. Results revealed that PTCAE process related with ECAP process can impose higher strain values in different shear planes simultaneously in one deformation zone. Therefore, PTCAE can produce UFG or nanostructured materials better than ECAP method which has simpler design and significantly higher efficiency compared with other new SPD processes.

  13. What's causing the world's largest deformation anomaly in southern Bolivia? Insights from Finite Element Analysis

    Science.gov (United States)

    Hickey, J.; Gottsmann, J.; del Potro, R.

    2012-04-01

    This study focuses on a Finite Element Analysis of the world's largest recorded ground deformation anomaly in the Altiplano-Puna region of southern Bolivia. We present a series of forward models to construe the 70 km wide ground displacement field identified by satellite geodesy between 1996 and 2000, with a mean inflation rate of ~1.5 cm/yr, centered at Uturuncu volcano. The causative pressure sources simulated in the models have spherical, prolate and oblate shapes and the resulting stresses are solved numerically, accounting for both homogeneous and heterogeneous mechanical rock properties, as well as elastic and time-dependent rheologies and source multiplicity. Crustal heterogeneity is constrained by published seismic velocity profiles that indicate the presence of a large low-velocity region, the Altiplano-Puna Magma Body (APMB), at depths less than roughly 17 km below the surface. For the case of crustal elasticity, we find that the observed uplift is best explained by a single prolate source, in a mechanically heterogeneous medium, centered between 16.1 and 18.9 km below local elevation, with a semi-major axis of 5.2 - 9.8 km, semi-minor axes of 2.9 - 5.5 km and a uniform pressure change of between 5.6 and 29.1 MPa, as determined by bootstrapping of the best-fitting models at 90% confidence. We then further explore the sensitivity of the model fits by first-order approximations of varying Poisson ratio with depth, crustal viscoelasticity and source multiplicity, to account for a wider range of conditions at upper crustal levels in the Altiplano-Puna region. We find that such mechanisms play a primary role in explaining the observed deformation at Uturuncu. Both crustal viscoelasticity and source multiplicity reduce the pressure requirement of a source while maintaining the same amplitude of deformation. But in particular, the presence of a mechanically soft layer at source depths, such as the APMB, significantly alters surface displacement patterns.

  14. Neural network solution for finite-horizon H-infinity constrained optimal control of nonlinear systems

    Institute of Scientific and Technical Information of China (English)

    Tao CHENG; Frank L.LEWIS

    2007-01-01

    In this paper,neural networks are used to approximately solve the finite-horizon constrained input H-infiniy state feedback control problem.The method is based on solving a related Hamilton-Jacobi-Isaacs equation of the corresponding finite-horizon zero-sum game.The game value function is approximated by a neural network wlth timevarying weights.It is shown that the neural network approximation converges uniformly to the game-value function and the resulting almost optimal constrained feedback controller provides closed-loop stability and bounded L2 gain.The result is an almost optimal H-infinity feedback controller with time-varying coefficients that is solved a priori off-line.The effectiveness of the method is shown on the Rotational/Translational Actuator benchmark nonlinear control problem.

  15. Input-output finite-time stabilisation of nonlinear stochastic system with missing measurements

    Science.gov (United States)

    Song, Jun; Niu, Yugang; Jia, Tinggang

    2016-09-01

    This paper considers the problem of the input-output finite-time stabilisation for a class of nonlinear stochastic system with state-dependent noise. The phenomenon of the missing measurements may occur when state signals are transmitted via communication networks. An estimating method is proposed to compensate the lost state information. And then, a compensator-based controller is designed to ensure the input-output finite-time stochastic stability (IO-FTSS) of the closed-loop system. Some parameters-dependent sufficient conditions are derived and the corresponding solving approach is given. Finally, numerical simulations are provided to demonstrate the feasibility and effectiveness of the developed IO-FTSS scheme.

  16. A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation

    Energy Technology Data Exchange (ETDEWEB)

    Banks, J W; Hittinger, J A

    2009-11-24

    Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.

  17. A nonlinear deformed su(2) algebra with a two-colour quasitriangular Hopf structure

    CERN Document Server

    Bonatsos, Dennis; Kolokotronis, P; Ludu, A; Quesne, C

    1996-01-01

    Nonlinear deformations of the enveloping algebra of su(2), involving two arbitrary functions of J_0 and generalizing the Witten algebra, were introduced some time ago by Delbecq and Quesne. In the present paper, the problem of endowing some of them with a Hopf algebraic structure is addressed by studying in detail a specific example, referred to as ${\\cal A}^+_q(1)$. This algebra is shown to possess two series of (N+1)-dimensional unitary irreducible representations, where N=0, 1, 2, .... To allow the coupling of any two such representations, a generalization of the standard Hopf axioms is proposed by proceeding in two steps. In the first one, a variant and extension of the deforming functional technique is introduced: variant because a map between two deformed algebras, su_q(2) and ${\\cal A}^+_q(1)$, is considered instead of a map between a Lie algebra and a deformed one, and extension because use is made of a two-valued functional, whose inverse is singular. As a result, the Hopf structure of su_q(2) is car...

  18. Nonlinear damping of a finite amplitude whistler wave due to modified two stream instability

    Energy Technology Data Exchange (ETDEWEB)

    Saito, Shinji, E-mail: saito@stelab.nagoya-u.ac.jp [Graduate School of Science, Nagoya University, Nagoya (Japan); Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya (Japan); Nariyuki, Yasuhiro, E-mail: nariyuki@edu.u-toyama.ac.jp [Faculty of Human Development, University of Toyama, Toyama (Japan); Umeda, Takayuki, E-mail: umeda@stelab.nagoya-u.ac.jp [Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya (Japan)

    2015-07-15

    A two-dimensional, fully kinetic, particle-in-cell simulation is used to investigate the nonlinear development of a parallel propagating finite amplitude whistler wave (parent wave) with a wavelength longer than an ion inertial length. The cross field current of the parent wave generates short-scale whistler waves propagating highly oblique directions to the ambient magnetic field through the modified two-stream instability (MTSI) which scatters electrons and ions parallel and perpendicular to the magnetic field, respectively. The parent wave is largely damped during a time comparable to the wave period. The MTSI-driven damping process is proposed as a cause of nonlinear dissipation of kinetic turbulence in the solar wind.

  19. Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term

    Directory of Open Access Journals (Sweden)

    Y. J. Choi

    2012-01-01

    Full Text Available We consider finite element Galerkin solutions for the space fractional diffusion equation with a nonlinear source term. Existence, stability, and order of convergence of approximate solutions for the backward Euler fully discrete scheme have been discussed as well as for the semidiscrete scheme. The analytical convergent orders are obtained as O(k+hγ˜, where γ˜ is a constant depending on the order of fractional derivative. Numerical computations are presented, which confirm the theoretical results when the equation has a linear source term. When the equation has a nonlinear source term, numerical results show that the diffusivity depends on the order of fractional derivative as we expect.

  20. Solution of nonlinear finite difference ocean models by optimization methods with sensitivity and observational strategy analysis

    Science.gov (United States)

    Schroeter, Jens; Wunsch, Carl

    1986-01-01

    The paper studies with finite difference nonlinear circulation models the uncertainties in interesting flow properties, such as western boundary current transport, potential and kinetic energy, owing to the uncertainty in the driving surface boundary condition. The procedure is based upon nonlinear optimization methods. The same calculations permit quantitative study of the importance of new information as a function of type, region of measurement and accuracy, providing a method to study various observing strategies. Uncertainty in a model parameter, the bottom friction coefficient, is studied in conjunction with uncertain measurements. The model is free to adjust the bottom friction coefficient such that an objective function is minimized while fitting a set of data to within prescribed bounds. The relative importance of the accuracy of the knowledge about the friction coefficient with respect to various kinds of observations is then quantified, and the possible range of the friction coefficients is calculated.

  1. NONLINEAR ANALYSIS OF CFRP- PRESTRESSED CONCRETE BEAMS SUBJECTED TO INCREMENTAL STATIC LOADING BY FINITE ELEMENTS

    Directory of Open Access Journals (Sweden)

    Husain M. Husain

    2013-05-01

    Full Text Available In this work a program is developed to carry out the nonlinear analysis (material nonlinearity of prestressed concrete beams using tendons of carbon fiber reinforced polymer (CFRP instead of steel. The properties of this material include high strength, light weight, and insusceptibility to corrosion and magnetism. This material is still under investigation, therefore it needs continuous work to make it beneficial in concrete design. Four beams which are tested experimentally by Yan et al. are examined by the developed computer program to reach a certain analytical approach of the design and analysis of such beams because there is no available restrictions or recommendations covering this material in the codes. The program uses the finite element analysis by dividing the beams into isoparametric 20-noded brick elements. The results obtained are good in comparison with experimental results.

  2. Nonlinear constitutive law for ferroelectric/ ferroelastic material and its finite element realization

    Institute of Scientific and Technical Information of China (English)

    LI YaoChen

    2007-01-01

    The hysteresis phenomena of ferroelectric/ferroelastic material in polarization procedure are investigated.Some assumptions are presented based on the published experimental data.The electrical yielding criterion,mechanical yielding criterion and isotropic hardening model are established.The flow theory in incremental forms in polarization procedure is presented.The nonlinear constitutive law for electrical-mechanical coupling is proposed phenomenologically.Finally,the nonlinear constitutive law expressed in a form of matrices and vectors,which is immediately associated with finite element analysis,is formulated.In the example problem of a rectangular specimen subjected to a uniaxial electric field,the procedure from virgin state to fully polarized state is simulated.Afterward,a uniaxial compressive loading is applied to depolarizing the specimen.Results are in agreement with the experimental data.

  3. Propagation dynamics of finite-energy Airy beams in nonlocal nonlinear media

    Science.gov (United States)

    Wu, Zhen-Kun; Li, Peng; Gu, Yu-Zong

    2017-10-01

    We investigate periodic inversion and phase transition of normal and displaced finite-energy Airy beams propagating in nonlocal nonlinear media with the split-step Fourier method. Numerical simulation results show that parameters such as the degree of nonlocality and amplitude have profound effects on the intensity distribution of the period of an Airy beam. Nonlocal nonlinear media will reduce into a harmonic potential if the nonlocality is strong enough, which results in the beam fluctuating in an approximately cosine mode. The beam profile changes from an Airy profile to a Gaussian one at a critical point, and during propagation the process repeats to form an unusual oscillation. We also briefly discus the two-dimensional case, being equivalent to a product of two one-dimensional cases.

  4. Nonlinear constitutive law for ferroelectric/ferroelastic material and its finite element realization

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The hysteresis phenomena of ferroelectric/ferroelastic material in polarization procedure are investigated. Some assumptions are presented based on the published experimental data. The electrical yielding criterion, mechanical yielding criterion and isotropic hardening model are established. The flow theory in incremental forms in polarization procedure is presented. The nonlinear constitutive law for electrical-mechanical coupling is proposed phenomenologically. Finally, the nonlinear constitutive law expressed in a form of matrices and vectors, which is immediately associated with finite element analysis, is formulated. In the example problem of a rectangular specimen subjected to a uniaxial electric field, the procedure from virgin state to fully polarized state is simulated. Afterward, a uniaxial compressive loading is applied to depolarizing the specimen. Results are in agreement with the experimental data.

  5. On the development of hierarchical solution strategies for nonlinear finite element formulations

    Science.gov (United States)

    Padovan, J.; Lackney, J.

    1984-01-01

    This paper develops a hierarchical type solution scheme which can handle the field equations associated with nonlinear finite element simulations. The overall procedure possesses various levels of application namely degree of freedom, nodal, elemental, substructural as well as global. In particular iteration, updating, assembly and solution control occurs at the various hierarchical levels. Due to the manner of formulation, the degree of matrix inversion depends on the size of the various hierarchical partitioned groups. In this context, degree of freedom partitioning requires no inversion. To benchmark the overall scheme, the results of several numerical examples are presented.

  6. High-order Finite Difference Solution of Euler Equations for Nonlinear Water Waves

    DEFF Research Database (Denmark)

    Christiansen, Torben Robert Bilgrav; Bingham, Harry B.; Engsig-Karup, Allan Peter

    2012-01-01

    The incompressible Euler equations are solved with a free surface, the position of which is captured by applying an Eulerian kinematic boundary condition. The solution strategy follows that of [1, 2], applying a coordinate-transformation to obtain a time-constant spatial computational domain which...... with a two-dimensional implementation of the model are compared with highly accurate stream function solutions to the nonlinear wave problem, which show the approximately expected convergence rates and a clear advantage of using high-order finite difference schemes in combination with the Euler equations....

  7. Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains

    Science.gov (United States)

    Yang, Z.; Yuan, Z.; Nie, Y.; Wang, J.; Zhu, X.; Liu, F.

    2017-02-01

    In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully discrete scheme to solve Riesz space fractional diffusion equations. Our breakthrough is developing an algorithm to form stiffness matrix on unstructured triangular meshes, which can help us to deal with space fractional terms on any convex domain. The stability and convergence of the scheme are also discussed. Numerical examples are given to verify accuracy and stability of our scheme.

  8. Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

    Science.gov (United States)

    Jameson, A.

    1976-01-01

    A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

  9. ALE Fractional Step Finite Element Method for Fluid-Structure Nonlinear Interaction Problem

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.

  10. Solution of Nonlinear Coupled Heat and Moisture Transport Using Finite Element Method

    Directory of Open Access Journals (Sweden)

    T. Krejčí

    2004-01-01

    Full Text Available This paper deals with a numerical solution of coupled of heat and moisture transfer using the finite element method. The mathematical model consists of balance equations of mass, energy and linear momentum and of the appropriate constitutive equations. The chosen macroscopic field variables are temperature, capillary pressures, gas pressure and displacement. In contrast with pure mechanical problems, there are several difficulties which require special attention. Systems of algebraic equations arising from coupled problems are generally nonlinear, and the matrices of such systems are nonsymmetric and indefinite. The first experiences of solving complicated coupled problems are mentioned in this paper. 

  11. Finite difference schemes for a nonlinear black-scholes model with transaction cost and volatility risk

    DEFF Research Database (Denmark)

    Mashayekhi, Sima; Hugger, Jens

    2015-01-01

    Several nonlinear Black-Scholes models have been proposed to take transaction cost, large investor performance and illiquid markets into account. One of the most comprehensive models introduced by Barles and Soner in [4] considers transaction cost in the hedging strategy and risk from an illiquid...... market. In this paper, we compare several finite difference methods for the solution of this model with respect to precision and order of convergence within a computationally feasible domain allowing at most 200 space steps and 10000 time steps. We conclude that standard explicit Euler comes out...

  12. Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity.

    Science.gov (United States)

    Merhasin, Ilya M; Gisin, Boris V; Driben, Rodislav; Malomed, Boris A

    2005-01-01

    We present a model combining a periodic array of rectangular potential wells [the Kronig-Penney (KP) potential] and the cubic-quintic (CQ) nonlinearity. A plethora of soliton states is found in the system: fundamental single-humped solitons, symmetric and antisymmetric double-humped ones, three-peak solitons with and without the phase shift pi between the peaks, etc. If the potential profile is shallow, the solitons belong to the semi-infinite gap beneath the band structure of the linear KP model, while finite gaps between the Bloch bands remain empty. However, in contrast with the situation known in the model combining a periodic potential and the self-focusing Kerr nonlinearity, the solitons fill only a finite zone near the top of the semi-infinite gap, which is a consequence of the saturable character of the CQ nonlinearity. If the potential structure is much deeper, then fundamental and double (both symmetric and antisymmetric) solitons with a flat-top shape are found in the finite gaps. Computation of stability eigenvalues for small perturbations and direct simulations show that all the solitons are stable. In the shallow KP potential, the soliton characteristics, in the form of the integral power Q (or width w) versus the propagation constant k, reveal strong bistability, with two and, sometimes, four different solutions found for a given k (the bistability disappears with the increase of the depth of the potential). Disobeying the Vakhitov-Kolokolov criterion, the solution branches with both dQ/dk > 0 and dQ/dk < 0 are stable. The curve Q(k) corresponding to each particular type of the solution (with a given number of local peaks and definite symmetry) ends at a finite maximum value of Q (breathers are found past the end points). The increase of the integral power gives rise to additional peaks in the soliton's shape, each corresponding to a subpulse trapped in a local channel of the KP structure (a beam-splitting property). It is plausible that these

  13. IMPROVED ERROR ESTIMATES FOR MIXED FINITE ELEMENT FOR NONLINEAR HYPERBOLIC EQUATIONS: THE CONTINUOUS-TIME CASE

    Institute of Scientific and Technical Information of China (English)

    Yan-ping Chen; Yun-qing Huang

    2001-01-01

    Improved L2-error estimates are computed for mixed finite element methods for second order nonlinear hyperbolic equations. Results are given for the continuous-time case. The convergence of the values for both the scalar function and the flux is demonstrated. The technique used here covers the lowest-order Raviart-Thomas spaces, as well as the higherorder spaces. A second paper will present the analysis of a fully discrete scheme (Numer.Math. J. Chinese Univ. vol.9, no.2, 2000, 181-192).

  14. Modeling of nonlinear multiaxial deformation of concrete on the base of hyperelastic orthotropic model

    Directory of Open Access Journals (Sweden)

    Lavrov Kirill

    2016-01-01

    Full Text Available The hyperelastic orthotropic material model is proposed to describe the nonlinear behavior of concrete under monotonic multiaxial loading with taking into account the tension-compression anisotropy. The orthotropy is introduced for the correct description of concrete cracking. The hyperelasticity provides unconditional thermodynamical consistency and advantages in numerical solving of boundary value problems. Identification of model parameters is based on four experimental deformation diagrams of concrete: axial stress - axial strain and axial stress - transverse strain under uniaxial tension and compression. The results of the hyperelastic orthotropic model are compared with Karpenko’s orthotropic model and experimental data for multiaxial loading.

  15. Homotopy deform method for reproducing kernel space for nonlinear boundary value problems

    Indian Academy of Sciences (India)

    MIN-QIANG XU; YING-ZHEN LIN

    2016-10-01

    In this paper, the combination of homotopy deform method (HDM) and simplified reproducing kernel method (SRKM) is introduced for solving the boundary value problems (BVPs) of nonlinear differential equations. The solution methodology is based on Adomian decomposition and reproducing kernel method (RKM). By the HDM, the nonlinear equations can be converted into a series of linear BVPs. After that, the simplified reproducing kernel method, which not only facilitates the reproducing kernel but also avoids the time-consuming Schmidt orthogonalization process, is proposed to solve linear equations. Some numerical test problems including ordinary differential equations and partial differential equations are analysed to illustrate the procedure and confirm the performance of the proposed method. The results faithfully reveal that our algorithm is considerably accurate and effective as expected.

  16. A force-level theory of the rheology of entangled rod and chain polymer liquids. I. Tube deformation, microscopic yielding, and the nonlinear elastic limit

    Science.gov (United States)

    Schweizer, Kenneth S.; Sussman, Daniel M.

    2016-12-01

    We employ a first-principles-based, force-level approach to construct the anharmonic tube confinement field for entangled fluids of rigid needles, and also for chains described at the primitive-path (PP) level in two limiting situations where chain stretch is assumed to either be completely equilibrated or unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear elastic limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a self-consistent analysis of transverse polymer harmonic dynamical fluctuations predicts that deformation-induced orientation leads to tube weakening or widening. In contrast, for deformed polymers in which chain stretch does not relax, we find tube strengthening or compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome by an externally applied force associated with macroscopic deformation can be crisply defined in the nonlinear elastic limit, and the possibility of a "microscopic absolute yielding" event destroying the tube confinement can be analyzed. For needles and contour-relaxed PP chains, this force imbalance occurs at a stress of order the equilibrium shear modulus and a strain of order unity, corresponding to a mechanically fragile entanglement tube field. However, for unrelaxed stretched chains, tube compression stabilizes transverse polymer confinement, and there appears to be no force imbalance. These results collectively suggest that the crossover from elastic to irreversible viscous response requires chain retraction to initiate disentanglement. We qualitatively discuss comparisons with existing phenomenological models for nonlinear startup shear, step strain, and creep rheology experiments.

  17. Nonlinear simulation of arch dam cracking with mixed finite element method

    Directory of Open Access Journals (Sweden)

    Ren Hao

    2008-06-01

    Full Text Available This paper proposes a new, simple and efficient method for nonlinear simulation of arch dam cracking from the construction period to the operation period, which takes into account the arch dam construction process and temperature loads. In the calculation mesh, the contact surface of pair nodes is located at places on the arch dam where cracking is possible. A new effective iterative method, the mixed finite element method for friction-contact problems, is improved and used for nonlinear simulation of the cracking process. The forces acting on the structure are divided into two parts: external forces and contact forces. The displacement of the structure is chosen as the basic variable and the nodal contact force in the possible contact region of the local coordinate system is chosen as the iterative variable, so that the nonlinear iterative process is only limited within the possible contact surface and is much more economical. This method was used to simulate the cracking process of the Shuanghe Arch Dam in Southwest China. In order to prove the validity and accuracy of this method and to study the effect of thermal stress on arch dam cracking, three schemes were designed for calculation. Numerical results agree with actual measured data, proving that it is feasible to use this method to simulate the entire process of nonlinear arch dam cracking.

  18. Stochastic filtering for damage identification through nonlinear structural finite element model updating

    Science.gov (United States)

    Astroza, Rodrigo; Ebrahimian, Hamed; Conte, Joel P.

