Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
We introduce a new stabilized high-order and unstructured numerical model for modeling fully nonlinear and dispersive water waves. The model is based on a nodal spectral element method of arbitrary order in space and a -transformed formulation due to Cai, Langtangen, Nielsen and Tveito (1998). In...
A stabilised nodal spectral element method for fully nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, C.; Bigoni, Daniele
2016-01-01
can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively......We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998) [5], although...... the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2 projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions...
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.
The spectral cell method in nonlinear earthquake modeling
Giraldo, Daniel; Restrepo, Doriam
2017-12-01
This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.
Spectral analysis of noisy nonlinear maps
International Nuclear Information System (INIS)
Hirshman, S.P.; Whitson, J.C.
1982-01-01
A path integral equation formalism is developed to obtain the frequency spectrum of nonlinear mappings exhibiting chaotic behavior. The one-dimensional map, x/sub n+1/ = f(x/sub n/), where f is nonlinear and n is a discrete time variable, is analyzed in detail. This map is introduced as a paradigm of systems whose exact behavior is exceedingly complex, and therefore irretrievable, but which nevertheless possess smooth, well-behaved solutions in the presence of small sources of external noise. A Boltzmann integral equation is derived for the probability distribution function p(x,n). This equation is linear and is therefore amenable to spectral analysis. The nonlinear dynamics in f(x) appear as transition probability matrix elements, and the presence of noise appears simply as an overall multiplicative scattering amplitude. This formalism is used to investigate the band structure of the logistic equation and to analyze the effects of external noise on both the invariant measure and the frequency spectrum of x/sub n/ for several values of lambda epsilon [0,1
Spectral theory and nonlinear functional analysis
Lopez-Gomez, Julian
2001-01-01
This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems.The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.
Finite elements of nonlinear continua
Oden, John Tinsley
1972-01-01
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
Spectral decomposition of nonlinear systems with memory
Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J.
2016-02-01
We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.
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...
Introduction to nonlinear finite element analysis
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 · ...
Spectral theory and nonlinear analysis with applications to spatial ecology
Cano-Casanova, S; Mora-Corral , C
2005-01-01
This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology. The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis - from the most abstract developments up to the most concrete applications to population dynamics and socio-biology - in an effort to fill the existing gaps between these fields.
Spectral/hp element methods for CFD
Karniadakis, George Em
1999-01-01
Traditionally spectral methods in fluid dynamics were used in direct and large eddy simulations of turbulent flow in simply connected computational domains. The methods are now being applied to more complex geometries, and the spectral/hp element method, which incorporates both multi-domain spectral methods and high-order finite element methods, has been particularly successful. This book provides a comprehensive introduction to these methods. Written by leaders in the field, the book begins with a full explanation of fundamental concepts and implementation issues. It then illustrates how these methods can be applied to advection-diffusion and to incompressible and compressible Navier-Stokes equations. Drawing on both published and unpublished material, the book is an important resource for experienced researchers and for those new to the field.
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
Introduction to finite and spectral element methods using Matlab
Pozrikidis, Constantine
2014-01-01
The Finite Element Method in One Dimension. Further Applications in One Dimension. High-Order and Spectral Elements in One Dimension. The Finite Element Method in Two Dimensions. Quadratic and Spectral Elements in Two Dimensions. Applications in Mechanics. Viscous Flow. Finite and Spectral Element Methods in Three Dimensions. Appendices. References. Index.
Nonlinear finite element modeling of corrugated board
A. C. Gilchrist; J. C. Suhling; T. J. Urbanik
1999-01-01
In this research, an investigation on the mechanical behavior of corrugated board has been performed using finite element analysis. Numerical finite element models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...
Linear and Nonlinear Finite Elements.
1983-12-01
Metzler. Con/ ugte rapdent solution of a finite element elastic problem with high Poson rato without scaling and once with the global stiffness matrix K...nonzero c, that makes u(0) = 1. According to the linear, small deflection theory of the membrane the central displacement given to the membrane is not... theory is possible based on the approximations (l-y 2 )t = +y’ 2 +y , (1-y)’ 1-y’ 2 - y" (6) that change eq. (5) to V) = , [yŖ(1 + y") - Qy
Convergence of spectral methods for nonlinear conservation laws. Final report
International Nuclear Information System (INIS)
Tadmor, E.