    2015-03-01

    This paper describes a novel framework that combines advanced mechanics-based nonlinear (hysteretic) finite element (FE) models and stochastic filtering techniques to estimate unknown time-invariant parameters of nonlinear inelastic material models used in the FE model. Using input-output data recorded during earthquake events, the proposed framework updates the nonlinear FE model of the structure. The updated FE model can be directly used for damage identification and further used for damage prognosis. To update the unknown time-invariant parameters of the FE model, two alternative stochastic filtering methods are used: the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). A three-dimensional, 5-story, 2-by-1 bay reinforced concrete (RC) frame is used to verify the proposed framework. The RC frame is modeled using fiber-section displacement-based beam-column elements with distributed plasticity and is subjected to the ground motion recorded at the Sylmar station during the 1994 Northridge earthquake. The results indicate that the proposed framework accurately estimate the unknown material parameters of the nonlinear FE model. The UKF outperforms the EKF when the relative root-mean-square error of the recorded responses are compared. In addition, the results suggest that the convergence of the estimate of modeling parameters is smoother and faster when the UKF is utilized.

  19. A Study of Hardening Behavior Based on a Finite-Deformation Gradient Crystal-Plasticity Model

    CERN Document Server

    Pouriayevali, Habib

    2016-01-01

    A systematic study on the different roles of the governing components of a well-defined finite-deformation gradient crystal-plasticity model proposed by (Gurtin, 2008b) is carried out, in order to visualize the capability of the model in the prediction of a wide range of hardening behaviors as well as rate-dependent, scale-variation and Bauschinger-like responses in a single crystal. A function of accumulation rates of dislocations is employed and viewed as a measure of formation of short-range interactions which impede dislocation movements within a crystal. The model is first represented in the reference configuration for the purpose of numerical implementation, and then implemented in the FEM software ABAQUS via a user-defined subroutine (UEL). Our simulation results reveal that the dissipative gradient-strengthening is also identified as a source of isotropic-hardening behavior, which represents the effect of cold work introduced by (Gurtin and Ohno, 2011). Moreover, plastic flows in predefined slip syste...

  20. Exact Holography of the Mass-deformed M2-brane Theory at Finite $N$

    CERN Document Server

    Jang, Dongmin; Kwon, O-Kab; Tolla, D D

    2016-01-01

    We test the holographic relation between the vacuum expectation values (vevs) of gauge invariant operators in ${\\cal N} = 6$ ${\\rm U}_{k}(N)\\times {\\rm U}_{-k}(N)$ mass-deformed ABJM theory and the LLM geometries with $\\mathbb{Z}_k$ orbifold in 11-dimensional supergravity. To do that, we apply the Kaluza-Klein reduction to construct a 4-dimensional gravity theory and implement the holographic renormalization procedure. We obtain an exact holographic relation for the vevs of the chiral primary operator with conformal dimension $\\Delta = 1$, which is given by $\\langle {\\cal O}^{(\\Delta=1)}\\rangle= N^{\\frac32} \\, f_{(\\Delta=1)}$, for {\\it finite} $N$ and $k=1$. Here factor $f_{(\\Delta)}$ is independent of $N$. Our results involve infinite number of exact dual relations for all possible supersymmetric Higgs vacua and so provide a nontrivial test of gauge/gravity duality away from the conformal fixed point without taking the usual large $N$ limit. We also extend our results to the case of $k\

  1. Deforming fluid domains within the finite element method: Five mesh-based tracking methods in comparison

    CERN Document Server

    Elgeti, Stefanie

    2015-01-01

    Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled with a domain deformation approach. This work reviews five of those approaches: interface tracking using a boundary-conforming mesh and, in the interface capturing context, the level-set method, the volume-of-fluid method, particle methods, as well as the phase-field method. The history of each method is presented in combination with the most recent developments in the field. Particularly, the topics of extended finite elements (XFEM) and NURBS-based methods, such as Isogeometric Analysis (IGA), are addressed. For illustration purposes, two applications have been chosen: two-phase flow involving drops or bubbles and sloshing tanks. The challenges of these applications, such as the geometrically correct representation of the free surface or the incorporation of surface tension ...

  2. Corotational formulation for 3d solids. An analysis of geometrically nonlinear foam deformation

    CERN Document Server

    Kaczmarczyk, Łukasz; Pearce, Chris J

    2011-01-01

    This paper presents theory for the Lagrange co-rotational (CR) formulation of finite elements in the geometrically nonlinear analysis of 3D structures. In this paper strains are assumed to be small while the magnitude of rotations from the reference configuration is not restricted. A new best fit rotator and consistent spin filter are derived. Lagrange CR formulation is applied with Hybrid Trefftz Stress elements, although presented methodology can be applied to arbitrary problem formulation and discretization technique, f.e. finite volume methods and lattice models, discreet element methods. Efficiency of CR formulation can be utilized in post-buckling stability analysis, damage and fracture mechanics, modelling of dynamic fragmentation of bodies made from quasi-brittle materials, solid fluid interactions and analysis of post-stressed structures, discreet body dynamics.

  3. Finite-size effect of \\eta-deformed AdS_5 x S^5 at strong coupling

    CERN Document Server

    Ahn, Changrim

    2016-01-01

    We compute Luscher corrections for a giant magnon in the \\eta-deformed (AdS_5\\times S^5)_{\\eta} using the su(2|2)_q-invariant S-matrix at strong coupling and compare with the finite-size effect of the corresponding string state, derived previously. We find that these two results match and confirm that the su(2|2)_q-invariant S-matrix is describing world-sheet excitations of the \\eta-deformed background.

  4. Finite-size giant magnons on η-deformed AdS5×S5

    Directory of Open Access Journals (Sweden)

    Changrim Ahn

    2014-10-01

    Full Text Available We consider strings moving in the Rt×Sη3 subspace of the η-deformed AdS5×S5 and obtain a class of solutions depending on several parameters. They are characterized by the string energy and two angular momenta. Finite-size dyonic giant magnon belongs to this class of solutions. Further on, we restrict ourselves to the case of giant magnon with one nonzero angular momentum, and obtain the leading finite-size correction to the dispersion relation.

  5. Analysis of Retrofitting Non-Linear Finite Element Of RCC Beam And Column Using Ansys

    Directory of Open Access Journals (Sweden)

    T. Subramani

    2014-12-01

    Full Text Available Many of the existing reinforced concrete structures throughout the world are in urgent need of strengthening, repair or reconstruction because of deterioration due to various factors like corrosion, lack of detailing, failure of bonding between beam-column joints, increase in service loads, etc., leading to cracking, spalling, loss of strength, deflection, etc., Direct observation of these damaged structures has shown that damage occurs usually at the beam-column joints, with failure in bending or shear, depending on geometry and reinforcement distribution type.A nonlinear finite element analysis that is a simulation technique is used in this work to evaluate the effectiveness of retrofitting technique called “wrapping technique” for using carbon fibres (FRP for strengthening of RC beam-column connections damaged due to various reasons. After carrying out a nonlinear finite element analysis of a reinforced concrete frame (Controlled Specimen and reinforced concrete frame where carbon fibres are attached to the beam column joint portion in different patterns ,the measured response histories of the original and strengthened specimens are then subsequently compared. It is seen that the strengthened specimens exhibit significant increase in strength, stiffness, and stability as compared to controlled specimens. It appears that the proposed simulation technique will have a significant impact in engineering practice in the near future.

  6. Phase sensitivity in deformed-state superposition considering nonlinear phase shifts

    Science.gov (United States)

    Berrada, K.

    2016-07-01

    We study the problem of the phase estimation for the deformation-state superposition (DSS) under perfect and lossy (due to a dissipative interaction of DSS with their environment) regimes. The study is also devoted to the phase enhancement of the quantum states resulting from a generalized non-linearity of the phase shifts, both without and with losses. We find that such a kind of superposition can give the smallest variance in the phase parameter in comparison with usual Schrödinger cat states in different order of non-linearity even if for a larger average number of photons. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement between the DSS and its environment is investigated during the dissipation. We show that partial entanglement trapping occurs during the dynamics depending on the kind of deformation and mean photon number. These features make the DSS with a larger average number of photons a good candidate for implementation of schemes of quantum optics and information with high precision.

  7. A bimodular theory for finite deformations: Comparison of orthotropic second-order and exponential stress constitutive equations for articular cartilage.

    Science.gov (United States)

    Klisch, Stephen M

    2006-06-01

    Cartilaginous tissues, such as articular cartilage and the annulus fibrosus, exhibit orthotropic behavior with highly asymmetric tensile-compressive responses. Due to this complex behavior, it is difficult to develop accurate stress constitutive equations that are valid for finite deformations. Therefore, we have developed a bimodular theory for finite deformations of elastic materials that allows the mechanical properties of the tissue to differ in tension and compression. In this paper, we derive an orthotropic stress constitutive equation that is second-order in terms of the Biot strain tensor as an alternative to traditional exponential type equations. Several reduced forms of the bimodular second-order equation, with six to nine parameters, and a bimodular exponential equation, with seven parameters, were fit to an experimental dataset that captures the highly asymmetric and orthotropic mechanical response of cartilage. The results suggest that the bimodular second-order models may be appealing for some applications with cartilaginous tissues.

  8. SANTOS - a two-dimensional finite element program for the quasistatic, large deformation, inelastic response of solids

    Energy Technology Data Exchange (ETDEWEB)

    Stone, C.M.

    1997-07-01

    SANTOS is a finite element program designed to compute the quasistatic, large deformation, inelastic response of two-dimensional planar or axisymmetric solids. The code is derived from the transient dynamic code PRONTO 2D. The solution strategy used to compute the equilibrium states is based on a self-adaptive dynamic relaxation solution scheme, which is based on explicit central difference pseudo-time integration and artificial mass proportional damping. The element used in SANTOS is a uniform strain 4-node quadrilateral element with an hourglass control scheme to control the spurious deformation modes. Finite strain constitutive models for many common engineering materials are included. A robust master-slave contact algorithm for modeling sliding contact is implemented. An interface for coupling to an external code is also provided. 43 refs., 22 figs.

  9. SU-E-J-111: Finite Element-Based Deformable Image Registration of Pleural Cavity for Photodynamic Therapy

    Energy Technology Data Exchange (ETDEWEB)

    Penjweini, R; Zhu, T [Univ Pennsylvania, Philadelphia, PA (United States)

    2015-06-15

    Purpose: The pleural volumes will deform during surgery portion of the pleural photodynamic therapy (PDT) of lung cancer when the pleural cavity is opened. This impact the delivered dose when using highly conformal treatment techniques. In this study, a finite element-based (FEM) deformable image registration is used to quantify the anatomical variation between the contours for the pleural cavities obtained in the operating room and those determined from pre-surgery computed tomography (CT) scans. Methods: An infrared camera-based navigation system (NDI) is used during PDT to track the anatomical changes and contour the lung and chest cavity. A series of CTs of the lungs, in the same patient, are also acquired before the surgery. The structure contour of lung and the CTs are processed and contoured in Matlab and MeshLab. Then, the contours are imported into COMSOL Multiphysics 5.0, where the FEM-based deformable image registration is obtained using the deformed mesh - moving mesh (ALE) model. The NDI acquired lung contour is considered as the reference contour, and the CT contour is used as the target one, which will be deformed. Results: The reconstructed three-dimensional contours from both NDI and CT can be converted to COMSOL so that a three-dimensional ALE model can be developed. The contours can be registered using COMSOL ALE moving mesh model, which takes into account the deformation along x, y and z-axes. The deformed contour has good matches to the reference contour after the dynamic matching process. The resulting 3D deformation map can be used to obtain the locations of other critical anatomic structures, e.g., heart, during surgery. Conclusion: Deformable image registration can fuse images acquired by different modalities. It provides insights into the development of phenomenon and variation in normal anatomical structures over time. The initial assessments of three-dimensional registration show good agreement.

  10. Large Deformation Dynamic Three-Dimensional Coupled Finite Element Analysis of Soft Biological Tissues Treated as Biphasic Porous Media

    Science.gov (United States)

    2014-11-01

    2006; White and Borja, 2008; Sun, Ostien, and Salinger , 2013) Q8P8 hexahedral element is also implemented within the coupled dynamics framework, and...but based on our implementation, it was ineffective for our particular applications of soft tissues at finite strain. Sun, Ostien, and Salinger ...large deformation. Int. J. Numer. Methods Engrg., vol. 32, pp. 1411–1439. Sun, W.-C.; Ostien, J.; Salinger , A. (2013): A stabilized assumed

  11. Solving nonlinear nonstationary problem of heat-conductivity by finite element method

    Directory of Open Access Journals (Sweden)

    Антон Янович Карвацький

    2016-11-01

    Full Text Available Methodology and effective solving algorithm of non-linear dynamic problems of thermal and electric conductivity with significant temperature dependence of thermal and physical properties are given on the basis of finite element method (FEM and Newton linearization method. Discrete equations system FEM was obtained with the use of Galerkin method, where the main function is the finite element form function. The methodology based on successive solving problems of thermal and electrical conductivity has been examined in the work in order to minimize the requirements for calculating resources (RAM. in particular. Having used Mathcad software original programming code was developed to solve the given problem. After investigation of the received results, comparative analyses of accurate solution data and results of numerical solutions, obtained with the use of Matlab programming products, was held. The geometry of one fourth part of the finite sized cylinder was used to test the given numerical model. The discretization of the calculation part was fulfilled using the open programming software for automated Gmsh nets with tetrahedral units, while ParaView, which is an open programming code as well, was used to visualize the calculation results. It was found out that the maximum value violation of potential and temperature determination doesn`t exceed 0,2-0,83% in the given work according to the problem conditions

  12. Three-Dimensional Crystal Plasticity Finite Element Simulation of Hot Compressive Deformation Behaviors of 7075 Al Alloy

    Science.gov (United States)

    Li, Lei-Ting; Lin, Y. C.; Li, Ling; Shen, Lu-Ming; Wen, Dong-Xu

    2015-03-01

    Three-dimensional crystal plasticity finite element (CPFE) method is used to investigate the hot compressive deformation behaviors of 7075 aluminum alloy. Based on the grain morphology and crystallographic texture of 7075 aluminum alloy, the microstructure-based representative volume element (RVE) model was established by the pole figure inversion approach. In order to study the macroscopic stress-strain response and microstructural evolution, the CPFE simulations are performed on the established microstructure-based RVE model. It is found that the simulated stress-strain curves and deformation texture well agree with the measured results of 7075 aluminum alloy. With the increasing deformation degree, the remained initial weak Goss texture component tends to be strong and stable, which may result in the steady flow stress. The grain orientation and grain misorientation have significant effects on the deformation heterogeneity during hot compressive deformation. In the rolling-normal plane, the continuity of strain and misorientation can maintain across the low-angle grain boundaries, while the discontinuity of strain and misorientation is observed at the high-angle grain boundaries. The simulated results demonstrate that the developed CPFE model can well describe the hot compressive deformation behaviors of 7075 aluminum alloy under elevated temperatures.

  13. Nonlinear flexural waves and chaos behavior in finite-deflection Timoshenko beam

    Institute of Scientific and Technical Information of China (English)

    Shan-yuan ZHANG; Zhi-fang LIU

    2010-01-01

    Based on the Timoshenko beam theory,the finite-deflection and the axial inertia are taken into account,and the nonlinear partial differential equations for flexural waves in a beam are derived. Using the traveling wave method and integration skills,the nonlinear partial differential equations can be converted into an ordinary differential equation. The qualitative analysis indicates that the corresponding dynamic system has a heteroclinic orbit under a certain condition. An exact periodic solution of the nonlinear wave equation is obtained using the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function tends to one in the degenerate case,a shock wave solution is given. The small perturbations are further introduced,arising from the damping and the external load to an original Hamilton system,and the threshold condition of the existence of the transverse heteroclinic point is obtained using Melnikov's method. It is shown that the perturbed system has a chaotic property under the Smale horseshoe transform.

  14. Analysis of Nonlinear Vibration of Hard Coating Thin Plate by Finite Element Iteration Method

    Directory of Open Access Journals (Sweden)

    Hui Li

    2014-01-01

    Full Text Available This paper studies nonlinear vibration mechanism of hard coating thin plate based on macroscopic vibration theory and proposes finite element iteration method (FEIM to theoretically calculate its nature frequency and vibration response. First of all, strain dependent mechanical property of hard coating is briefly introduced and polynomial method is adopted to characterize the storage and loss modulus of coating material. Then, the principle formulas of inherent and dynamic response characteristics of the hard coating composite plate are derived. And consequently specific analysis procedure is proposed by combining ANSYS APDL and self-designed MATLAB program. Finally, a composite plate coated with MgO + Al2O3 is taken as a study object and both nonlinear vibration test and analysis are conducted on the plate specimen with considering strain dependent mechanical parameters of hard coating. Through comparing the resulting frequency and response results, the practicability and reliability of FEIM have been verified and the corresponding analysis results can provide an important reference for further study on nonlinear vibration mechanism of hard coating composite structure.

  15. A quantitative evaluation of the deformation texture predictions for aluminium alloys from crystal plasticity finite element method

    Science.gov (United States)

    Li, Saiyi; Van Houtte, Paul; Kalidindi, Surya R.

    2004-09-01

    Crystal plasticity finite element (CPFE) models are useful tools in modelling the anisotropic stress-strain responses in large deformation of polycrystalline metals. In this study, a CPFE model is applied to simulate the evolution of crystallographic textures during cold rolling of hot-rolled aluminium plates and during uniaxial tensile, uniaxial compression and simple shear tests of annealed aluminium sheets. The performance of the model is critically evaluated through quantitative comparisons of the simulated textures with those predicted by the full constraints (FC) Taylor model and the experimentally measured textures. It is shown that the CPFE model performs better than the FC Taylor model in all the cases. However, the quality of the texture predictions deteriorates with increasing strain values. The CPFE model gives better texture predictions in the moderately deformed tensile and compression samples (~20% strain), compared to the more heavily deformed simple shear (0.85-0.95 shear strain) and cold-rolled (40-98% thickness reduction) samples. It is also shown that the CPFE predictions for cold rolling can be improved with finer discretization, i.e. by assigning multiple elements per grain instead of one element per grain in the finite element model. The improvement is mainly reflected in an improved prediction of the copper component and, in some cases, an improved prediction of the brass component. Inspection of the local deformation gradients reveals that these texture changes can be attributed to the increase of shear relaxations in the RD-ND and RD-TD planes.

  16. Finite element analysis of controlling the TC4 thin plate weldment wave-like deformation by welding with impacting rotation

    Institute of Scientific and Technical Information of China (English)

    Zhang Yong; Yang Jianguo; Liu Xuesong; Fang Hongyuan

    2010-01-01

    The new technology of welding with impacting rotation is put forward to decrease the wave-like deformation of the TC4 thin plate weldment.The thermal stress and strain are vital to understand the mechanism of controlling the wave-like deformation.In order to know the development of internal thermal stress and strain,finite element method is utilized for the stress and strain are difficult to be investigated by experimental methods during the welding process.Temperature field,thermal stress evolution and distortion of thin plate are compared with the test results such as weld thermal cycle,residual stress sectioning measurement,and the deflection of the thin plate respectively.By the finite element analysis and test results verification,the mechanism of the technology to control the wave-like deformation is brought forward,non-uniform thermal elastic strain between compressive plastic region and elastic extensive region is diminished by a certain amount of extensive plastic deformation by welding with impacting rotation process.

  17. TWO-GRID METHOD FOR CHARACTERISTICS FINITE-ELEMENT SOLUTION OF 2D NONLINEAR CONVECTION-DOMINATED DIFFUSION PROBLEM

    Institute of Scientific and Technical Information of China (English)

    QIN Xin-qiang; MA Yi-chen; ZHANG Yin

    2005-01-01

    For two-dimension nonlinear convection diffusion equation, a two-grid method of characteristics finite-element solution was constructed. In this method the nonlinear iterations is only to execute on the coarse grid and the fine-grid solution can be obtained in a single linear step. For the nonlinear convection-dominated diffusion equation, this method can not only stabilize the numerical oscillation but also accelerate the convergence and improve the computational efficiency. The error analysis demonstrates if the mesh sizes between coarse-grid and fine-grid satisfy the certain relationship, the two-grid solution and the characteristics finite-element solution have the same order of accuracy. The numerical example confirms that the two-grid method is more efficient than that of characteristics finite-element method.

  18. Dynamic Modelling of Tooth Deformation Using Occlusal Kinematics and Finite Element Analysis.

    Directory of Open Access Journals (Sweden)

    Stefano Benazzi

    Full Text Available Dental biomechanics based on finite element (FE analysis is attracting enormous interest in dentistry, biology, anthropology and palaeontology. Nonetheless, several shortcomings in FE modeling exist, mainly due to unrealistic loading conditions. In this contribution we used kinematics information recorded in a virtual environment derived from occlusal contact detection between high resolution models of an upper and lower human first molar pair (M1 and M1, respectively to run a non-linear dynamic FE crash colliding test.MicroCT image data of a modern human skull were segmented to reconstruct digital models of the antagonistic right M1 and M1 and the dental supporting structures. We used the Occlusal Fingerprint Analyser software to reconstruct the individual occlusal pathway trajectory during the power stroke of the chewing cycle, which was applied in a FE simulation to guide the M1 3D-path for the crash colliding test.FE analysis results showed that the stress pattern changes considerably during the power stroke, demonstrating that knowledge about chewing kinematics in conjunction with a morphologically detailed FE model is crucial for understanding tooth form and function under physiological conditions.Results from such advanced dynamic approaches will be applicable to evaluate and avoid mechanical failure in prosthodontics/endodontic treatments, and to test material behavior for modern tooth restoration in dentistry. This approach will also allow us to improve our knowledge in chewing-related biomechanics for functional diagnosis and therapy, and it will help paleoanthropologists to illuminate dental adaptive processes and morphological modifications in human evolution.

  19. Development of experimental verification techniques for non-linear deformation and fracture.

    Energy Technology Data Exchange (ETDEWEB)

    Moody, Neville Reid; Bahr, David F. (Washington State University, Pullman, WA)

    2003-12-01

    This project covers three distinct features of thin film fracture and deformation in which the current experimental technique of nanoindentation demonstrates limitations. The first feature is film fracture, which can be generated either by nanoindentation or bulge testing thin films. Examples of both tests will be shown, in particular oxide films on metallic or semiconductor substrates. Nanoindentations were made into oxide films on aluminum and titanium substrates for two cases; one where the metal was a bulk (effectively single crystal) material and the other where the metal was a 1 pm thick film grown on a silica or silicon substrate. In both cases indentation was used to produce discontinuous loading curves, which indicate film fracture after plastic deformation of the metal. The oxides on bulk metals fractures occurred at reproducible loads, and the tensile stress in the films at fracture were approximately 10 and 15 GPa for the aluminum and titanium oxides respectively. Similarly, bulge tests of piezoelectric oxide films have been carried out and demonstrate film fracture at stresses of only 100's of MPa, suggesting the importance of defects and film thickness in evaluating film strength. The second feature of concern is film adhesion. Several qualitative and quantitative tests exist today that measure the adhesion properties of thin films. A relatively new technique that uses stressed overlayers to measure adhesion has been proposed and extensively studied. Delamination of thin films manifests itself in the form of either telephone cord or straight buckles. The buckles are used to calculate the interfacial fracture toughness of the film-substrate system. Nanoindentation can be utilized if more energy is needed to initiate buckling of the film system. Finally, deformation in metallic systems can lead to non-linear deformation due to 'bursts' of dislocation activity during nanoindentation. An experimental study to examine the structure of

  20. Finite element based nonlinear normalization of human lumbar intervertebral disc stiffness to account for its morphology.

    Science.gov (United States)

    Maquer, Ghislain; Laurent, Marc; Brandejsky, Vaclav; Pretterklieber, Michael L; Zysset, Philippe K

    2014-06-01

    Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently

  1. A New Energy-Based Method for 3-D Finite-Element Nonlinear Flux Linkage computation of Electrical Machines

    DEFF Research Database (Denmark)

    Lu, Kaiyuan; Rasmussen, Peter Omand; Ritchie, Ewen

    2011-01-01

    This paper presents a new method for computation of the nonlinear flux linkage in 3-D finite-element models (FEMs) of electrical machines. Accurate computation of the nonlinear flux linkage in 3-D FEM is not an easy task. Compared to the existing energy-perturbation method, the new technique......-perturbation method. The new method proposed is validated using experimental results on two different permanent magnet machines....

  2. A finite volume approach for the simulation of nonlinear dissipative acoustic wave propagation

    CERN Document Server

    Velasco-Segura, Roberto

    2013-01-01

    A form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A CLAWPACK based, 2D finite volume method using the Roe linearization was implemented to obtain numerically the solution of the proposed equations. In order to validate the code, two different tests have been performed: one against a special Taylor shock-like analytic solution, the other against published results on a HIFU system, both with satisfactory results. The code is based on CLAWPACK and is written for parallel execution on a GPU, thus improving performance by a factor of over 60 when compared to the standard CLAWPACK code.

  3. Massively parallel-in-space-time, adaptive finite element framework for non-linear parabolic equations

    CERN Document Server

    Dyja, Robert; van der Zee, Kristoffer G

    2016-01-01

    We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns instead of marching sequentially in time. The methodology is a combination of a computationally efficient implementation of a parallel-in-space-time finite element solver coupled with a posteriori space-time error estimates and a parallel mesh generator. This methodology enables, in principle, simultaneous adaptivity in both space and time (within the block) domains. We explore this basic concept in the context of a variety of time-steppers including $\\Theta$-schemes and Backward Differentiate Formulas. We specifically illustrate this framework with applications involving time dependent linear, quasi-linear and semi-linear diffusion equations. We focus on investigating how the coupled space-time refinement indicators for this class of problems affect spatial adaptivity. Final...

  4. Nonlinear dynamics of beam-plasma instability in a finite magnetic field

    Science.gov (United States)

    Bogdankevich, I. L.; Goncharov, P. Yu.; Gusein-zade, N. G.; Ignatov, A. M.

    2017-06-01

    The nonlinear dynamics of beam-plasma instability in a finite magnetic field is investigated numerically. In particular, it is shown that decay instability can develop. Special attention is paid to the influence of the beam-plasma coupling factor on the spectral characteristics of a plasma relativistic microwave accelerator (PRMA) at different values of the magnetic field. It is shown that two qualitatively different physical regimes take place at two values of the external magnetic field: B 0 = 4.5 kG (Ω ω B p ) and 20 kG (Ω B ≫ ωp). For B 0 = 4.5 kG, close to the actual experimental value, there exists an optimal value of the gap length between the relativistic electron beam and the plasma (and, accordingly, an optimal value of the coupling factor) at which the PRMA output power increases appreciably, while the noise level decreases.

  5. A HIGH ORDER ADAPTIVE FINITE ELEMENT METHOD FOR SOLVING NONLINEAR HYPERBOLIC CONSERVATION LAWS

    Institute of Scientific and Technical Information of China (English)

    Zhengfu Xu; Jinchao Xu; Chi-Wang Shu

    2011-01-01

    In this note,we apply the h-adaptive streamline diffusion finite element method with a small mesh-dependent artificial viscosity to solve nonlinear hyperbolic partial differential equations,with the objective of achieving high order accuracy and mesh efficiency.We compute the numerical solution to a steady state Burgers equation and the solution to a converging-diverging nozzle problem.The computational results verify that,by suitably choosing the artificial viscosity coefficient and applying the adaptive strategy based on a posterior error estimate by Johnson et al.,an order of N-3/2 accuracy can be obtained when continuous piecewise linear elements are used,where N is the number of elements.

  6. A refined mixed shear flexible finite element for the nonlinear analysis of laminated plates

    Science.gov (United States)

    Putcha, N. S.; Reddy, J. N.

    1986-01-01

    The present study is concerned with the development of a mixed shear flexible finite element with relaxed continuity for the geometrically linear and nonlinear analysis of laminated anisotropic plates. The formulation of the element is based on a refined higher-order theory. This theory satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate. Shear correction coefficients are not needed. The developed element consists of 11 degrees-of-freedom per node, taking into account three displacements, two rotations, and six moment resultants. An evaluation of the element is conducted with respect to the accuracy obtained in the bending of laminated anistropic rectangular plates with different lamination schemes, loadings, and boundary conditions.

  7. General Formulations of Finite-field Method Classified by Symmetry for Molecular Linear and Nonlinear Polarizabilities

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    The formulations of the finite-field approach to calculate the linear and non-linear optical coefficients mi, aij, bijk and gijkl of a molecular system with different symmetries have been deduced and summarized. The possible choices of the energy sets of the 48 frequent point groups have been optimized and categorized into 11 classes. With the restriction of symmetry operators, a minimum of 9, no more than 21 energy points have to be calculated in order to determine the coefficients, except in the case of the first class to which C1 point group belongs and in which the 34 non-relative energy points selected in our uniform and general scheme are all needed. The symmetric operators that cause some of the tensor components to vanish have been demonstrated as well.

  8. Parametric Nonlinear Finite Element Analysis of Strain Ratcheting in Pressurized Elbows Based on Random Vibration

    Directory of Open Access Journals (Sweden)

    Yong Zhao

    1996-01-01

    Full Text Available The large strain ratcheting in cyclic plasticity of a typical pressurized pipe elbow in a realistic nuclear piping system was investigated in a more quantitative manner than previously. The elbow was modeled using a fine mesh of shell elements that can provide the completed information of detailed time varying strain distributions in the whole elbow area. The nonlinear time history stress analyses performed were based on a pseudostatic concept using the vector-valued stochastic displacement response time series loaded at the elbow ends. The response time series were synthesized using a simulation approach based on the random vibration analyses of the piping system and its supporting building. After a finite element mesh convergence study, parametric analyses were conducted that included the effects due to the magnitude changes in excitation level, internal pressure, material yield stress, and material strain hardening.

  9. A parallel high-order accurate finite element nonlinear Stokes ice sheet model and benchmark experiments

    Energy Technology Data Exchange (ETDEWEB)

    Leng, Wei [Chinese Academy of Sciences; Ju, Lili [University of South Carolina; Gunzburger, Max [Florida State University; Price, Stephen [Los Alamos National Laboratory; Ringler, Todd [Los Alamos National Laboratory,

    2012-01-01

    The numerical modeling of glacier and ice sheet evolution is a subject of growing interest, in part because of the potential for models to inform estimates of global sea level change. This paper focuses on the development of a numerical model that determines the velocity and pressure fields within an ice sheet. Our numerical model features a high-fidelity mathematical model involving the nonlinear Stokes system and combinations of no-sliding and sliding basal boundary conditions, high-order accurate finite element discretizations based on variable resolution grids, and highly scalable parallel solution strategies, all of which contribute to a numerical model that can achieve accurate velocity and pressure approximations in a highly efficient manner. We demonstrate the accuracy and efficiency of our model by analytical solution tests, established ice sheet benchmark experiments, and comparisons with other well-established ice sheet models.

  10. A numerical study of the RG equation for the deformed O(3) nonlinear sigma model

    Science.gov (United States)

    Belardinelli, L.; Destri, C.; Onofri, E.

    1995-02-01

    The Renormalization Group equation describing the evolution of the metric of the nonlinear sigma model poses some nice mathematical problems involving functional analysis, differential geometry and numerical analysis. In this article we briefly report some results obtained from the numerical study of the solutions in the case of a two-dimensional target space (deformation of the O(3) σ-model In particular, our analysis shows that the so-called sausages define an attracting manifold in the U(1)-symmetric case, at one-loop level. Moreover, data from two-loop evolution are used to test the association (Fateev, Onofri and ALB. Zamolodchikov, Nucl. Phys. B 406 (1993) 521) between the so-called SSM η field theory and a certain U(1)-symmetric, factorized scattering theory (FST).

  11. Finite-horizon control-constrained nonlinear optimal control using single network adaptive critics.

    Science.gov (United States)

    Heydari, Ali; Balakrishnan, Sivasubramanya N

    2013-01-01

    To synthesize fixed-final-time control-constrained optimal controllers for discrete-time nonlinear control-affine systems, a single neural network (NN)-based controller called the Finite-horizon Single Network Adaptive Critic is developed in this paper. Inputs to the NN are the current system states and the time-to-go, and the network outputs are the costates that are used to compute optimal feedback control. Control constraints are handled through a nonquadratic cost function. Convergence proofs of: 1) the reinforcement learning-based training method to the optimal solution; 2) the training error; and 3) the network weights are provided. The resulting controller is shown to solve the associated time-varying Hamilton-Jacobi-Bellman equation and provide the fixed-final-time optimal solution. Performance of the new synthesis technique is demonstrated through different examples including an attitude control problem wherein a rigid spacecraft performs a finite-time attitude maneuver subject to control bounds. The new formulation has great potential for implementation since it consists of only one NN with single set of weights and it provides comprehensive feedback solutions online, though it is trained offline.

  12. An Extension of Mapping Deformation Method and New Exact Solution for Three Coupled Nonlinear Partial Differential Equations

    Institute of Scientific and Technical Information of China (English)

    LI Hua-Mei

    2003-01-01

    In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained.

  13. Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem

    Science.gov (United States)

    Terekhov, Kirill M.; Mallison, Bradley T.; Tchelepi, Hamdi A.

    2017-02-01

    We present two new cell-centered nonlinear finite-volume methods for the heterogeneous, anisotropic diffusion problem. The schemes split the interfacial flux into harmonic and transversal components. Specifically, linear combinations of the transversal vector and the co-normal are used that lead to significant improvements in terms of the mesh-locking effects. The harmonic component of the flux is represented using a conventional monotone two-point flux approximation; the component along the parameterized direction is treated nonlinearly to satisfy either positivity of the solution as in [29], or the discrete maximum principle as in [9]. In order to make the method purely cell-centered, we derive a homogenization function that allows for seamless interpolation in the presence of heterogeneity following a strategy similar to [46]. The performance of the new schemes is compared with existing multi-point flux approximation methods [3,5]. The robustness of the scheme with respect to the mesh-locking problem is demonstrated using several challenging test cases.

  14. Finite element simulation of magnetohydrodynamic convective nanofluid slip flow in porous media with nonlinear radiation

    Directory of Open Access Journals (Sweden)

    M.J. Uddin

    2016-06-01

    Full Text Available A numerical investigation of two dimensional steady state laminar boundary layer flow of a viscous electrically-conducting nanofluid in the vicinity of a stretching/shrinking porous flat plate located in a Darcian porous medium is performed. The nonlinear Rosseland radiation effect is taken into account. Velocity slip and thermal slip at the boundary as well as the newly developed zero mass flux boundary conditions are also implemented to achieve physically applicable results. The governing transport equations are reduced to a system of nonlinear ordinary differential equations using appropriate similarity transformations and these are then solved numerically using a variational finite element method (FEM. The influence of the governing parameters (Darcy number, magnetic field, velocity and thermal slip, temperature ratio, transpiration, Brownian motion, thermophoresis, Lewis number and Reynolds number on the dimensionless velocity, temperature, nanoparticle volume fraction as well as the skin friction, the heat transfer rates and the mass transfer rates are examined and illustrated in detail. The FEM code is validated with earlier studies for non-magnetic non-slip flow demonstrating close correlation. The present study is relevant to high-temperature nano-materials processing operations.

  15. A NURBS-based finite element model applied to geometrically nonlinear elastodynamics using a corotational approach

    KAUST Repository

    Espath, L. F R

    2015-02-03

    A numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on NURBS (Non-Uniform Rational B-Spline) basis is presented. A comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted. The state equation is written in terms of corotational variables according to the hypoelastic theory, relating the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.The generalized-α method (Gα) method and Generalized Energy-Momentum Method with an additional parameter (GEMM+ξ) are employed in order to obtain a stable and controllable dissipative time-stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses.The main contribution is to show that the energy-momentum conservation properties and numerical stability may be improved once a NURBS-based FEM in the spatial discretization is used. Also it is shown that high continuity can postpone the numerical instability when GEMM+ξ with consistent mass is employed; likewise, increasing the continuity class yields a decrease in the numerical dissipation. A parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class, spectral radius and lumped as well as consistent mass matrices.

  16. Finite Larmor radius effects in the nonlinear dynamics of collisionless magnetic reconnection

    Energy Technology Data Exchange (ETDEWEB)

    Del Sarto, D [Institut Jean Lamour, UMR 7198 CNRS-Nancy University, Campus Victor Grignard - BP 70239, 54506 Vandoeuvre-les-Nancy Cedex (France); Marchetto, C [Associazione EURATOM-ENEA sulla Fusione, IFP-CNR, Via R. Cozzi 53, 20125 Milano (Italy); Pegoraro, F; Califano, F, E-mail: daniele.delsarto@ijl.nancy-universite.fr, E-mail: marchetto@ifp.cnr.it, E-mail: pegoraro@df.unipi.it, E-mail: califano@df.unipi.it [Physics Department and CNISM, Pisa University, Largo Pontecorvo 3, 56127 Pisa (Italy)

    2011-03-15

    We provide numerical evidence of the role of finite Larmor radius effects in the nonlinear dynamics of magnetic field line reconnection in high-temperature, strong guide field plasmas in a slab configuration, in the large {Delta}' regime. Both ion and electron temperature effects introduce internal energy variations related to mechanical compression terms in the energy balance, thus contributing to regularize the gradients of the ion density with respect to the cold regimes. For values of the Larmor radii that are not asymptotically small, the two temperature effects are no longer interchangeable, in contrast to what is expected from linear theory, and the differences are measurable in the numerical growth rates and in the nonlinear evolution of the density layers. We interpret such differences in terms of the change, due to ion temperature effects, of the Lagrangian advection of the 'plasma invariants' that are encountered in the cold-ion, warm-electron regime. The different roles of the ion and ion-sound Larmor radii in the reconnection dynamics near the X- and O-points are evidenced by means of a local quadratic expansion of the fields.

  17. A Space-Time Finite Element Model for Design and Control Optimization of Nonlinear Dynamic Response

    Directory of Open Access Journals (Sweden)

    P.P. Moita

    2008-01-01

    Full Text Available A design and control sensitivity analysis and multicriteria optimization formulation is derived for flexible mechanical systems. This formulation is implemented in an optimum design code and it is applied to the nonlinear dynamic response. By extending the spatial domain to the space-time domain and treating the design variables as control variables that do not change with time, the design space is included in the control space. Thus, one can unify in one single formulation the problems of optimum design and optimal control. Structural dimensions as well as lumped damping and stiffness parameters plus control driven forces, are considered as decision variables. The dynamic response and its sensitivity with respect to the design and control variables are discretized via space-time finite elements, and are integrated at-once, as it is traditionally used for static response. The adjoint system approach is used to determine the design sensitivities. Design optimization numerical examples are performed. Nonlinear programming and optimality criteria may be used for the optimization process. A normalized weighted bound formulation is used to handle multicriteria problems.

  18. A finite element perspective on non-linear FFT-based micromechanical simulations

    CERN Document Server

    Zeman, Jan; Vondřejc, Jaroslav; Peerlings, Ron H J; Geers, Marc G D

    2016-01-01

    Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the Lippmann-Schwinger type integral equation. Their computational efficiency results from handling the kernel of this equation by the Fast Fourier Transform (FFT). However, the kernel is derived from an auxiliary homogeneous linear problem, which renders the extension of FFT-based schemes to non-linear problems conceptually difficult. This paper aims to establish a link between FE- and FFT-based methods, in order to develop a solver applicable to general history- and time-dependent material models. For this purpose, we follow the standard steps of the FE method, starting from the weak form, proceeding to the Galerkin discretization and the numerical quadrature, up to the solution of non-linear equilibrium equations by an iterative Newton-Krylov solver. No auxiliary linear problem is thus nee...

  19. Work-hardening behavior of mild steel under cyclic deformation at finite strains

    Energy Technology Data Exchange (ETDEWEB)

    Hu, Z. (Univ. Paris-Nord, Villetaneuse (France))

    1994-10-01

    The work-hardening behavior of mild steel under monotonic deformation at large shears and cyclic deformation under a wide range of shear amplitudes (from 3 to 34%) has been experimentally investigated and modeled. The influence of shear amplitude, the effect of the amount of pre-shear and that of pre-cyclic deformation have been studied. Considering the evolution of both polarized persistent dislocation structures and no-polarized low-energy dislocation configurations, a physically-based phenomenological model with four internal variables has been proposed. The model explains the cyclic hardening behavior at large strains, the work-hardening stagnation followed by a resumption of work-hardening under Bauschinger deformation with large pre-strains and under cyclic deformation with moderate strain amplitudes. A good qualitative and quantitative agreement has been achieved between experimental results and model predictions.

  20. Component mode synthesis and large deflection vibration of complex structures. Volume 3: Multiple-mode nonlinear free and forced vibrations of beams using finite element method

    Science.gov (United States)

    Mei, Chuh; Shen, Mo-How

    1987-01-01

    Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.

  1. Run-up on a body in waves and current. Fully nonlinear and finite-order calculations

    DEFF Research Database (Denmark)

    Büchmann, Bjarne; Ferrant, P.; Skourup, J.

    2001-01-01

    Run-up on a large fixed body in waves and current have been calculated using both a fully nonlinear time-domain boundary element model and a finite-order time-domain boundary element model, the latter being correct to second order in the wave steepness and to first-order in the current strength...

  2. Linear and non-linear stability analysis for finite difference discretizations of high-order Boussinesq equations

    DEFF Research Database (Denmark)

    Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.

    2004-01-01

    This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly non-linear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann...

  3. A lumped mass nonconforming finite element method for nonlinear parabolic integro-differential equations on anisotropic meshes

    Institute of Scientific and Technical Information of China (English)

    SHI Dong-yang; WANG Hui-min; LI Zhi-yan

    2009-01-01

    A lumped mass approximation scheme of a low order Crouzeix-Raviart type nonconforming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is derived on anisotropic meshes without referring to the traditional nonclassical elliptic projection.

  4. An Optimal Error Estimates of H1-Galerkin Expanded Mixed Finite Element Methods for Nonlinear Viscoelasticity-Type Equation

    Directory of Open Access Journals (Sweden)

    Haitao Che

    2011-01-01

    Full Text Available We investigate a H1-Galerkin mixed finite element method for nonlinear viscoelasticity equations based on H1-Galerkin method and expanded mixed element method. The existence and uniqueness of solutions to the numerical scheme are proved. A priori error estimation is derived for the unknown function, the gradient function, and the flux.