1987-08-01
The convergence of the Fourier method for scalar nonlinear conservation laws which exhibit spontaneous shock discontinuities is discussed. Numerical tests indicate that the convergence may (and in fact in some cases must) fail, with or without post-processing of the numerical solution. Instead, a new kind of spectrally accurate vanishing viscosity is introduced to augment the Fourier approximation of such nonlinear conservation laws. Using compensated compactness arguments, it is shown that this spectral viscosity prevents oscillations, and convergence to the unique entropy solution follows
Linear and nonlinear optical spectroscopy: Spectral, temporal and spatial resolution
DEFF Research Database (Denmark)
Hvam, Jørn Marcher
1997-01-01
Selected linear and nonlinear optical spectroscopies are being described with special emphasis on the possibility of obtaining simultaneous spectral, temporal and spatial resolution. The potential of various experimental techniques is being demonstrated by specific examples mostly taken from inve...... investigations of the electronic, and opto-electronic, properties of semiconductor nanostructures....
Stabilization of numerical interchange in spectral-element magnetohydrodynamics
Sovinec, C. R.
2016-08-01
Auxiliary numerical projections of the divergence of flow velocity and vorticity parallel to magnetic field are developed and tested for the purpose of suppressing unphysical interchange instability in magnetohydrodynamic simulations. The numerical instability arises with equal-order C0 finite- and spectral-element expansions of the flow velocity, magnetic field, and pressure and is sensitive to behavior at the limit of resolution. The auxiliary projections are motivated by physical field-line bending, and coercive responses to the projections are added to the flow-velocity equation. Their incomplete expansions are limited to the highest-order orthogonal polynomial in at least one coordinate of the spectral elements. Cylindrical eigenmode computations show that the projections induce convergence from the stable side with first-order ideal-MHD equations during h-refinement and p-refinement. Hyperbolic and parabolic projections and responses are compared, together with different methods for avoiding magnetic divergence error. The projections are also shown to be effective in linear and nonlinear time-dependent computations with the NIMROD code Sovinec et al. [17], provided that the projections introduce numerical dissipation.
Automated computation of autonomous spectral submanifolds for nonlinear modal analysis
Ponsioen, Sten; Pedergnana, Tiemo; Haller, George
2018-04-01
We discuss an automated computational methodology for computing two-dimensional spectral submanifolds (SSMs) in autonomous nonlinear mechanical systems of arbitrary degrees of freedom. In our algorithm, SSMs, the smoothest nonlinear continuations of modal subspaces of the linearized system, are constructed up to arbitrary orders of accuracy, using the parameterization method. An advantage of this approach is that the construction of the SSMs does not break down when the SSM folds over its underlying spectral subspace. A further advantage is an automated a posteriori error estimation feature that enables a systematic increase in the orders of the SSM computation until the required accuracy is reached. We find that the present algorithm provides a major speed-up, relative to numerical continuation methods, in the computation of backbone curves, especially in higher-dimensional problems. We illustrate the accuracy and speed of the automated SSM algorithm on lower- and higher-dimensional mechanical systems.
Spectral transform and solvability of nonlinear evolution equations
International Nuclear Information System (INIS)
Degasperis, A.
1979-01-01
These lectures deal with an exciting development of the last decade, namely the resolving method based on the spectral transform which can be considered as an extension of the Fourier analysis to nonlinear evolution equations. Since many important physical phenomena are modeled by nonlinear partial wave equations this method is certainly a major breakthrough in mathematical physics. We follow the approach, introduced by Calogero, which generalizes the usual Wronskian relations for solutions of a Sturm-Liouville problem. Its application to the multichannel Schroedinger problem will be the subject of these lectures. We will focus upon dynamical systems described at time t by a multicomponent field depending on one space coordinate only. After recalling the Fourier technique for linear evolution equations we introduce the spectral transform method taking the integral equations of potential scattering as an example. The second part contains all the basic functional relationships between the fields and their spectral transforms as derived from the Wronskian approach. In the third part we discuss a particular class of solutions of nonlinear evolution equations, solitons, which are considered by many physicists as a first step towards an elementary particle theory, because of their particle-like behaviour. The effect of the polarization time-dependence on the motion of the soliton is studied by means of the corresponding spectral transform, leading to new concepts such as the 'boomeron' and the 'trappon'. The rich dynamic structure is illustrated by a brief report on the main results of boomeron-boomeron and boomeron-trappon collisions. In the final section we discuss further results concerning important properties of the solutions of basic nonlinear equations. We introduce the Baecklund transform for the special case of scalar fields and demonstrate how it can be used to generate multisoliton solutions and how the conservation laws are obtained. (HJ)
The next step in coastal numerical models: spectral/hp element methods?