  5. Superconvergence of Continuous Finite Elements with Interpolated Coefficients for Initial Value Problems of Nonlinear Ordinary Differential Equation

    Institute of Scientific and Technical Information of China (English)

    Zhiguang Xiong; Chuanmiao Chen

    2007-01-01

    In this paper,n-degree continuous finite element method with interpolated coefficients for nonlinear initial value problem of ordinary differential equation is introduced and analyzed. An optimal superconvergence u - uh = O(hn+2),n ≥ 2,at (n + 1)-order Lobatto points in each element respectively is proved. Finally the theoretical results are tested by a numerical example.

  6. Non-Linear finite element analysis of cone penetration in layered sandy loam soil-considering precompression stress state

    Science.gov (United States)

    Axisymmetric finite element (FE) method was developed using a commercial computer program to simulate cone penetration process in layered granular soil. Soil was considered as a non-linear elastic plastic material which was modeled using variable elastic parameters of Young’s Modulus and Poisson’s r...

  7. Influence of Installation Effects on Pile Bearing Capacity in Cohesive Soils – Large Deformation Analysis Via Finite Element Method

    Directory of Open Access Journals (Sweden)

    Konkol Jakub

    2017-03-01

    Full Text Available In this paper, the whole process of pile construction and performance during loading is modelled via large deformation finite element methods such as Coupled Eulerian Lagrangian (CEL and Updated Lagrangian (UL. Numerical study consists of installation process, consolidation phase and following pile static load test (SLT. The Poznań site is chosen as the reference location for the numerical analysis, where series of pile SLTs have been performed in highly overconsolidated clay (OCR ≈ 12. The results of numerical analysis are compared with corresponding field tests and with so-called “wish-in-place” numerical model of pile, where no installation effects are taken into account. The advantages of using large deformation numerical analysis are presented and its application to the pile designing is shown.

  8. Finite-element analysis of the deformation of thin Mylar films due to measurement forces.

    Energy Technology Data Exchange (ETDEWEB)

    Baker, Michael Sean; Robinson, Alex Lockwood; Tran, Hy D.

    2012-01-01

    Significant deformation of thin films occurs when measuring thickness by mechanical means. This source of measurement error can lead to underestimating film thickness if proper corrections are not made. Analytical solutions exist for Hertzian contact deformation, but these solutions assume relatively large geometries. If the film being measured is thin, the analytical Hertzian assumptions are not appropriate. ANSYS is used to model the contact deformation of a 48 gauge Mylar film under bearing load, supported by a stiffer material. Simulation results are presented and compared to other correction estimates. Ideal, semi-infinite, and constrained properties of the film and the measurement tools are considered.

  9. Numerical simulation of mechanical deformation of semi-solid material using a level-set based finite element method

    Science.gov (United States)

    Sun, Zhidan; Bernacki, Marc; Logé, Roland; Gu, Guochao

    2017-09-01

    In this work, a level-set based finite element method was used to numerically evaluate the mechanical behavior in a small deformation range of semi-solid materials with different microstructure configurations. For this purpose, a finite element model of the semi-solid phase was built based on Voronoï diagram. Interfaces between the solid and the liquid phases were implicitly described by level-set functions coupled to an anisotropic meshing technique. The liquid phase was considered as a Newtonian fluid, whereas the behavior of the solid phase was described by a viscoplastic law. Simulations were performed to study the effect of different parameters such as solid phase fraction and solid bridging. Results show that the macroscopic mechanical behavior of semi-solid material strongly depends on the solid fraction and the local microstructure which play important roles in the formation of hot tearing. These results could provide valuable information for the processing of semi-solid materials.

  10. Numerical simulation of strain localization and damage evolution in large plastic deformation using mixed finite element method

    Institute of Scientific and Technical Information of China (English)

    Zhanghua Chen; Jiajian Jin; Jiumei Xiao

    2004-01-01

    An investigation of computer simulation is presented to analyze the effects of strain localization and damage evolution in large plastic deformation. The simulation is carried out by using an elastic-plastic-damage coupling finite element program that is developed based on the concept of mixed interpolation of displacement/pressure. This program has been incorporated into a damage mechanics model as well as the corresponding damage criterion. To illustrate the performance of the proposed approach, a typical strain localization problem has been simulated. The results show that the proposed approach is of good capability to capture strain localization and predict the damage evolution.

  11. Persistent inflation at Aira caldera accompanying explosive activity at Sakurajima volcano: Constraining deformation source parameters from Finite Element inversions

    Science.gov (United States)

    Hickey, James; Gottsmann, Jo; Iguchi, Masato; Nakamichi, Haruhisa

    2015-04-01

    Aira caldera is located within Kagoshima Bay at the southern end of Kyushu, Japan. Sakurajima is an active post-caldera andesitic stratovolcano that sits on the caldera's southern rim. Despite frequent Vulcanian-type explosive activity, the area is experiencing continued uplift at a maximum rate of approximately 1.5 cm/yr with a footprint of 40 km, indicating that magma is being supplied faster than it is erupted. This is of particular concern as the amplitude of deformation is approaching the level inferred prior to the 1914 VEI 4 eruption. Using GPS data from 1996 - 2007 we explore causes for the uplift. To solve for the optimum deformation source parameters we use an inverse Finite Element method accounting for three-dimensional material heterogeneity (inferred from seismic tomography) and the surrounding topography of the region. The same inversions are also carried out using Finite Element models that incorporate simplified homogeneous or one-dimensional subsurface material properties, with and without topography. Results from the comparison of the six different models show statistically significant differences in the inferred deformation sources. This indicates that both subsurface heterogeneity and surface topography are essential in geodetic modelling to extract the most realistic deformation source parameters. The current best-fit source sits within a seismic low-velocity zone in the north-east of the caldera at a depth of approximately 14 km with a volume increase of 1.2 x 108 m3. The source location underlies a region of active underwater fumaroles within the Wakamiko crater and differs significantly from previous analytical modelling results. Seismic data further highlights areas of high seismic attenuation as well as large aseismic zones, both of which could allude to inelastic behaviour and a significant heat source at depth. To integrate these observations, subsequent forward Finite Element models will quantify the importance of rheology and

  12. Finite Element Modeling of Passive Material Influence on the Deformation and Force Output of Skeletal Muscle

    OpenAIRE

    Hodgson, John A.; Chi, Sheng-Wei; Yang, Judy P.; Chen, Jiun-Shyan; Edgerton, V. Reggie; Sinha, Shantanu

    2012-01-01

    The pattern of deformation of the different structural components of a muscle-tendon complex when it is activated provides important information about the internal mechanics of the muscle. Recent experimental observations of deformations in contracting muscle have presented inconsistencies with current widely held assumption about muscle behavior. These include negative strain in aponeuroses, non-uniform strain changes in sarcomeres, even of individual muscle fibers and evidence that muscle f...

  13. Mitral valve finite element modeling: implications of tissues' nonlinear response and annular motion.

    Science.gov (United States)

    Stevanella, Marco; Votta, Emiliano; Redaelli, Alberto

    2009-12-01

    Finite element modeling represents an established method for the comprehension of the mitral function and for the simulation of interesting clinical scenarios. However, current models still do not include all the key aspects of the real system. We implemented a new structural finite element model that considers (i) an accurate morphological description of the valve, (ii) a description of the tissues' mechanical properties that accounts for anisotropy and nonlinearity, and (iii) dynamic boundary conditions that mimic annulus and papillary muscles' contraction. The influence of such contraction on valve biomechanics was assessed by comparing the computed results with the ones obtained through an auxiliary model with fixed annulus and papillary muscles. At the systolic peak, the leaflets' maximum principal stress contour showed peak values in the anterior leaflet at the strut chordae insertion zone (300 kPa) and near the annulus (200-250 kPa), while much lower values were detected in the posterior leaflet. Both leaflets underwent larger tensile strains in the longitudinal direction, while in the circumferential one the anterior leaflet experienced nominal tensile strains up to 18% and the posterior one experienced compressive strains up to 23% associated with the folding of commissures and paracommissures, consistently with tissue redundancy. The force exerted by papillary muscles at the systolic peak was equal to 4.11 N, mainly borne by marginal chordae (76% of the force). Local reaction forces up to 45 mN were calculated on the annulus, leading to tensions of 89 N/m and 54 N/m for its anterior and posterior tracts, respectively. The comparison with the results of the auxiliary model showed that annular contraction mainly affects the leaflets' circumferential strains. When it was suppressed, no more compressive strains could be observed and peak strain values were located in the belly of the anterior leaflet. Computational results agree to a great extent with

  14. Modeling energy storage and structural evolution during finite viscoplastic deformation of glassy polymers

    Science.gov (United States)

    Xiao, Rui; Ghazaryan, Gagik; Tervoort, Theo A.; Nguyen, Thao D.

    2017-06-01

    The enthalpic response of amorphous polymers depends strongly on their thermal and deformation history. Annealing just below the glass transition temperature (Tg) causes a large endothermic overshoot of the isobaric heat capacity at Tg as measured by differential scanning calorimetry, while plastic deformation (cold work) can erase this overshoot and create an exothermic undershoot. This indicates that a strong coupling exists between the polymer structure, thermal response, and mechanical deformation. In this work, we apply a recently developed thermomechanical model for glassy polymers that couples structural evolution and viscoplastic deformation to investigate the effect of annealing and plastic deformation on the accumulation of stored energy during cold work and calorimetry measurements of heat flow. The thermomechanical model introduces the effective temperature as an additional state variable in a nonequilibrium thermodynamics setting to describe the structural evolution of the material. The results show that the model accurately describes the stress and enthalpy response of quenched and annealed polymers with different plastic predeformations. The model also shows that at 30% strain in uniaxial compression, 45% of the applied work is converted into stored energy, which is consistent with experimental data from literature.

  15. New version of Optimal Homotopy Asymptotic Method for the solution of nonlinear boundary value problems in finite and infinite intervals

    Directory of Open Access Journals (Sweden)

    Liaqat Ali

    2016-09-01

    Full Text Available In this research work a new version of Optimal Homotopy Asymptotic Method is applied to solve nonlinear boundary value problems (BVPs in finite and infinite intervals. It comprises of initial guess, auxiliary functions (containing unknown convergence controlling parameters and a homotopy. The said method is applied to solve nonlinear Riccati equations and nonlinear BVP of order two for thin film flow of a third grade fluid on a moving belt. It is also used to solve nonlinear BVP of order three achieved by Mostafa et al. for Hydro-magnetic boundary layer and micro-polar fluid flow over a stretching surface embedded in a non-Darcian porous medium with radiation. The obtained results are compared with the existing results of Runge-Kutta (RK-4 and Optimal Homotopy Asymptotic Method (OHAM-1. The outcomes achieved by this method are in excellent concurrence with the exact solution and hence it is proved that this method is easy and effective.

  16. Nonlinear analysis of drainage systems to examine surface deformation: an example from Potwar Plateau (Northern Pakistan)

    Science.gov (United States)

    Shahzad, F.; Mahmood, S. A.; Gloaguen, R.

    2010-03-01

    We devise a procedure in order to characterize the relative vulnerability of the Earth's surface to tectonic deformation using the geometrical characteristics of drainage systems. The present study focuses on the nonlinear analysis of drainage networks extracted from Digital Elevation Models in order to localize areas strongly influenced by tectonics. We test this approach on the Potwar Plateau in northern Pakistan. This area is regularly affected by damaging earthquakes. Conventional studies cannot pinpoint the zones at risk, as the whole region is characterized by a sparse and diffuse seismicity. Our approach is based on the fact that rivers tend to linearize under tectonic forcing. Thus, the low fractal dimensions of the Swan, Indus and Jehlum Rivers are attributed to neotectonic activity. A detailed textural analysis is carried out to investigate the linearization, heterogeneity and connectivity of the drainage patterns. These textural aspects are quantified using the fractal dimension, as well as lacunarity and succolarity analysis. These three methods are complimentary in nature, i.e. objects with similar fractal dimensions can be distinguished further with lacunarity and/or succolarity analysis. We generate maps of fractal dimensions, lacunarity and succolarity values using a sliding window of 2.5 arc minutes by 2.5 arc minutes (2.5'×2.5'). These maps are then interpreted in terms of land surface vulnerability to tectonics. This approach allowed us to localize several zones where the drainage system is highly structurally controlled on the Potwar Plateau. The region located between Muree and Muzaffarabad is found to be prone to destructive events whereas the area westward from the Indus seems relatively unaffected. We conclude that a nonlinear analysis of the drainage system is an efficient additional tool to locate areas likely to be affected by massive destructing events affecting the Earth's surface and therefore threaten human activities.

  17. Nonlinear analysis of drainage systems to examine surface deformation: an example from Potwar Plateau (Northern Pakistan

    Directory of Open Access Journals (Sweden)

    F. Shahzad

    2010-03-01

    Full Text Available We devise a procedure in order to characterize the relative vulnerability of the Earth's surface to tectonic deformation using the geometrical characteristics of drainage systems. The present study focuses on the nonlinear analysis of drainage networks extracted from Digital Elevation Models in order to localize areas strongly influenced by tectonics. We test this approach on the Potwar Plateau in northern Pakistan. This area is regularly affected by damaging earthquakes. Conventional studies cannot pinpoint the zones at risk, as the whole region is characterized by a sparse and diffuse seismicity. Our approach is based on the fact that rivers tend to linearize under tectonic forcing. Thus, the low fractal dimensions of the Swan, Indus and Jehlum Rivers are attributed to neotectonic activity. A detailed textural analysis is carried out to investigate the linearization, heterogeneity and connectivity of the drainage patterns. These textural aspects are quantified using the fractal dimension, as well as lacunarity and succolarity analysis. These three methods are complimentary in nature, i.e. objects with similar fractal dimensions can be distinguished further with lacunarity and/or succolarity analysis. We generate maps of fractal dimensions, lacunarity and succolarity values using a sliding window of 2.5 arc minutes by 2.5 arc minutes (2.5'×2.5'. These maps are then interpreted in terms of land surface vulnerability to tectonics. This approach allowed us to localize several zones where the drainage system is highly structurally controlled on the Potwar Plateau. The region located between Muree and Muzaffarabad is found to be prone to destructive events whereas the area westward from the Indus seems relatively unaffected. We conclude that a nonlinear analysis of the drainage system is an efficient additional tool to locate areas likely to be affected by massive destructing events affecting the Earth's surface and therefore threaten human

  18. COYOTE : a finite element computer program for nonlinear heat conduction problems. Part I, theoretical background.

    Energy Technology Data Exchange (ETDEWEB)

    Glass, Micheal W.; Hogan, Roy E., Jr.; Gartling, David K.

    2010-03-01

    The need for the engineering analysis of systems in which the transport of thermal energy occurs primarily through a conduction process is a common situation. For all but the simplest geometries and boundary conditions, analytic solutions to heat conduction problems are unavailable, thus forcing the analyst to call upon some type of approximate numerical procedure. A wide variety of numerical packages currently exist for such applications, ranging in sophistication from the large, general purpose, commercial codes, such as COMSOL, COSMOSWorks, ABAQUS and TSS to codes written by individuals for specific problem applications. The original purpose for developing the finite element code described here, COYOTE, was to bridge the gap between the complex commercial codes and the more simplistic, individual application programs. COYOTE was designed to treat most of the standard conduction problems of interest with a user-oriented input structure and format that was easily learned and remembered. Because of its architecture, the code has also proved useful for research in numerical algorithms and development of thermal analysis capabilities. This general philosophy has been retained in the current version of the program, COYOTE, Version 5.0, though the capabilities of the code have been significantly expanded. A major change in the code is its availability on parallel computer architectures and the increase in problem complexity and size that this implies. The present document describes the theoretical and numerical background for the COYOTE program. This volume is intended as a background document for the user's manual. Potential users of COYOTE are encouraged to become familiar with the present report and the simple example analyses reported in before using the program. The theoretical and numerical background for the finite element computer program, COYOTE, is presented in detail. COYOTE is designed for the multi-dimensional analysis of nonlinear heat conduction

  19. Nonlinear Thermo-mechanical Finite Element Analysis of Polymer Foam Cored Sandwich Structures including Geometrical and Material Nonlinearity

    DEFF Research Database (Denmark)

    Palleti, Hara Naga Krishna Teja; Thomsen, Ole Thybo; Taher, Siavash Talebi;

    In this paper, polymer foam cored sandwich structures with fibre reinforced composite face sheets subjected to combined mechanical and thermal loads will be analysed using the commercial FE code ABAQUS® incorporating both material and geometrical nonlinearity. Large displacements and rotations ar...... are included in the analysis. The full nonlinear stress-strain curves up to failure will be considered for the polymer foams at different temperatures to study the effect of material nonlinearity in detail....

  20. Nonlinear finite element model updating for damage identification of civil structures using batch Bayesian estimation

    Science.gov (United States)

    Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.; de Callafon, Raymond A.

    2017-02-01

    This paper presents a framework for structural health monitoring (SHM) and damage identification of civil structures. This framework integrates advanced mechanics-based nonlinear finite element (FE) modeling and analysis techniques with a batch Bayesian estimation approach to estimate time-invariant model parameters used in the FE model of the structure of interest. The framework uses input excitation and dynamic response of the structure and updates a nonlinear FE model of the structure to minimize the discrepancies between predicted and measured response time histories. The updated FE model can then be interrogated to detect, localize, classify, and quantify the state of damage and predict the remaining useful life of the structure. As opposed to recursive estimation methods, in the batch Bayesian estimation approach, the entire time history of the input excitation and output response of the structure are used as a batch of data to estimate the FE model parameters through a number of iterations. In the case of non-informative prior, the batch Bayesian method leads to an extended maximum likelihood (ML) estimation method to estimate jointly time-invariant model parameters and the measurement noise amplitude. The extended ML estimation problem is solved efficiently using a gradient-based interior-point optimization algorithm. Gradient-based optimization algorithms require the FE response sensitivities with respect to the model parameters to be identified. The FE response sensitivities are computed accurately and efficiently using the direct differentiation method (DDM). The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem by computing the exact Fisher Information matrix using the FE response sensitivities with respect to the model parameters. The accuracy of the proposed uncertainty quantification approach is verified using a sampling approach based on the unscented transformation. Two validation studies, based on realistic

  1. Nonlinear visco-elastic finite element analysis of different porcelain veneers configuration.

    Science.gov (United States)

    Sorrentino, Roberto; Apicella, Davide; Riccio, Carlo; Gherlone, Enrico; Zarone, Fernando; Aversa, Raffaella; Garcia-Godoy, Franklin; Ferrari, Marco; Apicella, Antonio

    2009-11-01

    This study is aimed at evaluating the biomechanical behavior of feldspathic versus alumina porcelain veneers. A 3D numerical model of a maxillary central incisor, with the periodontal ligament (PDL) and the alveolar bone was generated. Such model was made up of four main volumes: dentin, enamel, cement layer and veneer. Incisors restored with alumina and feldspathic porcelain veneers were compared with a natural sound tooth (control). Enamel, cementum, cancellous and cortical bone were considered as isotropic elastic materials; on the contrary, the tubular structure of dentin was designed as elastic orthotropic. The nonlinear visco-elatic behavior of the PDL was considered. The veneer volumes were coupled with alumina and feldspathic porcelain mechanical properties. The adhesive layers were modeled in the FE environment using spring elements. A 50N load applied at 60 degrees angle with tooth longitudinal axis was applied and validated. Compressive stresses were concentrated on the external surface of the buccal side of the veneer close to the incisal margin; such phenomenon was more evident in the presence of alumina. Tensile stresses were negligible when compared to compressive ones. Alumina and feldspathic ceramic were characterized by a different biomechanical behavior in terms of elastic deformations and stress distributions. The ultimate strength of both materials was not overcome in the performed analysis.

  2. Explicit Nonlinear Finite Element Geometric Analysis of Parabolic Leaf Springs under Various Loads

    Science.gov (United States)

    Kong, Y. S.; Omar, M. Z.; Chua, L. B.; Abdullah, S.

    2013-01-01

    This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability. PMID:24298209

  3. The calculation of steady non-linear transonic flow over finite wings with linear theory aerodynamics

    Science.gov (United States)

    Cunningham, A. M., Jr.

    1976-01-01

    The feasibility of calculating steady mean flow solutions for nonlinear transonic flow over finite wings with a linear theory aerodynamic computer program is studied. The methodology is based on independent solutions for upper and lower surface pressures that are coupled through the external flow fields. Two approaches for coupling the solutions are investigated which include the diaphragm and the edge singularity method. The final method is a combination of both where a line source along the wing leading edge is used to account for blunt nose airfoil effects; and the upper and lower surface flow fields are coupled through a diaphragm in the plane of the wing. An iterative solution is used to arrive at the nonuniform flow solution for both nonlifting and lifting cases. Final results for a swept tapered wing in subcritical flow show that the method converges in three iterations and gives excellent agreement with experiment at alpha = 0 deg and 2 deg. Recommendations are made for development of a procedure for routine application.

  4. Optimization of elstomeric micro-fluidic valve dimensions using non-linear finite element methods

    Directory of Open Access Journals (Sweden)

    H Khawaja

    2016-04-01

    Full Text Available We use a nonlinear finite element (FE method model to compare,optimize and determine the limits for useful geometries of microfluidicvalves in elastomer polydimethylsiloxane (PDMS. Simulations havebeen performed with the aim of finding the optimal shape, size andlocation of pressurization that minimizes the pressure required to operatethe valve. One important constraint governing the design parameters isthat the stresses should be within elastic limits, so that the componentremains safe from any type of structural failure. To obtain reliable results,non-linear stress analysis was performed using the Mooney-Rivlin 9parameter approximation which is based on the Hyper Elastic MaterialModel. A 20 noded brick element was used for the development of FEmodel. Mesh sensitivity analysis was also performed to assess the qualityof the results. The simulations were performed with commerciallyavailable FE modeling software, developed by ANSYS Inc. to determinethe effect of varying different geometric parameters on the performanceof micro-fluidic valves.The aim of this work is to determine the geometry of the channel crosssectionthat would result in the largest deflection for the least appliedpressure, i.e. to minimize the pressure needed to operate the valve.

  5. Nonlinear Brillouin amplification of finite-duration seeds in the strong coupling regime

    Science.gov (United States)

    Lehmann, G.; Spatschek, K. H.

    2013-07-01

    Parametric plasma processes received renewed interest in the context of generating ultra-intense and ultra-short laser pulses up to the exawatt-zetawatt regime. Both Raman as well as Brillouin amplifications of seed pulses were proposed. Here, we investigate Brillouin processes in the one-dimensional (1D) backscattering geometry with the help of numerical simulations. For optimal seed amplification, Brillouin scattering is considered in the so called strong coupling (sc) regime. Special emphasis lies on the dependence of the amplification process on the finite duration of the initial seed pulses. First, the standard plane-wave instability predictions are generalized to pulse models, and the changes of initial seed pulse forms due to parametric instabilities are investigated. Three-wave-interaction results are compared to predictions by a new (kinetic) Vlasov code. The calculations are then extended to the nonlinear region with pump depletion. Generation of different seed layers is interpreted by self-similar solutions of the three-wave interaction model. Similar to Raman amplification, shadowing of the rear layers by the leading layers of the seed occurs. The shadowing is more pronounced for initially broad seed pulses. The effect is quantified for Brillouin amplification. Kinetic Vlasov simulations agree with the three-wave interaction predictions and thereby affirm the universal validity of self-similar layer formation during Brillouin seed amplification in the strong coupling regime.

  6. Non-linear finite element simulations of injuries with free boundaries: application to surgical wounds

    Science.gov (United States)

    Valero, C.; Javierre, E.; García-Aznar, J. M.; Gómez-Benito, M. J.

    2015-01-01

    SUMMARY Wound healing is a process driven by biochemical and mechanical variables in which new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Due to the regularity of this morphology, we approximate the evolution of the wound through its cross-section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem while maintaining allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the non-linear problem we use the Finite Element Method and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds. PMID:24443355

  7. Nonlinear finite element simulations of injuries with free boundaries: application to surgical wounds.

    Science.gov (United States)

    Valero, C; Javierre, E; García-Aznar, J M; Gómez-Benito, M J

    2014-06-01

    Wound healing is a process driven by biochemical and mechanical variables in which a new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work, we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Because of the regularity of this morphology, we approximate the evolution of the wound through its cross section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem; while allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction, we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the nonlinear problem, we use the finite element method (FEM) and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds. Copyright © 2014 John Wiley & Sons, Ltd.

  8. Explicit nonlinear finite element geometric analysis of parabolic leaf springs under various loads.

    Science.gov (United States)

    Kong, Y S; Omar, M Z; Chua, L B; Abdullah, S

    2013-01-01

    This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability.

  9. Explicit Nonlinear Finite Element Geometric Analysis of Parabolic Leaf Springs under Various Loads

    Directory of Open Access Journals (Sweden)

    Y. S. Kong

    2013-01-01

    Full Text Available This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability.

  10. PyLith: A Finite-Element Code for Modeling Quasi-Static and Dynamic Crustal Deformation

    Science.gov (United States)

    Aagaard, B.; Williams, C. A.; Knepley, M. G.

    2011-12-01

    We have developed open-source finite-element software for 2-D and 3-D dynamic and quasi-static modeling of crustal deformation. This software, PyLith (current release is version 1.6) can be used for quasi-static viscoelastic modeling, dynamic spontaneous rupture and/or ground-motion modeling. Unstructured and structured finite-element discretizations allow for spatial scales ranging from tens of meters to hundreds of kilometers with temporal scales in dynamic problems ranging from milliseconds to minutes and temporal scales in quasi-static problems ranging from minutes to thousands of years. PyLith development is part of the NSF funded Computational Infrastructure for Geodynamics (CIG) and the software runs on a wide variety of platforms (laptops, workstations, and Beowulf clusters). Binaries (Linux, Darwin, and Windows systems) and source code are available from geodynamics.org. PyLith uses a suite of general, parallel, graph data structures called Sieve for storing and manipulating finite-element meshes. This permits use of a variety of 2-D and 3-D cell types including triangles, quadrilaterals, hexahedra, and tetrahedra. Current PyLith features include prescribed fault ruptures with multiple earthquakes and aseismic creep, spontaneous fault ruptures with a variety of fault constitutive models, time-dependent Dirichlet and Neumann boundary conditions, absorbing boundary conditions, time-dependent point forces, and gravitational body forces. PyLith supports infinitesimal and small strain formulations for linear elastic rheologies, linear and generalized Maxwell viscoelastic rheologies, power-law viscoelastic rheologies, and Drucker-Prager elastoplastic rheologies. Current software development focuses on coupling quasi-static and dynamic simulations to resolve multi-scale deformation across the entire seismic cycle and the coupling of elasticity to heat and/or fluid flow.

  11. An Anthropometric-Based Subject-Specific Finite Element Model of the Human Breast for Predicting Large Deformations

    Science.gov (United States)

    Pianigiani, Silvia; Ruggiero, Leonardo; Innocenti, Bernardo

    2015-01-01

    The large deformation of the human breast threatens proper nodules tracking when the subject mammograms are used as pre-planning data for biopsy. However, techniques capable of accurately supporting the surgeons during biopsy are missing. Finite element (FE) models are at the basis of currently investigated methodologies to track nodules displacement. Nonetheless, the impact of breast material modeling on the mechanical response of its tissues (e.g., tumors) is not clear. This study proposes a subject-specific FE model of the breast, obtained by anthropometric measurements, to predict breast large deformation. A healthy breast subject-specific FE parametric model was developed and validated by Cranio-caudal (CC) and Medio-Lateral Oblique (MLO) mammograms. The model was successively modified, including nodules, and utilized to investigate the effect of nodules size, typology, and material modeling on nodules shift under the effect of CC, MLO, and gravity loads. Results show that a Mooney–Rivlin material model can estimate healthy breast large deformation. For a pathological breast, under CC compression, the nodules displacement is very close to zero when a linear elastic material model is used. Finally, when nodules are modeled, including tumor material properties, under CC, or MLO or gravity loads, nodules shift shows ~15% average relative difference. PMID:26734604

  12. On mixed and displacement finite element models of a refined shear deformation theory for laminated anisotropic plates

    Science.gov (United States)

    Reddy, J. N.

    1986-01-01

    An improved plate theory that accounts for the transverse shear deformation is presented, and mixed and displacement finite element models of the theory are developed. The theory is based on an assumed displacement field in which the inplane displacements are expanded in terms of the thickness coordinate up to the cubic term and the transverse deflection is assumed to be independent of the thickness coordinate. The governing equations of motion for the theory are derived from the Hamilton's principle. The theory eliminates the need for shear correction factors because the transverse shear stresses are represented parabolically. A mixed finite element model that uses independent approximations of the displacements and moments, and a displacement model that uses only displacements as degrees of freedom are developed. A comparison of the numerical results for bending with the exact solutions of the new theory and the three-dimensional elasticity theory shows that the present theory (and hence the finite element models) is more accurate than other plate-theories of the same order.

  13. A Nonlinear Finite Element Method for Magnetoelectric Composite and the Study on the Influence of Interfacial Bonding

    Directory of Open Access Journals (Sweden)

    He-Ling Wang

    2013-01-01

    Full Text Available Magnetoelectric composite material is effective in transferring magnetic field into electric signal. In this paper, a nonlinear finite element method is present to model the magnetoelectric composite of ferroelectric and magnetostrictive material. In the method, the nonlinear and coupling behavior of magnetostrictive material such as Terfenol-D is considered. The nonuniform magnetic, electric, and mechanical field distributions are present. An interfacial transferring coefficient is defined to investigate the performance of interfacial mechanical coupling quantitatively, and the influence of the properties of interfacial bonding material and interfacial cracks on magnetoelectric coefficient is discussed. A new laminate ME composite of curved interface is proposed to overcome weak interfacial bonding.

  14. Effects of Radius and Orientation of Single-Walled Carbon Nanotubes on Their Nonlinear Tensile Deformation Behaviour

    Institute of Scientific and Technical Information of China (English)

    WANG Yu; FANG Dai-Ning; SOH Ai-Kah; LIU Bin

    2007-01-01

    @@ By capturing the atomic information and reflecting the behaviour governed by a nonlinear potential function, an analytical molecular mechanics approach is applied to establish the constitutive relation for single-walled carbon nanotubes (SWCNTs). The nonlinear tensile deformation curves of zigzag and armchair nanotubes with different radii are predicted, and the elastic properties of these SWCNTs are obtained. A conclusion is made that the nanotube radius has little effect on the mechanical behaviour of SWCNTs subject to simple tension, while the nanotube orientation has larger influence.

  15. Stress and Deformation Analysis in Base Isolation Elements Using the Finite Element Method

    Directory of Open Access Journals (Sweden)

    Claudiu Iavornic

    2011-01-01

    Full Text Available In Modern tools as Finite Element Method can be used to study the behavior of elastomeric isolation systems. The simulation results obtained in this way provide a large series of data about the behavior of elastomeric isolation bearings under different types of loads and help in taking right decisions regarding geometrical optimizations needed for improve such kind of devices.

  16. Integration of Large Deformation Finite Element Formulations in Flexible Multibody System Algorithms

    Science.gov (United States)

    2010-07-01

    project, the relationship between the B-spline and NURBS , which are widely used in the geometric modeling; and the ANCF finite elements was...required for the Bezier, B-spline and NURBS geometry. To this end, a coordinate transformation is used to write the ANCF gradient vectors in terms of

  17. Real-time volumetric deformable models for surgery simulation using finite elements and condensation

    DEFF Research Database (Denmark)

    Bro-Nielsen, Morten; Cotin, S.

    1996-01-01

    This paper discusses the application of SD solid volumetric Finite Element models to surgery simulation. In particular it introduces three new ideas for solving the problem of achieving real-time performance for these models. The simulation system we have developed is described and we demonstrate...

  18. Real-time volumetric deformable models for surgery simulation using finite elements and condensation

    DEFF Research Database (Denmark)

    Bro-Nielsen, Morten; Cotin, S.

    1996-01-01

    This paper discusses the application of SD solid volumetric Finite Element models to surgery simulation. In particular it introduces three new ideas for solving the problem of achieving real-time performance for these models. The simulation system we have developed is described and we demonstrate...

  19. Linear and nonlinear optical response of one-dimensional semiconductors: finite-size and Franz–Keldysh effects

    Science.gov (United States)

    Bonabi, Farzad; Pedersen, Thomas G.

    2017-04-01

    The dipole moment formalism for the optical response of finite electronic structures breaks down in infinite ones, for which a momentum-based method is better suited. Focusing on simple chain structures, we compare the linear and nonlinear optical response of finite and infinite one-dimensional semiconductors. This comparison is then extended to cases including strong electro-static fields breaking translational invariance. For large electro-static fields, highly non-perturbative Franz–Keldysh (FK) features are observed in both linear and nonlinear spectra. It is demonstrated that dipole and momentum formalisms agree in the limit of large structures provided the intraband momentum contributions are carefully treated. This convergence is established even in the presence of non-perturbative electro-static fields.

  20. How simple can nonlinear finite element modelling be for structural concrete?

    Directory of Open Access Journals (Sweden)

    Argirova, G.

    2014-12-01

    Full Text Available This paper discusses on the required level of simplicity for suitable modelling of structural concrete. Traditional equilibrium- based approaches (as strut-and-tie models are too coarse in some cases, as they account for the cracking state of concrete in a sometimes excessively simplified manner. The alternative of complex nonlinear numerical modelling is also not always satisfactory for design as the number of parameters required, their definition and the sensitivity of the structural response to them is complex and requires a high level of experience. Contrary to these approaches, this paper introduces the elastic plastic stress field method. This method is grounded on the theory of plasticity but allows considering deformation compatibility. The results are consistent both in terms of the strength and deformation field of the member. It also has the advantage of requiring only two physical material properties (modulus of elasticity and plastic strength which can be easily determined by designers.Este artículo discute sobre el nivel de sencillez ideal para un análisis no lineal de elementos de hormigón estructural. Los métodos de cálculo basados únicamente en condiciones de equilibrio (como los modelos de bielas-y-tirantes no son siempre adecuados ya que el estado de fisuración del hormigón se considera a veces de una manera excesivamente simplificada. Los análisis no lineales complejos tampoco son siempre adecuados, ya que el número de parámetros requeridos, su definición y la sensibilidad de la respuesta del elemento a sus variaciones requieren una gran experiencia. Como alternativa, se presenta el método de los campos de tensiones elasto-plásticos. Este método se basa en la teoría de la plasticidad pero incorporando condiciones de compatibilidad. Los resultados son coherentes en términos de resistencia y de deformaciones. Además, sólo necesita la definición de dos parámetros mecánicos (módulo de elasticidad y

  1. Nonlinear Stochastic H∞ Control with Markov Jumps and (x,u,v-Dependent Noise: Finite and Infinite Horizon Cases

    Directory of Open Access Journals (Sweden)

    Li Sheng

    2014-01-01

    Full Text Available This paper is concerned with the H∞ control problem for nonlinear stochastic Markov jump systems with state, control, and external disturbance-dependent noise. By means of inequality techniques and coupled Hamilton-Jacobi inequalities, both finite and infinite horizon H∞ control designs of such systems are developed. Two numerical examples are provided to illustrate the effectiveness of the proposed design method.

  2. Development of a nonlinear 3D solid finite element model for the calculation of bending moments of flexural members

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    A numerical model is developed in this paper to calculate the bending moments of flexural members through integration in 3D solid finite element analyses according to the nonlinear constitutive model of concrete and the elastoplastic constitutive model of steel,utilizing the stress condition of the cross-section,considering the destruction characteristic of reinforced concrete members,and based on the plane cross-section assumption.The results of this model give good agreement with those of the classical me...

  3. On the roles of minimization and linearization in least-squares finite element models of nonlinear boundary-value problems

    Science.gov (United States)

    Payette, G. S.; Reddy, J. N.

    2011-05-01

    In this paper we examine the roles of minimization and linearization in the least-squares finite element formulations of nonlinear boundary-values problems. The least-squares principle is based upon the minimization of the least-squares functional constructed via the sum of the squares of appropriate norms of the residuals of the partial differential equations (in the present case we consider L2 norms). Since the least-squares method is independent of the discretization procedure and the solution scheme, the least-squares principle suggests that minimization should be performed prior to linearization, where linearization is employed in the context of either the Picard or Newton iterative solution procedures. However, in the least-squares finite element analysis of nonlinear boundary-value problems, it has become common practice in the literature to exchange the sequence of application of the minimization and linearization operations. The main purpose of this study is to provide a detailed assessment on how the finite element solution is affected when the order of application of these operators is interchanged. The assessment is performed mathematically, through an examination of the variational setting for the least-squares formulation of an abstract nonlinear boundary-value problem, and also computationally, through the numerical simulation of the least-squares finite element solutions of both a nonlinear form of the Poisson equation and also the incompressible Navier-Stokes equations. The assessment suggests that although the least-squares principle indicates that minimization should be performed prior to linearization, such an approach is often impractical and not necessary.

  4. Application of Finite Element Method of Numerical Modelling to Understand Toe Buckling Deformation in the Southern Alps of New Zealand.

    Science.gov (United States)

    Ridl, Romy; Bell, David; Villeneuve, Marlene

    2017-04-01

    Toe buckling deformation is a temporal product of induced stresses concentrated at the base of a slope. Prolonged induced stresses may lead to yielding of an anisotropic rock mass, either through rheological creep deformation (flexural toe buckling) or brittle failure (hinge buckling). Progressive deformation can lead to the breakout at the buckled toe and ultimately result in deep seated displacements on a mountain range scale, referred to as deep seated gravitational slope deformation (DSGSD). DSGSD can have a considerable impact on civil infrastructure and should be well understood for hazard identification, to inform civil engineering design and for resource management purposes. Toe buckling deformation was identified beneath the basal sliding zone of three large (≥50 Mm3) landslides in the Cromwell Gorge, New Zealand. This area was subjected to extensive geotechnical investigations for the Clyde Hydropower Scheme. During these investigations seventeen major landslides were identified in the Cromwell Gorge and subsequently stabilised. The data from the landslide stabilisation project, including 26.7 km of boreholes and 9 km of tunnels, for the three landslides exhibiting toe buckling was made available for this study. This comprehensive database has enabled comparison and validation of numerical simulations carried out for the Cromwell Gorge. The application of numerical modelling has demonstrated that toe buckling within the Cromwell Gorge is a result of the combination of induced stresses acting on an anisotropic schistose rock mass. The induced stresses comprise: i) topographically-induced gravitational stresses parallel to the slope, associated with the evolution of the Cromwell Gorge from a relatively low relief surface to present day topography (1400 m deep valley), and ii) active far-field tectonic stresses associated with the obliquely convergent stress regime of the Australian-Pacific continent plate boundary. Finite Element Method (FEM) numerical

  5. On Advantages of the Kelvin Mapping in Finite Element Implementations of Deformation Processes

    CERN Document Server

    Nagel, Thomas; Moerman, Kevin M; Kolditz, Olaf

    2016-01-01

    Classical continuum mechanical theories operate on three-dimensional Eu-clidian space using scalar, vector, and tensor-valued quantities usually up to the order of four. For their numerical treatment, it is common practice to transform the relations into a matrix-vector format. This transformation is usually performed using the so-called Voigt mapping. This mapping does not preserve tensor character leaving significant room for error as stress and strain quantities follow from different mappings and thus have to be treated differently in certain mathematical operations. Despite its conceptual and notational difficulties having been pointed out, the Voigt mapping remains the foundation of most current finite element programmes. An alternative is the so-called Kelvin mapping which has recently gained recognition in studies of theoretical mechanics. This article is concerned with benefits of the Kelvin mapping in numerical modelling tools such as finite element software. The decisive difference to the Voigt mapp...

  6. Continuum Multiscale Modeling of Finite Deformation Plasticity and Anisotropic Damage in Polycrystals

    Science.gov (United States)

    2006-09-01

    neighboring grains cannot be spa- tially resolved. 3.5. Homogenization of damage Effects from mechanisms modeled individually— elastoplasticity within each...crystal plasticity routines are available, as the damage computations are effectively uncoupled from the constitutive update of the elastoplastic response... elastoplasticity and damage : multiscale kinematics, Int. J. Solids Struct. 40 (2003) 5669–5688. [17] C. Teodosiu, F. Sidoroff, A finite theory of

  7. Implementation of the full viscoresistive magnetohydrodynamic equations in a nonlinear finite element code

    Energy Technology Data Exchange (ETDEWEB)

    Haverkort, J.W. [Centrum Wiskunde & Informatica, P.O. Box 94079, 1090 GB Amsterdam (Netherlands); Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Blank, H.J. de [Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Huysmans, G.T.A. [ITER Organization, Route de Vinon sur Verdon, 13115 Saint Paul Lez Durance (France); Pratt, J. [Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Koren, B., E-mail: b.koren@tue.nl [Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands)

    2016-07-01

    Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more complete modeling through the full MHD equations is addressed here. Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity. The problem of ensuring continuity of solutions in the center of a polar grid is addressed in the context of a finite element discretization of the full MHD equations. A rigorous and generally applicable solution is proposed here. Useful analytical test cases are devised to verify the correct implementation of the momentum and induction equation, the hyperdiffusive terms, and the accuracy with which highly anisotropic diffusion can be simulated. A striking observation is that highly anisotropic diffusion can be treated with the same order of accuracy as isotropic diffusion, even on non-aligned grids, as long as these grids are generated with sufficient care. This property is shown to be associated with our use of a magnetic vector potential to describe the magnetic field. Several well-known instabilities are simulated to demonstrate the capabilities of the new method. The linear growth rate of an internal kink mode and a tearing mode are benchmarked against the results of a linear MHD code. The evolution of a tearing mode and the resulting magnetic islands are simulated well into the nonlinear regime. The results are compared with predictions from the reduced MHD model. Finally, a simulation of a ballooning mode illustrates the possibility to use our method as an ideal MHD method without the need to add any physical dissipation.

  8. Efficiency of wave impeding barrier in pipeline construction under earthquake excitation using nonlinear finite element analysis

    Indian Academy of Sciences (India)

    Fatih Goktepe; H Serdar Kuyuk; Erkan Celebi

    2014-04-01

    Earthquakes have caused colossal casualties and severe damages to engineering structures and especially leading to substantial economic loss to the underground structures and/or infrastructures. Pipelines are one of most important component of lifeline engineering. For instance, the Southern Caucasus- Eastern Turkey energy corridors are formed by several key pipelines carrying crude oil and natural gas from Azerbaijan, via Georgia, to world markets through Mediterranean Sea. Many project accomplished recently and construction of new corridors are still going on. They should be protected from earthquake disaster especially when they pass through high seismicity zones. The installation of wave impeding barriers (WIB) below the vulnerable infrastructures as pipelines established in soft soil can be used to reduce the effect of the earthquake induced ground borne vibrations. In this paper, a WIB as artificial bedrock based on the cut-off frequency of a soil layer over bedrock is proposed as isolation measurement in order to mitigate the dynamic response of the buried pipelines under earthquake strong ground motion. The computational simulation of the wave propagation problem is directly achieved by employing nonlinear 2D finite element modelling for prediction of screening performance of WIB on the dynamic response of vibrating coupled soil-pipeline system. Energy absorbing boundaries along the truncated interfaces of the unbounded nature of the underlying soil media are implemented in the time domain along with Newmark’s integration. An extensive parametric investigation and systematic computations are performed with different controlling parameters. The obtained numerical results point out that WIB can be very promising as an isolator to protect pipelines when they establish for a certain depth.