DEFF Research Database (Denmark)
Eskilsson, Claes; Engsig-Karup, Allan Peter; Sherwin, Spencer J.
2005-01-01
In this paper we outline the application of spectral/hp element methods for modelling nonlinear and dispersive waves. We present one- and two-dimensional test cases for the shallow water equations and Boussinesqtype equations – including highly dispersive Boussinesq-type equations....
Energy Technology Data Exchange (ETDEWEB)
Cai, X C; Marcinkowski, L; Vassilevski, P S
2005-02-10
This paper extends previous results on nonlinear Schwarz preconditioning ([4]) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The non-local finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in [8]. Then, the algebraic construction from [9] of the corresponding non-linear finite element subproblems is applied to generate the subspace based nonlinear preconditioner. The overall nonlinearly preconditioned problem is solved by an inexact Newton method. Numerical illustration is also provided.
Stability estimates for hp spectral element methods for general ...
Indian Academy of Sciences (India)
We establish basic stability estimates for a non-conforming ℎ- spectral element method which allows for simultaneous mesh refinement and variable polynomial degree. The spectral element functions are non-conforming if the boundary conditions are Dirichlet. For problems with mixed boundary conditions they are ...
Spectral element method for wave propagation on irregular domains
Indian Academy of Sciences (India)
Yan Hui Geng
2018-03-14
Mar 14, 2018 ... Abstract. A spectral element approximation of acoustic propagation problems combined with a new mapping method on irregular domains is proposed. Following this method, the Gauss–Lobatto–Chebyshev nodes in the standard space are applied to the spectral element method (SEM). The nodes in the ...
Spectral element method for wave propagation on irregular domains
Indian Academy of Sciences (India)
A spectral element approximation of acoustic propagation problems combined with a new mapping method on irregular domains is proposed. Following this method, the Gauss–Lobatto–Chebyshev nodes in the standard space are applied to the spectral element method (SEM). The nodes in the physical space are ...
hp Spectral element methods for three dimensional elliptic problems
Indian Academy of Sciences (India)
This is the first of a series of papers devoted to the study of h-p spec- .... element functions defined on mesh elements in the new system of variables with a uni- ... the spectral element functions on these elements and give construction of the stability .... By Hm( ), we denote the usual Sobolev space of integer order m ≥ 0 ...
Finite element model for nonlinear shells of revolution
International Nuclear Information System (INIS)
Cook, W.A.
1979-01-01
Nuclear material shipping containers have shells of revolution as basic structural components. Analytically modeling the response of these containers to severe accident impact conditions requires a nonlinear shell-of-revolution model that accounts for both geometric and material nonlinearities. Existing models are limited to large displacements, small rotations, and nonlinear materials. The paper presents a finite element model for a nonlinear shell of revolution that will account for large displacements, large strains, large rotations, and nonlinear materials
Spectral decomposition in advection-diffusion analysis by finite element methods
International Nuclear Information System (INIS)
Nickell, R.E.; Gartling, D.K.; Strang, G.
1978-01-01
In a recent study of the convergence properties of finite element methods in nonlinear fluid mechanics, an indirect approach was taken. A two-dimensional example with a known exact solution was chosen as the vehicle for the study, and various mesh refinements were tested in an attempt to extract information on the effect of the local Reynolds number. However, more direct approaches are usually preferred. In this study one such direct approach is followed, based upon the spectral decomposition of the solution operator. Spectral decomposition is widely employed as a solution technique for linear structural dynamics problems and can be applied readily to linear, transient heat transfer analysis; in this case, the extension to nonlinear problems is of interest. It was shown previously that spectral techniques were applicable to stiff systems of rate equations, while recent studies of geometrically and materially nonlinear structural dynamics have demonstrated the increased information content of the numerical results. The use of spectral decomposition in nonlinear problems of heat and mass transfer would be expected to yield equally increased flow of information to the analyst, and this information could include a quantitative comparison of various solution strategies, meshes, and element hierarchies
Nonlinear spectral mixing theory to model multispectral signatures
Energy Technology Data Exchange (ETDEWEB)
Borel, C.C. [Los Alamos National Lab., NM (United States). Astrophysics and Radiation Measurements Group
1996-02-01
Nonlinear spectral mixing occurs due to multiple reflections and transmissions between discrete surfaces, e.g. leaves or facets of a rough surface. The radiosity method is an energy conserving computational method used in thermal engineering and it models nonlinear spectral mixing realistically and accurately. In contrast to the radiative transfer method the radiosity method takes into account the discreteness of the scattering surfaces (e.g. exact location, orientation and shape) such as leaves and includes mutual shading between them. An analytic radiosity-based scattering model for vegetation was developed and used to compute vegetation indices for various configurations. The leaf reflectance and transmittance was modeled using the PROSPECT model for various amounts of water, chlorophyll and variable leaf structure. The soil background was modeled using SOILSPEC with a linear mixture of reflectances of sand, clay and peat. A neural network and a geometry based retrieval scheme were used to retrieve leaf area index and chlorophyll concentration for dense canopies. Only simulated canopy reflectances in the 6 visible through short wave IR Landsat TM channels were used. The authors used an empirical function to compute the signal-to-noise ratio of a retrieved quantity.