  9. Linear and non-linear stability analysis for finite difference discretizations of high-order Boussinesq equations

    DEFF Research Database (Denmark)

    Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.;

    2004-01-01

    This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly non-linear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann......) techniques with matrix-based methods for formulations in both one and two horizontal dimensions. The matrix-based method is also extended to show the local de-stabilizing effects of the non-linear terms, as well as the stabilizing effects of numerical dissipation. A comparison of the relative stability...... moderately non-normal, suggesting that the eigenvalues are likely suitable for analysis purposes. Numerical experiments demonstrate excellent agreement with the linear analysis, and good qualitative agreement with the local non-linear analysis. The various methods of analysis combine to provide significant...

  10. SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

    1998-09-01

    This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.

  11. Discontinuous Deformation Analysis Coupling with Discontinuous Galerkin Finite Element Methods for Contact Simulations

    Directory of Open Access Journals (Sweden)

    Yue Sun

    2016-01-01

    Full Text Available A novel coupling scheme is presented to combine the discontinuous deformation analysis (DDA and the interior penalty Galerkin (IPG method for the modeling of contacts. The simultaneous equilibrium equations are assembled in a mixed strategy, where the entries are derived from both discontinuous Galerkin variational formulations and the strain energies of DDA contact springs. The contact algorithms of the DDA are generalized for element contacts, including contact detection criteria, open-close iteration, and contact submatrices. Three representative numerical examples on contact problems are conducted. Comparative investigations on the results obtained by our coupling scheme, ANSYS, and analytical theories demonstrate the accuracy and effectiveness of the proposed method.

  12. A finite element simulation on transient large deformation and mass diffusion in electrodes for lithium ion batteries

    Science.gov (United States)

    An, Yonghao; Jiang, Hanqing

    2013-10-01

    Lithium-ion batteries have attracted great deal of attention recently. Silicon is one of the most promising anode materials for high-performance lithium-ion batteries, due to its highest theoretical specific capacity. However, the short lifetime confined by mechanical failure in the silicon anode is now considered to be the biggest challenge in desired applications. High stress induced by the huge volume change due to lithium insertion/extraction is the main reason underlying this problem. Some theoretical models have been developed to address this issue. In order to properly implement these models, we develop a finite element based numerical method using a commercial software package, ABAQUS, as a platform at the continuum level to study fully coupled large deformation and mass diffusion problem. Using this method, large deformation, elasticity-plasticity of the electrodes, various spatial and temporal conditions, arbitrary geometry and dimension could be fulfilled. The interaction between anode and other components of the lithium ion batteries can also be studied as an integrated system. Several specific examples are presented to demonstrate the capability of this numerical platform.

  13. Machining Deformation Prediction of Thin-Walled Part Based on Finite Element Analysis

    Institute of Scientific and Technical Information of China (English)

    Hongxiang Wang; Yabin Tang; Zhanshan Liu; Shi Gao

    2015-01-01

    For the problems of machining distortion and the low accepted product during milling process of aluminum alloy thin⁃walled part, this paper starts from the analysis of initial stress state in material preparation process, the change process of residual stress within aluminum alloy pre⁃stretching plate is researched, and the distribution law of residual stress is indirectly obtained by delamination measurement methods, so the effect of internal residual stress on machining distortion is considered before finite element simulation. Considering the coupling effects of residual stress, dynamic milling force and clamping force on machining distortion, a three⁃dimensional dynamic finite element simulation model is established, and the whole cutting process is simulated from the blank material to finished product, a novel prediction method is proposed, which can availably predict the machining distortion accurately. The machining distortion state of the thin⁃walled part is achieved at different processing steps, the machining distortion of the thin⁃walled part is detected with three coordinate measuring machine tools, show that the simulation results are in good agreement with experimental data.

  14. Finite Element Modeling and Analysis of Nonlinear Impact and Frictional Motion Responses Including Fluid—Structure Coupling Effects

    Directory of Open Access Journals (Sweden)

    Yong Zhao

    1997-01-01

    Full Text Available A nonlinear three dimensional (3D single rack model and a nonlinear 3D whole pool multi-rack model are developed for the spent fuel storage racks of a nuclear power plant (NPP to determine impacts and frictional motion responses when subjected to 3D excitations from the supporting building floor. The submerged free standing rack system and surrounding water are coupled due to hydrodynamic fluid-structure interaction (FSI using potential theory. The models developed have features that allow consideration of geometric and material nonlinearities including (1 the impacts of fuel assemblies to rack cells, a rack to adjacent racks or pool walls, and rack support legs to the pool floor; (2 the hydrodynamic coupling of fuel assemblies with their storing racks, and of a rack with adjacent racks, pool walls, and the pool floor; and (3 the dynamic motion behavior of rocking, twisting, and frictional sliding of rack modules. Using these models 3D nonlinear time history dynamic analyses are performed per the U.S. Nuclear Regulatory Commission (USNRC criteria. Since few such modeling, analyses, and results using both the 3D single and whole pool multiple rack models are available in the literature, this paper emphasizes description of modeling and analysis techniques using the SOLVIA general purpose nonlinear finite element code. Typical response results with different Coulomb friction coefficients are presented and discussed.

  15. Finite element modelling of moisture related and visco-elastic deformations in inhomogeneous timber beams

    DEFF Research Database (Denmark)

    Ormarsson, Sigurdur; Dahlblom, Ola

    2013-01-01

    Wood is a hygro-mechanical, non-isotropic and inhomogeneous material concerning both modulus of elasticity (MOE) and shrinkage properties. In stress calculations associated with ordinary timber design, these matters are often not dealt with properly. The main reason for this is that stress...... distributions in inhomogeneous glued laminated members (glulam) and in composite beams exposed to combined mechanical action and variable climate conditions are extremely difficult to predict by hand. Several experimental studies of Norway spruce have shown that the longitudinal modulus of elasticity...... composites behave during both mechanical and environmental load action. The beam element is exposed to both axial and lateral deformation. The material model employed concerns the elastic, shrinkage, mechano-sorption and visco-elastic behaviour of the wood material. It is used here to simulate the behaviour...

  16. Advanced finite element technologies

    CERN Document Server

    Wriggers, Peter

    2016-01-01

    The book presents an overview of the state of research of advanced finite element technologies. Besides the mathematical analysis, the finite element development and their engineering applications are shown to the reader. The authors give a survey of the methods and technologies concerning efficiency, robustness and performance aspects. The book covers the topics of mathematical foundations for variational approaches and the mathematical understanding of the analytical requirements of modern finite element methods. Special attention is paid to finite deformations, adaptive strategies, incompressible, isotropic or anisotropic material behavior and the mathematical and numerical treatment of the well-known locking phenomenon. Beyond that new results for the introduced approaches are presented especially for challenging nonlinear problems.

  17. Finite-Horizon Approximate Optimal Guaranteed Cost Control of Uncertain Nonlinear Systems With Application to Mars Entry Guidance.

    Science.gov (United States)

    Wu, Huai-Ning; Li, Mao-Mao; Guo, Lei

    2015-07-01

    This paper studies the finite-horizon optimal guaranteed cost control (GCC) problem for a class of time-varying uncertain nonlinear systems. The aim of this problem is to find a robust state feedback controller such that the closed-loop system has not only a bounded response in a finite duration of time for all admissible uncertainties but also a minimal guaranteed cost. A neural network (NN) based approximate optimal GCC design is developed. Initially, by modifying the cost function to account for the nonlinear perturbation of system, the optimal GCC problem is transformed into a finite-horizon optimal control problem of the nominal system. Subsequently, with the help of the modified cost function together with a parametrized bounding function for all admissible uncertainties, the solution to the optimal GCC problem is given in terms of a parametrized Hamilton-Jacobi-Bellman (PHJB) equation. Then, a NN method is developed to solve offline the PHJB equation approximately and thus obtain the nearly optimal GCC policy. Furthermore, the convergence of approximate PHJB equation and the robust admissibility of nearly optimal GCC policy are also analyzed. Finally, by applying the proposed design method to the entry guidance problem of the Mars lander, the achieved simulation results show the effectiveness of the proposed controller.

  18. Global Behavior Of Finite Energy Solutions To The $d$-Dimensional Focusing Nonlinear Schr\\"odinger Equation

    CERN Document Server

    Guevara, Cristi

    2012-01-01

    We study the global behavior of finite energy solutions to the $d$-dimensional focusing nonlinear Schr\\"odinger equation (NLS), $i \\partial_t u+\\Delta u+ |u|^{p-1}u=0, $ with initial data $u_0\\in H^1,\\; x \\in R^n$. The nonlinearity power $p$ and the dimension $d$ are such that the scaling index $s=\\frac{d}2-\\frac2{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s1,$ then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle.

  19. Finite difference method–based calculation of gravity deformation curve for the large-span beam of heavy-duty vertical lathe

    Directory of Open Access Journals (Sweden)

    Zhenyu Han

    2016-04-01

    Full Text Available To solve the problem that gravity deformation curve of large-span cast-iron beam analyzed by finite element method simulation is inaccurate due to material imperfection, a discretization calculation considering the inhomogeneity of the material based on finite difference method is proposed. Supposing the flexural rigidity of the beam is different along the length, the continuous beam is discretized into segments based on finite difference method, and equivalent flexural rigidity is presented to characterize the inhomogeneity of the material. Correction model of bending deformation is constructed to revise the results of finite element method simulation applying equivalent flexural rigidity that could be obtained by combining the discretization model and deformation data acquired in a simple self-load experiment in which the beam is simply supported without any assembly process. Finally, flowchart of application is presented, and the approach is illustrated through an example from real case. The experimental results show that the computational accuracy is improved from 73.14% to 88.33%, compared with just finite element method simulation.

  20. Lagrangian three-dimensional finite-element formulation for the nonlinear fluid-structural response of reactor components. [LMFBR

    Energy Technology Data Exchange (ETDEWEB)

    Kulak, R. F.; Fiala, C.

    1980-03-01

    This report presents the formulations used in the NEPTUNE code. Specifically, it describes the finite-element formulation of a three-dimensional hexahedral element for simulating the behavior of either fluid or solid continua. Since the newly developed hexahedral element and the original triangular plate element are finite elements, they are compatible in the sense that they can be combined arbitrarily to simulate complex reactor components in three-dimensional space. Because rate-type constitutive relations are used in conjunction with a velocity-strain tensor, the formulation is applicable to large deformation problems. This development can be used to simulate (1) the fluid adjacent to reactor components and (2) the concrete fill found in large reactor head closures.

  1. Progress of adaptive finite element(FE) method in solving nonlinear partial differential equation(PDE)

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    @@ Scientific computation is widely used in multiple cross-disciplinary areas. Most of the issues coming from this area finally result in solving PDE. In the process of solving PDE, the meshes are firstly generated within the area where PDE is functional; then, the methods of FE,Finite Difference (FD), and Finite Volume (FV) are applied on the meshes to solve the PDE.

  2. Estimation of independent non-linear deformation modes for analysis of craniofacial malformations in crouzon mice

    DEFF Research Database (Denmark)

    Hansen, Michael Sass; Olafsdóttir, Hildur; Darvann, Tron Andre;

    2007-01-01

    of wild-type (normal) mice and Crouzon mice were investigated. We present for what we believe is the first time, a statistical deformation model based on independent component analysis (ICA). A set of deformation parameters for each mouse was calculated using a B-spline-based nonrigid registration. From...

  3. Finite Element Analysis of the Deformation of Functionally Graded Plates under Thermomechanical Loads

    Directory of Open Access Journals (Sweden)

    A. E. Alshorbagy

    2013-01-01

    Full Text Available The first-order shear deformation plate model, accounting for the exact neutral plane position, is exploited to investigate the uncoupled thermomechanical behavior of functionally graded (FG plates. Functionally graded materials are mainly constructed to operate in high temperature environments. Also, FG plates are used in many applications (such as mechanical, electrical, and magnetic, where an amount of heat may be generated into the FG plate whenever other forms of energy (electrical, magnetic, etc. are converted into thermal energy. Several simulations are performed to study the behavior of FG plates, subjected to thermomechanical loadings, and focus the attention on the effect of the heat source intensity. Most of the previous studies have considered the midplane neutral one, while the actual position of neutral plane for functionally graded plates is shifted and should be firstly determined. A comparative study is performed to illustrate the effect of considering the neutral plane position. The volume fraction of the two constituent materials of the FG plate is varied smoothly and continuously, as a continuous power function of the material position, along the thickness of the plate.

  4. Applications of a General Finite-Difference Method for Calculating Bending Deformations of Solid Plates

    Science.gov (United States)

    Walton, William C., Jr.

    1960-01-01

    This paper reports the findings of an investigation of a finite - difference method directly applicable to calculating static or simple harmonic flexures of solid plates and potentially useful in other problems of structural analysis. The method, which was proposed in doctoral thesis by John C. Houbolt, is based on linear theory and incorporates the principle of minimum potential energy. Full realization of its advantages requires use of high-speed computing equipment. After a review of Houbolt's method, results of some applications are presented and discussed. The applications consisted of calculations of the natural modes and frequencies of several uniform-thickness cantilever plates and, as a special case of interest, calculations of the modes and frequencies of the uniform free-free beam. Computed frequencies and nodal patterns for the first five or six modes of each plate are compared with existing experiments, and those for one plate are compared with another approximate theory. Beam computations are compared with exact theory. On the basis of the comparisons it is concluded that the method is accurate and general in predicting plate flexures, and additional applications are suggested. An appendix is devoted t o computing procedures which evolved in the progress of the applications and which facilitate use of the method in conjunction with high-speed computing equipment.

  5. Finite Element Solution: Nonlinear Flapping Beams for Use with Micro Air Vehicle Design

    Science.gov (United States)

    2007-03-01

    used to approximate the nonlinearity in a beam is the SDOF Duffing Oscillator ӱ + C ẏ + ω0 2 y + βy3 = P sin(ωt...Hilbert Transform.......................................................................................................19 Duffing Equation...Amplitude vs Nonlinear Frequency: Fixed-Fixed Steel................................. 36 Figure 26. Duffing Equation Plot: Fixed-Fixed Steel Beam

  6. Finite time blow-up for a wave equation with a nonlocal nonlinearity

    CERN Document Server

    Fino, Ahmad; Georgiev, Vladimir

    2010-01-01

    In this article, we study the local existence of solutions for a wave equation with a nonlocal in time nonlinearity. Moreover, a blow-up results are proved under some conditions on the dimensional space, the initial data and the nonlinear forcing term.

  7. Finite-temperature Casimir effect in the presence of nonlinear dielectrics

    DEFF Research Database (Denmark)

    Kheirandish, Fardin; Amooghorban, Ehsan; Soltani, Morteza

    2011-01-01

    Starting from a Lagrangian, the electromagnetic field in the presence of a nonlinear dielectric medium is quantized using path-integral techniques, and correlation functions of different fields are calculated. The susceptibilities of the nonlinear medium are obtained, and their relations to coupl...

  8. The non-linear response of a muscle in transverse compression: assessment of geometry influence using a finite element model.

    Science.gov (United States)

    Gras, Laure-Lise; Mitton, David; Crevier-Denoix, Nathalie; Laporte, Sébastien

    2012-01-01

    Most recent finite element models that represent muscles are generic or subject-specific models that use complex, constitutive laws. Identification of the parameters of such complex, constitutive laws could be an important limit for subject-specific approaches. The aim of this study was to assess the possibility of modelling muscle behaviour in compression with a parametric model and a simple, constitutive law. A quasi-static compression test was performed on the muscles of dogs. A parametric finite element model was designed using a linear, elastic, constitutive law. A multi-variate analysis was performed to assess the effects of geometry on muscle response. An inverse method was used to define Young's modulus. The non-linear response of the muscles was obtained using a subject-specific geometry and a linear elastic law. Thus, a simple muscle model can be used to have a bio-faithful, biomechanical response.

  9. Nonlinear incompressible finite element for simulating loading of cardiac tissue--Part I: Two dimensional formulation for thin myocardial strips.

    Science.gov (United States)

    Horowitz, A; Sheinman, I; Lanir, Y; Perl, M; Sideman, S

    1988-02-01

    A two-dimensional incompressible plane-stress finite element is formulated for the simulation of the passive-state mechanics of thin myocardial strips. The formulation employs a total Lagrangian and materially nonlinear approach, being based on a recently proposed structural material law, which is derived from the histological composition of the tissue. The ensuing finite element allows to demonstrate the mechanical properties of a single myocardial layer containing uniformly directed fibers by simulating various loading cases such as tension, compression and shear. The results of these cases show that the fiber direction is considerably stiffer than the cross-fiber direction, that there is significant coupling between these two directions, and that the shear stiffness of the tissue is lower than its tensile and compressive stiffness.

  10. A nonlinear, implicit, three-dimensional finite element code for solid and structural mechanics - User`s Manual

    Energy Technology Data Exchange (ETDEWEB)

    Maker, B.N.

    1995-04-14

    This report provides a user`s manual for NIKE3D, a fully implicit three-dimensional finite element code for analyzing the finite strain static and dynamic response of inelastic solids, shells, and beams. Spatial discretization is achieved by the use of 8-node solid elements, 2-node truss and beam elements, and 4-node membrane and shell elements. Over twenty constitutive models are available for representing a wide range of elastic, plastic, viscous, and thermally dependent material behavior. Contact-impact algorithms permit gaps, frictional sliding, and mesh discontinuities along material interfaces. Several nonlinear solution strategies are available, including Full-, Modified-, and Quasi-Newton methods. The resulting system of simultaneous linear equations is either solved iteratively by an element-by-element method, or directly by a factorization method, for which case bandwidth minimization is optional. Data may be stored either in or out of core memory to allow for large analyses.

  11. Noise generation in the solid Earth, oceans, and atmosphere, from non-linear interacting surface gravity waves in finite depth

    CERN Document Server

    Ardhuin, Fabrice

    2012-01-01

    Oceanic observations, even in very deep water, and atmospheric pressure or seismic records, from anywhere on Earth, contain noise with dominant periods between 3 and 10 seconds, that can be related to surface gravity waves in the oceans. This noise is consistent with a dominant source explained by a nonlinear wave-wave interaction mechanism, and takes the form of surface gravity waves, acoustic or seismic waves. Previous theoretical works on seismic noise focused on surface (Rayleigh) waves, and did not consider finite depth effects on the generating wave kinematics. These finite depth effects are introduced here, which requires the consideration of the direct wave-induced pressure at the ocean bottom, a contribution previously overlooked in the context of seismic noise. That contribution can lead to a considerable reduction of the seismic noise source, which is particularly relevant for noise periods larger than 10 s. The theory is applied to acoustic waves in the atmosphere, extending previous theories that...

  12. Problem of probabilistic calculation of the design on linearly and non-linearly deformable basis with casual parameters

    Directory of Open Access Journals (Sweden)

    Mkrtychev Oleg Vartanovich

    Full Text Available In the article the problem of calculation of a construction basis system in case of earthquake is considered taking into account casual properties of basis soil in various points of the soil body. As a stochastic function in the calculation of linearly deformable basis, the deformation module, which accepts different values in the direction x, y, z, was chosen. In the calculation of the system on non-linearly deformable basis as incidentally distributed sizes the following parameters were accepted: deformation module, shear modulus, specific adhesion, angle of internal friction. The authors of the article offer to consider initial seismic influence in the form of casual stationary process. In order to solve such problems modern software systems are proposed that solve differential equations of motion via direct integration with explicit schemes. The calculation in this case will be held on the synthesized accelerograms. A short review of the task solution of the beam lying on elastic basis, which was received by D.N. Sobolev at casual distribution of pastel coefficient in the direction x, is provided in article. In order to define the objective, D.N. Sobolev gives expressions for a population mean and correlation function of stochastic function. As a result of the task solution population means and dispersions of function of movements and its derivatives were received. The problem formulation considered in the article is more complicated, but at the same time important from a practical standpoint.

  13. Strengthening of RC Beams with Large Openings in Shear by CFRP Laminates: Experiment and 2D Nonlinear Finite Element Analysis

    Directory of Open Access Journals (Sweden)

    S.C. Chin

    2012-05-01

    Full Text Available This study presents the experimental study and numerical analysis of Reinforced Concrete (RC beams with large square openings placed in the shear region, at a distance 0.5d and d away from the support, strengthened by Carbon Fiber Reinforced Polymer (CFRP laminates. This research aims to investigate the strength losses in RC beam due to the presence of large square openings placed at two different locations in shear region. Also, in order to re-gain the beam structural capacity loss due to the openings, strengthening by CFRP laminates around the openings were studied. A total of six RC beams were tested to failure under four point loading including control beams, un-strengthened and strengthened RC beams with large square openings in shear region at a distance 0.5d and d away from the support. The CFRP strengthening configuration considered in this study was a full wrapping system around the square openings. A nonlinear finite element program, ATENA was used to validate the results of the tested beams. Comparisons between the finite element predictions and experimental results in terms of crack patterns and load deflection relationships are presented. The crack pattern results of the finite element model show good agreement with the experimental data. The load midspan deflection curves of the finite element models exhibited a stiffer result compared to the experimental beams. The possible reason may be due to the perfect bond assumption between the concrete and steel reinforcement.