Nonlinear finite element analysis of concrete structures
International Nuclear Information System (INIS)
Ottosen, N.S.
1980-05-01
This report deals with nonlinear finite element analysis of concrete structures loaded in the short-term up until failure. A profound discussion of constitutive modelling on concrete is performed; a model, applicable for general stress states, is described and its predictions are compared with experimental data. This model is implemented in the AXIPLANE-program applicable for axisymmetrick and plane structures. The theoretical basis for this program is given. Using the AXIPLANE-program various concrete structures are analysed up until failure and compared with experimental evidence. These analyses include panels pressure vessel, beams failing in shear and finally a specific pull-out test, the Lok-Test, is considered. In these analyses, the influence of different failure criteria, aggregate interlock, dowel action, secondary cracking, magnitude of compressive strenght, magnitude of tensile strenght and of different post-failure behaviours of the concrete are evaluated. Moreover, it is shown that a suitable analysis of the theoretical data results in a clear insight into the physical behaviour of the considered structures. Finally, it is demonstrated that the AXISPLANE-program for widely different structures exhibiting very delicate structural aspects gives predictions that are in close agreement with experimental evidence. (author)
Convergence analysis of spectral element method for electromechanical devices
Curti, M.; Jansen, J.W.; Lomonova, E.A.
2017-01-01
This paper concerns the comparison of the performance of the Spectral Element Method (SEM) and the Finite Element Method (FEM) for a magnetostatic problem. The convergence of the vector magnetic potential, the magnetic flux density, and the total stored energy in the system is compared with the
Convergence analysis of spectral element method for magnetic devices
Curti, M.; Jansen, J.W.; Lomonova, E.A.
2018-01-01
This paper concerns the comparison of the performance of the Spectral Element Method (SEM) and the Finite Element Method (FEM) for modeling a magnetostatic problem. The convergence of the vector magnetic potential, the magnetic flux density, and the total stored energy in the system is compared with
Spectral/ hp element methods: Recent developments, applications, and perspectives
Xu, Hui; Cantwell, Chris D.; Monteserin, Carlos; Eskilsson, Claes; Engsig-Karup, Allan P.; Sherwin, Spencer J.
2018-02-01
The spectral/ hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/ hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/ hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/ hp element method in more complex science and engineering applications are discussed.
Huang, Norden E.; Hu, Kun; Yang, Albert C. C.; Chang, Hsing-Chih; Jia, Deng; Liang, Wei-Kuang; Yeh, Jia Rong; Kao, Chu-Lan; Juan, Chi-Hung; Peng, Chung Kang; Meijer, Johanna H.; Wang, Yung-Hung; Long, Steven R.; Wu, Zhauhua
2016-01-01
The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert–Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through c...
Numerical and spectral investigations of novel infinite elements
International Nuclear Information System (INIS)
Barai, P.; Harari, I.; Barbonet, P.E.
1998-01-01
Exterior problems of time-harmonic acoustics are addressed by a novel infinite element formulation, defined on a bounded computational domain. For two-dimensional configurations with circular interfaces, the infinite element results match Quell both analytical values and those obtained from. other methods like DtN. Along 1uith the numerical performance of this formulation, of considerable interest are its complex-valued eigenvalues. Hence, a spectral analysis of the present scheme is also performed here, using various infinite elements
Efficiency of High Order Spectral Element Methods on Petascale Architectures
Hutchinson, Maxwell; Heinecke, Alexander; Pabst, Hans; Henry, Greg; Parsani, Matteo; Keyes, David E.
2016-01-01
High order methods for the solution of PDEs expose a tradeoff between computational cost and accuracy on a per degree of freedom basis. In many cases, the cost increases due to higher arithmetic intensity while affecting data movement minimally. As architectures tend towards wider vector instructions and expect higher arithmetic intensities, the best order for a particular simulation may change. This study highlights preferred orders by identifying the high order efficiency frontier of the spectral element method implemented in Nek5000 and NekBox: the set of orders and meshes that minimize computational cost at fixed accuracy. First, we extract Nek’s order-dependent computational kernels and demonstrate exceptional hardware utilization by hardware-aware implementations. Then, we perform productionscale calculations of the nonlinear single mode Rayleigh-Taylor instability on BlueGene/Q and Cray XC40-based supercomputers to highlight the influence of the architecture. Accuracy is defined with respect to physical observables, and computational costs are measured by the corehour charge of the entire application. The total number of grid points needed to achieve a given accuracy is reduced by increasing the polynomial order. On the XC40 and BlueGene/Q, polynomial orders as high as 31 and 15 come at no marginal cost per timestep, respectively. Taken together, these observations lead to a strong preference for high order discretizations that use fewer degrees of freedom. From a performance point of view, we demonstrate up to 60% full application bandwidth utilization at scale and achieve ≈1PFlop/s of compute performance in Nek’s most flop-intense methods.
Efficiency of High Order Spectral Element Methods on Petascale Architectures
Hutchinson, Maxwell
2016-06-14
High order methods for the solution of PDEs expose a tradeoff between computational cost and accuracy on a per degree of freedom basis. In many cases, the cost increases due to higher arithmetic intensity while affecting data movement minimally. As architectures tend towards wider vector instructions and expect higher arithmetic intensities, the best order for a particular simulation may change. This study highlights preferred orders by identifying the high order efficiency frontier of the spectral element method implemented in Nek5000 and NekBox: the set of orders and meshes that minimize computational cost at fixed accuracy. First, we extract Nek’s order-dependent computational kernels and demonstrate exceptional hardware utilization by hardware-aware implementations. Then, we perform productionscale calculations of the nonlinear single mode Rayleigh-Taylor instability on BlueGene/Q and Cray XC40-based supercomputers to highlight the influence of the architecture. Accuracy is defined with respect to physical observables, and computational costs are measured by the corehour charge of the entire application. The total number of grid points needed to achieve a given accuracy is reduced by increasing the polynomial order. On the XC40 and BlueGene/Q, polynomial orders as high as 31 and 15 come at no marginal cost per timestep, respectively. Taken together, these observations lead to a strong preference for high order discretizations that use fewer degrees of freedom. From a performance point of view, we demonstrate up to 60% full application bandwidth utilization at scale and achieve ≈1PFlop/s of compute performance in Nek’s most flop-intense methods.
About two new efficient nonlinear shell elements
International Nuclear Information System (INIS)
Yin, J.; Suo, X.Z.; Combescure, A.
1989-01-01
The aim of the paper is to present the development of two shell elements for non linear analysis. The first one is an axisymetric curved shell element and it is developed for buckling analysis. The formulation is given, as well as some typical applications. The second one is an extension of the classical DKT element to large strains taking into account all aspects of non linearities. This element is used for the simulation of four point bending of cracked pipes. The whole experiment is simulated by the calculation taking into account very large strains at the crack tip and propagation of the crack
Nonconforming h-p spectral element methods for elliptic problems
Indian Academy of Sciences (India)
In [6,7,13,14] h-p spectral element methods for solving elliptic boundary value problems on polygonal ... Let M denote the number of corner layers and W denote the number of degrees of .... β is given by Theorem 2.2 of [3] which can be stated.
hp Spectral element methods for three dimensional elliptic problems
Indian Academy of Sciences (India)
elliptic boundary value problems on non-smooth domains in R3. For Dirichlet problems, ... of variable degree bounded by W. Let N denote the number of layers in the geomet- ric mesh ... We prove a stability theorem for mixed problems when the spectral element functions vanish ..... Applying Theorem 3.1,. ∫ r l. |Mu|2dx −.