  14. Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model

    Science.gov (United States)

    Banerjee, Debasish; Chandrasekharan, Shailesh

    2010-06-01

    In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind nontrivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical nonlinear O(2) sigma model with a coupling β and chemical potential μ on a 2+1-dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the “worm algorithm.” Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the (β,μ) plane.

  15. Accuracy of specimen-specific nonlinear finite element analysis for evaluation of radial diaphysis strength in cadaver material.

    Science.gov (United States)

    Matsuura, Yusuke; Kuniyoshi, Kazuki; Suzuki, Takane; Ogawa, Yasufumi; Sukegawa, Koji; Rokkaku, Tomoyuki; Thoreson, Andrew Ryan; An, Kai-Nan; Takahashi, Kazuhisa

    2015-01-01

    The feasibility of a user-specific finite element model for predicting the in situ strength of the radius after implantation of bone plates for open fracture reduction was established. The effect of metal artifact in CT imaging was characterized. The results were verified against biomechanical test data. Fourteen cadaveric radii were divided into two groups: (1) intact radii for evaluating the accuracy of radial diaphysis strength predictions with finite element analysis and (2) radii with a locking plate affixed for evaluating metal artifact. All bones were imaged with CT. In the plated group, radii were first imaged with the plates affixed (for simulating digital plate removal). They were then subsequently imaged with the locking plates and screws removed (actual plate removal). Fracture strength of the radius diaphysis under axial compression was predicted with a three-dimensional, specimen-specific, nonlinear finite element analysis for both the intact and plated bones (bones with and without the plate captured in the scan). Specimens were then loaded to failure using a universal testing machine to verify the actual fracture load. In the intact group, the physical and predicted fracture loads were strongly correlated. For radii with plates affixed, the physical and predicted (simulated plate removal and actual plate removal) fracture loads were strongly correlated. This study demonstrates that our specimen-specific finite element analysis can accurately predict the strength of the radial diaphysis. The metal artifact from CT imaging was shown to produce an overestimate of strength.

  16. Influence of geometric and physical nonlinearities on the internal resonances of a finite continuous rod with a microstructure

    Science.gov (United States)

    Andrianov, Igor V.; Awrejcewicz, Jan; Danishevskyy, Vladyslav V.; Markert, Bernd

    2017-01-01

    In this work, nonlinear longitudinal vibrations of a finite composite rod are studied including geometric and physical nonlinearities. An original boundary value problem for a heterogeneous rod yielded by the macroscopic approximation obtained earlier by the higher-order asymptotic homogenization method is used. The effects of internal resonances and modes coupling are predicted, validated and analyzed. The defined novel continuous problem governed by PDEs is solved using space-discretization and the method of multiple time scales. We are aimed at understanding and analyzing how the presence of the microstructure influences the processes of mode interaction. It is shown that, depending on a scaling relation between the amplitude of the vibrations and the size of the unit cell, different scenarios of the modes coupling can be realized. Additionally to the asymptotic solution, numerical simulation of the modes coupling is performed by means of the Runge-Kutta fourth-order method. The obtained numerical and analytical results demonstrate good qualitative agreement.

  17. A Nonlinear Dynamic Finite Element Analysis of Drilling Shaft including Multispan Auxiliary Supports in Deep-Hole Machining

    Directory of Open Access Journals (Sweden)

    L. F. Kong

    2013-01-01

    Full Text Available This paper presents a method to enhance computational efficiency of the nonlinear dynamic analysis of the large-scale deep-hole drilling machine. Based on finite element model, the drilling shaft system is constructed into Timoshenko beam element on the basis of flexible rotary shaft so as to increase the accuracy of numerical calculation. In order to save the calculation time and resources, modal synthesis technique is adopted to reduce the feature modal of linear freedom degrees of drilling shaft system. As a result, the accuracy required by the non-linear analysis will not be loss. On the basis of these, the whirling characteristics of drilling shaft system are studied under the conditions of different shaft lengths, and simultaneously, the stability patterns of drilling shaft motion and its stability region are obtained in the selected drilling depth and cutting speed parameters while drilling intersection holes.

  18. Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ε-error bound.

    Science.gov (United States)

    Wang, Fei-Yue; Jin, Ning; Liu, Derong; Wei, Qinglai

    2011-01-01

    In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an ε-error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method.

  19. Distributed finite-time consensus tracking for nonlinear multi-agent systems with a time-varying reference state

    Science.gov (United States)

    Wen, Guoguang; Yu, Yongguang; Peng, Zhaoxia; Rahmani, Ahmed

    2016-06-01

    This paper investigates the consensus tracking problem for nonlinear multi-agent systems with a time-varying reference state. The consensus reference is taken as a virtual leader, whose output is only its position information that is available to only a subset of a group of followers. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position of its neighbours. In this paper, the consensus tracking problem is respectively considered under fixed and switching communication topologies. Some corresponding sufficient conditions are obtained to guarantee the states of followers can converge to the state of the virtual leader in finite time. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Simulations are presented to illustrate the theoretical analysis.

  20. A New Finite-Time Observer for Nonlinear Systems: Applications to Synchronization of Lorenz-Like Systems

    Directory of Open Access Journals (Sweden)

    Ricardo Aguilar-López

    2016-01-01

    Full Text Available This paper proposes a synchronization methodology of two chaotic oscillators under the framework of identical synchronization and master-slave configuration. The proposed methodology is based on state observer design under the frame of control theory; the observer structure provides finite-time synchronization convergence by cancelling the upper bounds of the main nonlinearities of the chaotic oscillator. The above is showed via an analysis of the dynamic of the so called synchronization error. Numerical experiments corroborate the satisfactory results of the proposed scheme.

  1. A New Finite-Time Observer for Nonlinear Systems: Applications to Synchronization of Lorenz-Like Systems

    Science.gov (United States)

    Aguilar-López, Ricardo

    2016-01-01

    This paper proposes a synchronization methodology of two chaotic oscillators under the framework of identical synchronization and master-slave configuration. The proposed methodology is based on state observer design under the frame of control theory; the observer structure provides finite-time synchronization convergence by cancelling the upper bounds of the main nonlinearities of the chaotic oscillator. The above is showed via an analysis of the dynamic of the so called synchronization error. Numerical experiments corroborate the satisfactory results of the proposed scheme. PMID:27738651

  2. Development of a nonlinear 3D solid finite element model for the calculation of bending moments of flexural members

    Institute of Scientific and Technical Information of China (English)

    Jin Wencheng; Zhou Xiaoyong; Li Na

    2008-01-01

    A numerical model is developed in this paper to calculate the bending moments of flexural members through integration in 3D solid finite element analyses according to the nonlinear constitutive model of concrete and the elastoplastic constitutive model of steel, utilizing the stress condition of the cross-section, considering the destruction characteristic of reinforced concrete members, and based on the plane cross-section assumption. The results of this model give good agreement with those of the classical method. Consequently, we can also deduce the corresponding numerical expression for eccentrically loaded members according to the analysis method.

  3. THE UPWIND FINITE DIFFERENCE FRACTIONAL STEPS METHOD FOR NONLINEAR COUPLED SYSTEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA

    Institute of Scientific and Technical Information of China (English)

    Yirang YUAN

    2006-01-01

    For nonlinear coupled system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward, and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L2 norm are derived to determine the error in the second order approximate solution.This method has already been applied to the numerical simulation of migration-accumulation of oil resources.

  4. Improving Stiffness-to-weight Ratio of Spot-welded Structures based upon Nonlinear Finite Element Modelling

    Science.gov (United States)

    Zhang, Shengyong

    2017-07-01

    Spot welding has been widely used for vehicle body construction due to its advantages of high speed and adaptability for automation. An effort to increase the stiffness-to-weight ratio of spot-welded structures is investigated based upon nonlinear finite element analysis. Topology optimization is conducted for reducing weight in the overlapping regions by choosing an appropriate topology. Three spot-welded models (lap, doubt-hat and T-shape) that approximate “typical” vehicle body components are studied for validating and illustrating the proposed method. It is concluded that removing underutilized material from overlapping regions can result in a significant increase in structural stiffness-to-weight ratio.

  5. Convergence of Galerkin truncation for dynamic response of finite beams on nonlinear foundations under a moving load

    Science.gov (United States)

    Ding, Hu; Chen, Li-Qun; Yang, Shao-Pu

    2012-05-01

    The present paper investigates the convergence of the Galerkin method for the dynamic response of an elastic beam resting on a nonlinear foundation with viscous damping subjected to a moving concentrated load. It also studies the effect of different boundary conditions and span length on the convergence and dynamic response. A train-track or vehicle-pavement system is modeled as a force moving along a finite length Euler-Bernoulli beam on a nonlinear foundation. Nonlinear foundation is assumed to be cubic. The Galerkin method is utilized in order to discretize the nonlinear partial differential governing equation of the forced vibration. The dynamic response of the beam is obtained via the fourth-order Runge-Kutta method. Three types of the conventional boundary conditions are investigated. The railway tracks on stiff soil foundation running the train and the asphalt pavement on soft soil foundation moving the vehicle are treated as examples. The dependence of the convergence of the Galerkin method on boundary conditions, span length and other system parameters are studied.

  6. Finite deformation analysis of crack tip opening in elastic-plastic materials and implications for fracture initiation

    Energy Technology Data Exchange (ETDEWEB)

    McMeeking, R M

    1976-05-01

    Analyses of the stress and strain fields around smoothly blunting crack tips in both non-hardening and hardening elastic-plastic materials, under contained plane strain yielding and subject to mode I opening loads, have been carried out by a finite element method suitably formulated to admit large geometry changes. The results include the crack tip shape and near-tip deformation field, and the crack tip opening displacement has been related to a parameter of the applied load, the J-integral. The hydrostatic stresses near the crack tip are limited due to the lack of constraint on the blunted tip, limiting achievable stress levels except in a very small region around the crack tip in power law hardening materials. The J-integral is found to be path independent except very close to the crack tip in the region affected by the blunted tip. Models for fracture are discussed in the light of these results including one based on the growth of voids. The rate of void growth near the tip in hardening materials seems to be little different from the rate in non-hardening materials when measured in terms of crack tip opening displacement, which leads to a prediction of higher toughness in hardening materials. It is suggested that improvement of this model would follow from better understanding of void-void and void-crack coalescence and void nucleation, and some criteria and models for these are discussed. The implications of the finite element results for fracture criteria based on critical stress, strain or both are discussed with respect to transition of fracture mode and the angle of initial crack growth. Localization of flow is discussed as a possible fracture model and as a model for void-crack coalescence.

  7. An investigation of deformation and fluid flow at subduction zones using newly developed instrumentation and finite element modeling

    Science.gov (United States)

    Labonte, Alison Louise

    Detecting seafloor deformation events in the offshore convergent margin environment is of particular importance considering the significant seismic hazard at subduction zones. Efforts to gain insight into the earthquake cycle have been made at the Cascadia and Costa Rica subduction margins through recent expansions of onshore GPS and seismic networks. While these studies have given scientists the ability to quantify and locate slip events in the seismogenic zone, there is little technology available for adequately measuring offshore aseismic slip. This dissertation introduces an improved flow meter for detecting seismic and aseismic deformation in submarine environments. The value of such hydrologic measurements for quantifying the geodetics at offshore margins is verified through a finite element modeling (FEM) study in which the character of deformation in the shallow subduction zone is determined from previously recorded hydrologic events at the Costa Rica Pacific margin. Accurately sensing aseismic events is one key to determining the stress state in subduction zones as these slow-slip events act to load or unload the seismogenic zone during the interseismic period. One method for detecting seismic and aseismic strain events is to monitor the hydrogeologic response to strain events using fluid flow meters. Previous instrumentation, the Chemical Aqueous Transport (CAT) meter which measures flow rates through the sediment-water interface, can detect transient events at very low flowrates, down to 0.0001 m/yr. The CAT meter performs well in low flow rate environments and can capture gradual changes in flow rate, as might be expected during ultra slow slip events. However, it cannot accurately quantify high flow rates through fractures and conduits, nor does it have the temporal resolution and accuracy required for detecting transient flow events associated with rapid deformation. The Optical Tracer Injection System (OTIS) developed for this purpose is an

  8. Law of “good and evil”, non-linear function of justice, political regimes and deformation of political systems

    Directory of Open Access Journals (Sweden)

    Sergey Gennadyevich Ol’kov

    2015-06-01

    Full Text Available Objective to clarify the law of good and evil the function rule of justice and to construct mathematical models of political regimes. Methods 1 observation analysis and synthesis 2 deduction and induction 3 using the laws of formal logic 4 formal legal method 5 mathematical modeling 6 the study of mathematical functions 7 differential calculus 8 plotting. Results the author has deduced 1 the nonlinear law function of good and evil 2 the nonlinear function of justice 3 the law function of political regimes. Scientific novelty the author has calculated and found 1 a nonlinear formula DLcol ndashLcol3 which represents the relationship between the acts of legal public relations subjects D and thecollective freedom Lcol ndash the law of quotgood and evilquot 2 a nonlinear formula YD D3 illustrating the relationship between the acts of legal relations subjects D and responsibility for their actions Y ndash a nonlinear function of justice 3 a nonlinear formulanbsp that shows the relationship between the individual Lind and collective freedom Lcol in the negative area of the function definition collective negative freedom and a formulanbsp reflecting the relationship between the individual and collective freedom in the positive area of the function definition collective positive freedom 4 has given a general classification of political regimes in the world describing their functions showing the types of political systems deformation that occur due to the leftwise and rightwise shifts of collective freedom. Practical value the possibility to use the obtained scientific results in the development of various legal theories. nbsp

  9. A non-linear constrained optimization technique for the mimetic finite difference method

    Energy Technology Data Exchange (ETDEWEB)

    Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Svyatskiy, Daniil [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Bertolazzi, Enrico [Univ. of Trento (Italy); Frego, Marco [Univ. of Trento (Italy)

    2014-09-30

    This is a strategy for the construction of monotone schemes in the framework of the mimetic finite difference method for the approximation of diffusion problems on unstructured polygonal and polyhedral meshes.

  10. Robust finite-time tracking control for nonlinear suspension systems via disturbance compensation

    Science.gov (United States)

    Pan, Huihui; Jing, Xingjian; Sun, Weichao

    2017-05-01

    This paper focuses on the finite-time tracking control with external disturbance for active suspension systems. In order to compensate unknown disturbance efficiently, a disturbance compensator with finite-time convergence property is studied. By analyzing the discontinuous phenomenon of classical disturbance compensation techniques, this study presents a simple approach to construct a continuous compensator satisfying the finite-time disturbance rejection performance. According to the finite-time separation principle, the design procedures of the nominal controller for the suspension system without disturbance and the disturbance compensator can be implemented in a completely independent manner. Therefore, the overall control law for the closed-loop system is continuous, which offers some distinct advantages over the existing discontinuous ones. From the perspective of practical implementation, the continuous controller can avoid effectively the unexpected chattering in active suspension control. Comparative experimental results are presented and discussed to illustrate the advantage and effectiveness of the proposed control strategy.

  11. LONG-TIME BEHAVIOR OF FINITE DIFFERENCE SOLUTIONS OF A NONLINEAR SCHRODINGER EQUATION WITH WEAKLY DAMPED

    Institute of Scientific and Technical Information of China (English)

    Fa-yong Zhang; Shu-juan Lu

    2001-01-01

    A weakly demped Schrodinger equation possessing a global attractor are considered.The dynamical properties of a class of finite difference scheme are analysed. The exsitence of global attractor is proved for the discrete system. The stability of the difference scheme and the error estimate of the difference solution are obtained in the autonomous system case. Finally, long-time stability and convergence of the class of finite difference scheme also are analysed in the nonautonomous system case.

  12. Numerical Analysis of Finite Deformation of Overbroken Rock Mass in Gob Area Based on Euler Model of Control Volume

    Institute of Scientific and Technical Information of China (English)

    LIU Wei-qun; MIAO Xie-xing

    2006-01-01

    The overbroken rock mass of gob areas is made up of broken and accumulated rock blocks compressed to some extent by the overlying strata. The bearing pressure of the gob can directly affect the safety of mining fields, formation of road retained along the next goaf and seepage of water and methane through the gob. In this paper, the software RFPA'2000 is used to construct numerical models. Especially the Euler method of control volume is proposed to solve the simulation difficulty arising from plastically finite deformations. The results show that three characteristic regions occurred in the gob area: (1) a naturally accumulated region, 0-10 m away from unbroken surrounding rock walls, where the bearing pressure is nearly zero; (2) an overcompacted region, 10-20 m away from unbroken walls, where the bearing pressure results in the maximum value of the gob area; (3) a stable compaction region, more than 20 m away from unbroken walls and occupying absolutely most of the gob area, where the bearing pressures show basically no differences. Such a characteristic can explain the easy-seepaged "O"-ring phenomena around mining fields very well.

  13. Parametric study on supersonic flutter of angle-ply laminated plates using shear deformable finite element method

    Institute of Scientific and Technical Information of China (English)

    Wei Xia; Qiao Ni

    2011-01-01

    The influence of fiber orientation,flow yaw angle and length-to-thickness ratio on flutter characteristics of angle-ply laminated plates in supersonic flow is studied by finite element approach.The structural model is established using the Reissner-Mindlin theory in which the transverse shear deformation is considered.The aerodynamic pressure is evaluated by the quasi-steady first-order piston theory.The equations of motion are formulated based on the principle of virtual work.With the harmonic motion assumption,the flutter boundary is determined by solving a series of complex eigenvalue problems.Numerical study shows that (1)The flutter dynamic pressure and the coalescence of flutter modes depend on fiber orientation,flow yaw angle and length-to-thickness ratio; (2) The laminated plate with all fibers aligned with the flow direction gives the highest flutter dynamic pressure,but a slight yawing of the flow from the fiber orientation results in a sharp decrease of the flutter dynamic pressure; (3) The angle-ply laminated plate with fiber orientation angle equal to flow yaw angle gives high flutter dynamic pressure,but not the maximum flutter dynamic pressure; (4) With the decrease of length-to-thickness ratio,an adverse effect due to mode transition on the flutter dynamic pressure is found.

  14. Deformation of articular cartilage during static loading of a knee joint--experimental and finite element analysis.

    Science.gov (United States)

    Halonen, K S; Mononen, M E; Jurvelin, J S; Töyräs, J; Salo, J; Korhonen, R K

    2014-07-18

    Novel conical beam CT-scanners offer high resolution imaging of knee structures with i.a. contrast media, even under weight bearing. With this new technology, we aimed to determine cartilage strains and meniscal movement in a human knee at 0, 1, 5, and 30 min of standing and compare them to the subject-specific 3D finite element (FE) model. The FE model of the volunteer׳s knee, based on the geometry obtained from magnetic resonance images, was created to simulate the creep. The effects of collagen fibril network stiffness, nonfibrillar matrix modulus, permeability and fluid flow boundary conditions on the creep response in cartilage were investigated. In the experiment, 80% of the maximum strain in cartilage developed immediately, after which the cartilage continued to deform slowly until the 30 min time point. Cartilage strains and meniscus movement obtained from the FE model matched adequately with the experimentally measured values. Reducing the fibril network stiffness increased the mean strains substantially, while the creep rate was primarily influenced by an increase in the nonfibrillar matrix modulus. Changing the initial permeability and preventing fluid flow through noncontacting surfaces had a negligible effect on cartilage strains. The present results improve understanding of the mechanisms controlling articular cartilage strains and meniscal movements in a knee joint under physiological static loading. Ultimately a validated model could be used as a noninvasive diagnostic tool to locate cartilage areas at risk for degeneration.

  15. Assessment of Two Analytical Methods in Solving the Linear and Nonlinear Elastic Beam Deformation Problems

    DEFF Research Database (Denmark)

    Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari

    2010-01-01

    Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...... and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However...