A three-dimensional spectral element model for the solution of the hydrostatic primitive equations
Iskandarani, M; Levin, J C
2003-01-01
We present a spectral element model to solve the hydrostatic primitive equations governing large-scale geophysical flows. The highlights of this new model include unstructured grids, dual h-p paths to convergence, and good scalability characteristics on present day parallel computers including Beowulf-class systems. The behavior of the model is assessed on three process-oriented test problems involving wave propagation, gravitational adjustment, and nonlinear flow rectification, respectively. The first of these test problems is a study of the convergence properties of the model when simulating the linear propagation of baroclinic Kelvin waves. The second is an intercomparison of spectral element and finite-difference model solutions to the adjustment of a density front in a straight channel. Finally, the third problem considers the comparison of model results to measurements obtained from a laboratory simulation of flow around a submarine canyon. The aforementioned tests demonstrate the good performance of th...
Impact of initial pulse shape on the nonlinear spectral compression in optical fibre
Boscolo, Sonia; Chaussard, Frederic; Andresen, Esben; Rigneault, Hervé; Finot, Christophe
2018-02-01
We theoretically study the effects of the temporal intensity profile of the initial pulse on the nonlinear propagation spectral compression process arising from nonlinear propagation in an optical fibre. Various linearly chirped input pulse profiles are considered, and their dynamics is explained with the aid of time-frequency representations. While initially parabolic-shaped pulses show enhanced spectral compression compared to Gaussian pulses, no significant spectral narrowing occurs when initially super-Gaussian pulses are used. Triangular pulses lead to a spectral interference phenomenon similar to the Fresnel bi-prism experiment.
Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling
Liu, Shaolin
2017-09-28
The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency-wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.
Advances in dynamic relaxation techniques for nonlinear finite element analysis
International Nuclear Information System (INIS)
Sauve, R.G.; Metzger, D.R.
1995-01-01
Traditionally, the finite element technique has been applied to static and steady-state problems using implicit methods. When nonlinearities exist, equilibrium iterations must be performed using Newton-Raphson or quasi-Newton techniques at each load level. In the presence of complex geometry, nonlinear material behavior, and large relative sliding of material interfaces, solutions using implicit methods often become intractable. A dynamic relaxation algorithm is developed for inclusion in finite element codes. The explicit nature of the method avoids large computer memory requirements and makes possible the solution of large-scale problems. The method described approaches the steady-state solution with no overshoot, a problem which has plagued researchers in the past. The method is included in a general nonlinear finite element code. A description of the method along with a number of new applications involving geometric and material nonlinearities are presented. They include: (1) nonlinear geometric cantilever plate; (2) moment-loaded nonlinear beam; and (3) creep of nuclear fuel channel assemblies
Finite element analysis of nonlinear creeping flows
International Nuclear Information System (INIS)
Loula, A.F.D.; Guerreiro, J.N.C.
1988-12-01
Steady-state creep problems with monotone constitutive laws are studied. Finite element approximations are constructed based on mixed Petrov-Galerkin formulations for constrained problems. Stability, convergence and a priori error estimates are proved for equal-order discontinuous stress and continuous velocity interpolations. Numerical results are presented confirming the rates of convergence predicted in the analysis and the good performance of this formulation. (author) [pt
Symplectic discretization for spectral element solution of Maxwell's equations
International Nuclear Information System (INIS)
Zhao Yanmin; Dai Guidong; Tang Yifa; Liu Qinghuo
2009-01-01
Applying the spectral element method (SEM) based on the Gauss-Lobatto-Legendre (GLL) polynomial to discretize Maxwell's equations, we obtain a Poisson system or a Poisson system with at most a perturbation. For the system, we prove that any symplectic partitioned Runge-Kutta (PRK) method preserves the Poisson structure and its implied symplectic structure. Numerical examples show the high accuracy of SEM and the benefit of conserving energy due to the use of symplectic methods.
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.
Xu, Tianhua; Karanov, Boris; Shevchenko, Nikita A; Lavery, Domaniç; Liga, Gabriele; Killey, Robert I; Bayvel, Polina
2017-10-11
Nyquist-spaced transmission and digital signal processing have proved effective in maximising the spectral efficiency and reach of optical communication systems. In these systems, Kerr nonlinearity determines the performance limits, and leads to spectral broadening of the signals propagating in the fibre. Although digital nonlinearity compensation was validated to be promising for mitigating Kerr nonlinearities, the impact of spectral broadening on nonlinearity compensation has never been quantified. In this paper, the performance of multi-channel digital back-propagation (MC-DBP) for compensating fibre nonlinearities in Nyquist-spaced optical communication systems is investigated, when the effect of signal spectral broadening is considered. It is found that accounting for the spectral broadening effect is crucial for achieving the best performance of DBP in both single-channel and multi-channel communication systems, independent of modulation formats used. For multi-channel systems, the degradation of DBP performance due to neglecting the spectral broadening effect in the compensation is more significant for outer channels. Our work also quantified the minimum bandwidths of optical receivers and signal processing devices to ensure the optimal compensation of deterministic nonlinear distortions.
Interferometric and nonlinear-optical spectral-imaging techniques for outer space and live cells
Itoh, Kazuyoshi
2015-12-01
Multidimensional signals such as the spectral images allow us to have deeper insights into the natures of objects. In this paper the spectral imaging techniques that are based on optical interferometry and nonlinear optics are presented. The interferometric imaging technique is based on the unified theory of Van Cittert-Zernike and Wiener-Khintchine theorems and allows us to retrieve a spectral image of an object in the far zone from the 3D spatial coherence function. The retrieval principle is explained using a very simple object. The promising applications to space interferometers for astronomy that are currently in progress will also be briefly touched on. An interesting extension of interferometric spectral imaging is a 3D and spectral imaging technique that records 4D information of objects where the 3D and spectral information is retrieved from the cross-spectral density function of optical field. The 3D imaging is realized via the numerical inverse propagation of the cross-spectral density. A few techniques suggested recently are introduced. The nonlinear optical technique that utilizes stimulated Raman scattering (SRS) for spectral imaging of biomedical targets is presented lastly. The strong signals of SRS permit us to get vibrational information of molecules in the live cell or tissue in real time. The vibrational information of unstained or unlabeled molecules is crucial especially for medical applications. The 3D information due to the optical nonlinearity is also the attractive feature of SRS spectral microscopy.
Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics
Carpenter, Mark H.
2016-01-04
Nonlinearly stable finite element methods of arbitrary type and order, are currently unavailable for discretizations of the compressible Navier-Stokes equations. Summation-by-parts (SBP) entropy stability analysis provides a means of constructing nonlinearly stable discrete operators of arbitrary order, but is currently limited to simple element types. Herein, recent progress is reported, on developing entropy-stable (SS) discontinuous spectral collocation formulations for hexahedral elements. Two complementary efforts are discussed. The first effort generalizes previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort extends previous work on entropy stability to include p-refinement at nonconforming interfaces. A generalization of existing entropy stability theory is required to accommodate the nuances of fully multidimensional SBP operators. The entropy stability of the compressible Euler equations on nonconforming interfaces is demonstrated using the newly developed LG operators and multidimensional interface interpolation operators. Preliminary studies suggest design order accuracy at nonconforming interfaces.
Nonlinear finite element analyses: advances and challenges in dental applications.
Wakabayashi, N; Ona, M; Suzuki, T; Igarashi, Y
2008-07-01
To discuss the development and current status of application of nonlinear finite element method (FEM) in dentistry. The literature was searched for original research articles with keywords such as nonlinear, finite element analysis, and tooth/dental/implant. References were selected manually or searched from the PUBMED and MEDLINE databases through November 2007. The nonlinear problems analyzed in FEM studies were reviewed and categorized into: (A) nonlinear simulations of the periodontal ligament (PDL), (B) plastic and viscoelastic behaviors of dental materials, (C) contact phenomena in tooth-to-tooth contact, (D) contact phenomena within prosthodontic structures, and (E) interfacial mechanics between the tooth and the restoration. The FEM in dentistry recently focused on simulation of realistic intra-oral conditions such as the nonlinear stress-strain relationship in the periodontal tissues and the contact phenomena in teeth, which could hardly be solved by the linear static model. The definition of contact area critically affects the reliability of the contact analyses, especially for implant-abutment complexes. To predict the failure risk of a bonded tooth-restoration interface, it is essential to assess the normal and shear stresses relative to the interface. The inclusion of viscoelasticity and plastic deformation to the program to account for the time-dependent, thermal sensitive, and largely deformable nature of dental materials would enhance its application. Further improvement of the nonlinear FEM solutions should be encouraged to widen the range of applications in dental and oral health science.
Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions
International Nuclear Information System (INIS)
Schulze-Halberg, Axel; Gordon, Christopher R.
2013-01-01
We analyze the spectral behaviour of a nonlinear quantum oscillator model under confinement. The underlying potential is given by a harmonic oscillator interaction plus a nonlinear term that can be weakened or strengthened through a parameter. Numerical eigenvalues of the model in one and three dimensions are presented. The asymptotic behaviour of the eigenvalues for confinement relaxation and for vanishing nonlinear term in the potential is investigated. Our findings are compared with existing results.