  16. Thermal effects on nonlinear vibration of a carbon nanotube-based mass sensor using finite element analysis

    Science.gov (United States)

    Kang, Dong-Keun; Kim, Chang-Wan; Yang, Hyun-Ik

    2017-01-01

    In the present study we carried out a dynamic analysis of a CNT-based mass sensor by using a finite element method (FEM)-based nonlinear analysis model of the CNT resonator to elucidate the combined effects of thermal effects and nonlinear oscillation behavior upon the overall mass detection sensitivity. Mass sensors using carbon nanotube (CNT) resonators provide very high sensing performance. Because CNT-based resonators can have high aspect ratios, they can easily exhibit nonlinear oscillation behavior due to large displacements. Also, CNT-based devices may experience high temperatures during their manufacture and operation. These geometrical nonlinearities and temperature changes affect the sensing performance of CNT-based mass sensors. However, it is very hard to find previous literature addressing the detection sensitivity of CNT-based mass sensors including considerations of both these nonlinear behaviors and thermal effects. We modeled the nonlinear equation of motion by using the von Karman nonlinear strain-displacement relation, taking into account the additional axial force associated with the thermal effect. The FEM was employed to solve the nonlinear equation of motion because it can effortlessly handle the more complex geometries and boundary conditions. A doubly clamped CNT resonator actuated by distributed electrostatic force was the configuration subjected to the numerical experiments. Thermal effects upon the fundamental resonance behavior and the shift of resonance frequency due to attached mass, i.e., the mass detection sensitivity, were examined in environments of both high and low (or room) temperature. The fundamental resonance frequency increased with decreasing temperature in the high temperature environment, and increased with increasing temperature in the low temperature environment. The magnitude of the shift in resonance frequency caused by an attached mass represents the sensing performance of a mass sensor, i.e., its mass detection

  17. Nonlinear oscillations of laminated plates using an accurate four-node rectangular shear flexible material finite element

    Indian Academy of Sciences (India)

    Gajbir Singh; G Venkateswara Rao

    2000-08-01

    The objective of the present paper is to investigate the large amplitude vibratory behaviour of unsymmetrically laminated plates. For this purpose, an efficient and accurate four-node shear flexible rectangular material finite element(MFE) with six degrees offreedom per node (three displacements $(u;v;w)$ along the $x, y$ and axes, two rotations ($\\theta_x$ and $\\theta_y$) about and axes and twist $(\\theta_{xy})$) is developed. The element assumes bi-cubic polynomial distribution with sixteen generalized undetermined coefficients for the transverse displacement. The fields for section rotations $\\theta_x$ and $\\theta_y$, and in-plane displacements and are derived using moment-shear equilibrium and in-plane equilibrium equations of composite strips along the - and -axes. The displacement field so derived not only depends on the element coordinates but is a function of extensional, bending-extensional coupling, bending and transverse shear stiffness as well. The element stiffness and mass matrices are computed numerically by employing 3 × 3 Gauss-Legendre product rules. The element is found to be free of shear locking and does not exhibit any spurious modes. In orderto compute the nonlinearfrequencies, linear mode shape corresponding to the fundamental frequency is assumed as the spatial distribution and nonlinear finite element equations are reduced to a single nonlinear second-order differential equation. This equation is solved by employing the direct numerical integration method. A series of numerical examples are solved to demonstrate the efficacy of the proposed element.

  18. [Establishment and biomechanical analysis of three-dimensional nonlinear finite element model of three-pieces segment arch].

    Science.gov (United States)

    Lu, Shijun; Wang, Zhendong; Ni, Xiaoyu; Wang, Lin

    2013-02-01

    To reconstruct a three-dimensional nonlinear finite element model of mandibular teeth with three-pieces segment arch, and analyze the mechanical properties of intrusive arch and the biomechanical characteristics of three-pieces segment arch. Three-dimensional nonlinear finite element model of mandible with three-pieces segment arch was reconstructed by multi-slice spiral CT scanning, Mimics, CATIA and Anasys software. Then, the mechanical properties of intrusive arch, the movement trend and stress distribution of three-pieces segment arch were calculated by Anasys software. In the range of 5 degrees-25 degrees, with the degree of intrusive arch increased, the force of intrusive arch also increased rapidly. The maximal force was 0.604 8 N in 30 degrees; the force was about 0.59 N in 30 degrees-65 degrees range. In condition of three-pieces segment arch mechanics, lateral incisor tipped labially and intruded; the first moral tipped distally and rotating; other teeth did not move clearly. The largest stress distribution in the whole arch was in the one-third labial cervical area of the lateral incisor root and the root bifurcations of first moral. Under an appropriate intrusive force, three-pieces segment arch can intrude incisors and control the extrusion of posterior teeth. It can be used to correct the deep overbite, especially with high mandibular planes, gummy smile or adult patients.

  19. A diffuse-interface modeling for liquid solution-solid gel phase transition of physical hydrogel with nonlinear deformation.

    Science.gov (United States)

    Li, Hua; Wu, Tao

    2016-10-01

    A diffuse-interface model is presented in this paper for simulation of the evolution of phase transition between the liquid solution and solid gel states for physical hydrogel with nonlinear deformation. The present domain covers the gel and solution states as well as a diffuse interface between them. They are indicated by the crosslink density in such a way that the solution phase is identified as the state when the crosslink density is small, while the gel as the state if the crosslink density becomes large. In this work, a novel order parameter is thus defined as the crosslink density, which is homogeneous in each distinct phase and smoothly varies over the interface from one phase to another. In this model, the constitutive equations, imposed on the two distinct phases and the interface, are formulated by the second law of thermodynamics, which are in the same form as those derived by a different approach. The present constitutive equations include a novel Ginzburg-Landau type of free energy with a double-well profile, which accounts for the effect of crosslink density. The present governing equations include the equilibrium of forces, the conservations of mass and energy, and an additional kinetic equation imposed for phase transition, in which nonlinear deformation is considered. The equilibrium state is investigated numerically, where two stable phases are observed in the free energy profile. As case studies, a spherically symmetrical solution-gel phase transition is simulated numerically for analysis of the phase transition of physical hydrogel.

  20. POSTBUCKLING OF PRESSURE-LOADED SHEAR DEFORMABLE LAMINATED CYLINDRICAL PANELS

    Institute of Scientific and Technical Information of China (English)

    沈惠申

    2003-01-01

    A postbuckling analysis is presented for a shear deformable laminated cylindrical panel of finite length subjected to lateral pressure. The governing equations are based on Reddy's higher order shear deformation shell theory with yon Kdrmdn-Donnell-type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of shear deformable laminated cylindrical panels under lateral pressure. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, cross-ply laminated cylindrical panels. The effects played by transverse shear deformation, panel geometric parameters, total number of plies, fiber orientation, and initial geometric imperfections are studied.

  1. Vertical slice modelling of nonlinear Eady waves using a compatible finite element method

    Science.gov (United States)

    Yamazaki, Hiroe; Shipton, Jemma; Cullen, Michael J. P.; Mitchell, Lawrence; Cotter, Colin J.

    2017-08-01

    A vertical slice model is developed for the Euler-Boussinesq equations with a constant temperature gradient in the direction normal to the slice (the Eady-Boussinesq model). The model is a solution of the full three-dimensional equations with no variation normal to the slice, which is an idealised problem used to study the formation and subsequent evolution of weather fronts. A compatible finite element method is used to discretise the governing equations. To extend the Charney-Phillips grid staggering in the compatible finite element framework, we use the same node locations for buoyancy as the vertical part of velocity and apply a transport scheme for a partially continuous finite element space. For the time discretisation, we solve the semi-implicit equations together with an explicit strong-stability-preserving Runge-Kutta scheme to all of the advection terms. The model reproduces several quasi-periodic lifecycles of fronts despite the presence of strong discontinuities. An asymptotic limit analysis based on the semi-geostrophic theory shows that the model solutions are converging to a solution in cross-front geostrophic balance. The results are consistent with the previous results using finite difference methods, indicating that the compatible finite element method is performing as well as finite difference methods for this test problem. We observe dissipation of kinetic energy of the cross-front velocity in the model due to the lack of resolution at the fronts, even though the energy loss is not likely to account for the large gap on the strength of the fronts between the model result and the semi-geostrophic limit solution.

  2. Programming finite element method based hysteresis loss computation software using non-linear superconductor resistivity and T - phiv formulation

    Science.gov (United States)

    Stenvall, A.; Tarhasaari, T.

    2010-07-01

    Due to the rapid development of personal computers from the beginning of the 1990s, it has become a reality to simulate current penetration, and thus hysteresis losses, in superconductors with other than very simple one-dimensional (1D) Bean model computations or Norris formulae. Even though these older approaches are still usable, they do not consider, for example, multifilamentary conductors, local critical current dependency on magnetic field or varying n-values. Currently, many numerical methods employing different formulations are available. The problem of hysteresis losses can be scrutinized via an eddy current formulation of the classical theory of electromagnetism. The difficulty of the problem lies in the non-linear resistivity of the superconducting region. The steep transition between the superconducting and the normal states often causes convergence problems for the most common finite element method based programs. The integration methods suffer from full system matrices and, thus, restrict the number of elements to a few thousands at most. The so-called T - phiv formulation and the use of edge elements, or more precisely Whitney 1-forms, within the finite element method have proved to be a very suitable method for hysteresis loss simulations of different geometries. In this paper we consider making such finite element method software from first steps, employing differential geometry and forms.

  3. Programming finite element method based hysteresis loss computation software using non-linear superconductor resistivity and T - {psi} formulation

    Energy Technology Data Exchange (ETDEWEB)

    Stenvall, A; Tarhasaari, T, E-mail: antti.stenvall@tut.f [Electromagnetics, Tampere University of Technology, PO Box 692, 33101 Tampere (Finland)

    2010-07-15

    Due to the rapid development of personal computers from the beginning of the 1990s, it has become a reality to simulate current penetration, and thus hysteresis losses, in superconductors with other than very simple one-dimensional (1D) Bean model computations or Norris formulae. Even though these older approaches are still usable, they do not consider, for example, multifilamentary conductors, local critical current dependency on magnetic field or varying n-values. Currently, many numerical methods employing different formulations are available. The problem of hysteresis losses can be scrutinized via an eddy current formulation of the classical theory of electromagnetism. The difficulty of the problem lies in the non-linear resistivity of the superconducting region. The steep transition between the superconducting and the normal states often causes convergence problems for the most common finite element method based programs. The integration methods suffer from full system matrices and, thus, restrict the number of elements to a few thousands at most. The so-called T - {psi} formulation and the use of edge elements, or more precisely Whitney 1-forms, within the finite element method have proved to be a very suitable method for hysteresis loss simulations of different geometries. In this paper we consider making such finite element method software from first steps, employing differential geometry and forms.

  4. Normal ordering for nonlinear deformed ladder operators and the f-generalization of the Stirling and Bell numbers

    Science.gov (United States)

    Aleixo, A. N. F.; Balantekin, A. B.

    2015-12-01

    We resolve the normal ordering problem for symmetric ( D ˆ + D ˆ - ) n and asymmetric ( Dˆ + r D ˆ - ) n strings of the nonlinear deformed ladder operators D ˆ ± for supersymmetric and shape-invariant potential systems, where r and n are positive integers. We provide exact and explicit expressions for their normal forms N { ( D ˆ + D ˆ - ) n } and N { ( Dˆ + r D ˆ - ) n } , where in N { . . . } all D ˆ - are at the right side. We find that the solutions involve sequence of expansion coefficients which, for r, n > 1, corresponds to the f-deformed generalization of the classical Stirling and Bell numbers of the second kind. We apply the general formalism for the translational shape-invariant potential systems as well as for the particular case of the harmonic oscillator potential system. We show that these numbers are obtained for families of polynomial expressions generated with the deformations parameters and the parameters related to the forms of the supersymmetric partner potentials.

  5. On Nonlinear Complexity and Shannon’s Entropy of Finite Length Random Sequences

    Directory of Open Access Journals (Sweden)

    Lingfeng Liu

    2015-04-01

    Full Text Available Pseudorandom binary sequences have important uses in many fields, such as spread spectrum communications, statistical sampling and cryptography. There are two kinds of method in evaluating the properties of sequences, one is based on the probability measure, and the other is based on the deterministic complexity measures. However, the relationship between these two methods still remains an interesting open problem. In this paper, we mainly focus on the widely used nonlinear complexity of random sequences, study on its distribution, expectation and variance of memoryless sources. Furthermore, the relationship between nonlinear complexity and Shannon’s entropy is also established here. The results show that the Shannon’s entropy is strictly monotonically decreased with nonlinear complexity.

  6. Output-only identification of civil structures using nonlinear finite element model updating

    Science.gov (United States)

    Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.

    2015-03-01

    This paper presents a novel approach for output-only nonlinear system identification of structures using data recorded during earthquake events. In this approach, state-of-the-art nonlinear structural FE modeling and analysis techniques are combined with Bayesian Inference method to estimate (i) time-invariant parameters governing the nonlinear hysteretic material constitutive models used in the FE model of the structure, and (ii) the time history of the earthquake ground motion. To validate the performance of the proposed framework, the simulated responses of a bridge pier to an earthquake ground motion is polluted with artificial output measurement noise and used to jointly estimate the unknown material parameters and the time history of the earthquake ground motion. This proof-of-concept example illustrates the successful performance of the proposed approach even in the presence of high measurement noise.

  7. Harmonic balance finite element method applications in nonlinear electromagnetics and power systems

    CERN Document Server

    Lu, Junwei; Yamada, Sotoshi

    2016-01-01

    The first book applying HBFEM to practical electronic nonlinear field and circuit problems * Examines and solves wide aspects of practical electrical and electronic nonlinear field and circuit problems presented by HBFEM * Combines the latest research work with essential background knowledge, providing an all-encompassing reference for researchers, power engineers and students of applied electromagnetics analysis * There are very few books dealing with the solution of nonlinear electric- power-related problems * The contents are based on the authors' many years' research and industry experience; they approach the subject in a well-designed and logical way * It is expected that HBFEM will become a more useful and practical technique over the next 5 years due to the HVDC power system, renewable energy system and Smart Grid, HF magnetic used in DC/DC converter, and Multi-pulse transformer for HVDC power supply * HBFEM can provide effective and economic solutions to R&D product development * Includes Matlab e...

  8. An adaptive patient specific deformable registration for breast images of positron emission tomography and magnetic resonance imaging using finite element approach

    Science.gov (United States)

    Xue, Cheng; Tang, Fuk-Hay

    2014-03-01

    A patient specific registration model based on finite element method was investigated in this study. Image registration of Positron Emission Tomography (PET) and Magnetic Resonance imaging (MRI) has been studied a lot. Surface-based registration is extensively applied in medical imaging. We develop and evaluate a registration method combine surface-based registration with biomechanical modeling. .Four sample cases of patients with PET and MRI breast scans performed within 30 days were collected from hospital. K-means clustering algorithm was used to segment images into two parts, which is fat tissue and neoplasm [2]. Instead of placing extrinsic landmarks on patients' body which may be invasive, we proposed a new boundary condition to simulate breast deformation during two screening. Then a three dimensional model with meshes was built. Material properties were assigned to this model according to previous studies. The whole registration was based on a biomechanical finite element model, which could simulate deformation of breast under pressure.

  9. A Domain Decomposition Approach to Implementing Fault Slip in Finite-Element Models of Quasi-static and Dynamic Crustal Deformation

    CERN Document Server

    Aagaard, Brad T; Williams, Charles A

    2013-01-01

    We employ a domain decomposition approach with Lagrange multipliers to implement fault slip in a finite-element code, PyLith, for use in both quasi-static and dynamic crustal deformation applications. This integrated approach to solving both quasi-static and dynamic simulations leverages common finite-element data structures and implementations of various boundary conditions, discretization schemes, and bulk and fault rheologies. We have developed a custom preconditioner for the Lagrange multiplier portion of the system of equations that provides excellent scalability with problem size compared to conventional additive Schwarz methods. We demonstrate application of this approach using benchmarks for both quasi-static viscoelastic deformation and dynamic spontaneous rupture propagation that verify the numerical implementation in PyLith.

  10. LINEAR AND NONLINEAR DIELECTRIC PROPERTIES OF PARTICULATE COMPOSITES AT FINITE CONCENTRATION

    Institute of Scientific and Technical Information of China (English)

    ZHOU Xiao-ming; HU Geng-kai

    2006-01-01

    An analytical method was proposed to calculate effective linear and nonlinear dielectric properties for particulate composites. The method is based on an approximate solution of two-particle interaction problem, and it can be applied to relatively high volume concentration of particles (up to 50%). Nonlinear dielectric property was also examined by means of secant method. It is found that for low applied electric filed the proposed method is close to Stroud and Hui's method and for high applied electric filed it is close to Yu's method.

  11. A Symmetric Characteristic Finite Volume Element Scheme for Nonlinear Convection-Diffusion Problems

    Institute of Scientific and Technical Information of China (English)

    Min Yang; Yi-rang Yuan

    2008-01-01

    In this paper, we implement alternating direction strategy and construct a symmetric FVE scheme for nonlinear convection-diffusion problems. Comparing to general FVE methods, our method has two advantages. First, the coefficient matrices of the discrete schemes will be symmetric even for nonlinear problems.Second, since the solution of the algebraic equations at each time step can be inverted into the solution of several one-dimensional problems, the amount of computation work is smaller. We prove the optimal H1-norm error estimates of order O(△t2 + h) and present some numerical examples at the end of the paper.

  12. A Leonard-Sanders-Budiansky-Koiter-Type Nonlinear Shell Theory with a Hierarchy of Transverse-Shearing Deformations

    Science.gov (United States)

    Nemeth, Michael P.

    2013-01-01

    A detailed exposition on a refined nonlinear shell theory suitable for nonlinear buckling analyses of laminated-composite shell structures is presented. This shell theory includes the classical nonlinear shell theory attributed to Leonard, Sanders, Koiter, and Budiansky as an explicit proper subset. This approach is used in order to leverage the exisiting experience base and to make the theory attractive to industry. In addition, the formalism of general tensors is avoided in order to expose the details needed to fully understand and use the theory. The shell theory is based on "small" strains and "moderate" rotations, and no shell-thinness approximations are used. As a result, the strain-displacement relations are exact within the presumptions of "small" strains and "moderate" rotations. The effects of transverse-shearing deformations are included in the theory by using analyst-defined functions to describe the through-the-thickness distributions of transverse-shearing strains. Constitutive equations for laminated-composite shells are derived without using any shell-thinness approximations, and simplified forms and special cases are presented.

  13. Looking-Free Mixed hp Finite Element Methods for Linear and Geometrically Nonlinear Elasticity

    Science.gov (United States)

    1997-06-09

    hp mixed methods has been addressed by Stenberg and Suri[20]. They identify sufficient conditions for selecting mixed method spaces on parallelogram...spaces of piecewise polynomials. Math. Modeling Num. Anal., 19:111-143, 1985. [20] R. Stenberg and M. Suri. Mixed hp finite element methods for

  14. High-order Finite Difference Solution of Euler Equations for Nonlinear Water Waves

    DEFF Research Database (Denmark)

    Christiansen, Torben Robert Bilgrav; Bingham, Harry B.; Engsig-Karup, Allan Peter

    2012-01-01

    is discretized using arbitrary-order finite difference schemes on a staggered grid with one optional stretching in each coordinate direction. The momentum equations and kinematic free surface condition are integrated in time using the classic fourth-order Runge-Kutta scheme. Mass conservation is satisfied...

  15. Finite difference schemes for a nonlinear black-scholes model with transaction cost and volatility risk

    DEFF Research Database (Denmark)

    Mashayekhi, Sima; Hugger, Jens

    2015-01-01

    market. In this paper, we compare several finite difference methods for the solution of this model with respect to precision and order of convergence within a computationally feasible domain allowing at most 200 space steps and 10000 time steps. We conclude that standard explicit Euler comes out...

  16. Nonlinear solid finite element analysis of mitral valves with heterogeneous leaflet layers

    Science.gov (United States)

    Prot, V.; Skallerud, B.

    2009-02-01

    An incompressible transversely isotropic hyperelastic material for solid finite element analysis of a porcine mitral valve response is described. The material model implementation is checked in single element tests and compared with a membrane implementation in an out-of-plane loading test to study how the layered structures modify the stress response for a simple geometry. Three different collagen layer arrangements are used in finite element analysis of the mitral valve. When the leaflets are arranged in two layers with the collagen on the ventricular side, the stress in the fibre direction through the thickness in the central part of the anterior leaflet is homogenized and the peak stress is reduced. A simulation using membrane elements is also carried out for comparison with the solid finite element results. Compared to echocardiographic measurements, the finite element models bulge too much in the left atrium. This may be due to evidence of active muscle fibres in some parts of the anterior leaflet, whereas our constitutive modelling is based on passive material.

  17. Nonfragile Robust Finite-Time L2-L∞ Controller Design for a Class of Uncertain Lipschitz Nonlinear Systems with Time-Delays

    Directory of Open Access Journals (Sweden)

    Jun Song

    2013-01-01

    Full Text Available The nonfragile robust finite-time L2-L∞ control problem for a class of nonlinear uncertain systems with uncertainties and time-delays is considered. The nonlinear parameters are considered to satisfy the Lipschitz conditions and the exogenous disturbances are unknown but energy bounded. By using the Lyapunov function approach, the sufficient condition for the existence of nonfragile robust finite-time L2-L∞ controller is given in terms of linear matrix inequalities (LMIs. The finite-time controller is designed such that the resulting closed-loop system is finite-time bounded for all admissible uncertainties and satisfies the given L2-L∞ control index. Simulation results illustrate the validity of the proposed approach.

  18. Slope Safety Calculation With A Non-Linear Mohr Criterion Using Finite Element Method

    DEFF Research Database (Denmark)

    Clausen, Johan; Damkilde, Lars

    2005-01-01

    Safety factors for soil slopes are calculated using a non-linear Mohr envelope. The often used linear Mohr-Coulomb envelope tends to overestimate the safety as the material parameters are usually determined at much higher stress levels, than those present at slope failure. Experimental data...

  19. Results on stabilization of nonlinear systems under finite data-rate constraints

    NARCIS (Netherlands)

    Persis, Claudio De

    2004-01-01

    We discuss in this paper a result concerning the stabilization problem of nonlinear systems under data-rate constraints using output feedback. To put the result in a broader context, we shall first review a number of recent contributions on the stabilization problem under data-rate constraints when

  20. Adaptive Kronrod-Patterson integration of non-linear finite-element matrices

    DEFF Research Database (Denmark)

    Janssen, Hans

    2010-01-01

    Efficient simulation of unsaturated moisture flow in porous media is of great importance in many engineering fields. The highly non-linear character of unsaturated flow typically gives sharp moving moisture fronts during wetting and drying of materials with strong local moisture permeability and ...