Spectral Analysis of Polynomial Nonlinearity with Applications to RF Power Amplifiers
Directory of Open Access Journals (Sweden)
G. Tong Zhou
2004-09-01
Full Text Available The majority of the nonlinearity in a communication system is attributed to the power amplifier (PA present at the final stage of the transmitter chain. In this paper, we consider Gaussian distributed input signals (such as OFDM, and PAs that can be modeled by memoryless or memory polynomials. We derive closed-form expressions of the PA output power spectral density, for an arbitrary nonlinear order, based on the so-called Leonov-Shiryaev formula. We then apply these results to answer practical questions such as the contribution of AM/PM conversion to spectral regrowth and the relationship between memory effects and spectral asymmetry.
PIXE-quantified AXSIA: Elemental mapping by multivariate spectral analysis
International Nuclear Information System (INIS)
Doyle, B.L.; Provencio, P.P.; Kotula, P.G.; Antolak, A.J.; Ryan, C.G.; Campbell, J.L.; Barrett, K.
2006-01-01
Automated, nonbiased, multivariate statistical analysis techniques are useful for converting very large amounts of data into a smaller, more manageable number of chemical components (spectra and images) that are needed to describe the measurement. We report the first use of the multivariate spectral analysis program AXSIA (Automated eXpert Spectral Image Analysis) developed at Sandia National Laboratories to quantitatively analyze micro-PIXE data maps. AXSIA implements a multivariate curve resolution technique that reduces the spectral image data sets into a limited number of physically realizable and easily interpretable components (including both spectra and images). We show that the principal component spectra can be further analyzed using conventional PIXE programs to convert the weighting images into quantitative concentration maps. A common elemental data set has been analyzed using three different PIXE analysis codes and the results compared to the cases when each of these codes is used to separately analyze the associated AXSIA principal component spectral data. We find that these comparisons are in good quantitative agreement with each other
Bessel smoothing filter for spectral-element mesh
Trinh, P. T.; Brossier, R.; Métivier, L.; Virieux, J.; Wellington, P.
2017-06-01
Smoothing filters are extremely important tools in seismic imaging and inversion, such as for traveltime tomography, migration and waveform inversion. For efficiency, and as they can be used a number of times during inversion, it is important that these filters can easily incorporate prior information on the geological structure of the investigated medium, through variable coherent lengths and orientation. In this study, we promote the use of the Bessel filter to achieve these purposes. Instead of considering the direct application of the filter, we demonstrate that we can rely on the equation associated with its inverse filter, which amounts to the solution of an elliptic partial differential equation. This enhances the efficiency of the filter application, and also its flexibility. We apply this strategy within a spectral-element-based elastic full waveform inversion framework. Taking advantage of this formulation, we apply the Bessel filter by solving the associated partial differential equation directly on the spectral-element mesh through the standard weak formulation. This avoids cumbersome projection operators between the spectral-element mesh and a regular Cartesian grid, or expensive explicit windowed convolution on the finite-element mesh, which is often used for applying smoothing operators. The associated linear system is solved efficiently through a parallel conjugate gradient algorithm, in which the matrix vector product is factorized and highly optimized with vectorized computation. Significant scaling behaviour is obtained when comparing this strategy with the explicit convolution method. The theoretical numerical complexity of this approach increases linearly with the coherent length, whereas a sublinear relationship is observed practically. Numerical illustrations are provided here for schematic examples, and for a more realistic elastic full waveform inversion gradient smoothing on the SEAM II benchmark model. These examples illustrate well the
Probabilistic finite elements for transient analysis in nonlinear continua
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.
Spectral element method for vector radiative transfer equation
International Nuclear Information System (INIS)
Zhao, J.M.; Liu, L.H.; Hsu, P.-F.; Tan, J.Y.
2010-01-01
A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted by spectral element approach. Chebyshev polynomial is used to build basis function on each element. Four various test problems are taken as examples to verify the performance of the SEM. The effectiveness of the SEM is demonstrated. The h and the p convergence characteristics of the SEM are studied. The convergence rate of p-refinement follows the exponential decay trend and is superior to that of h-refinement. The accuracy and efficiency of the higher order approximation in the SEM is well demonstrated for the solution of the VRTE. The predicted angular distribution of brightness temperature and Stokes vector by the SEM agree very well with the benchmark solutions in references. Numerical results show that the SEM is accurate, flexible and effective to solve multidimensional polarized radiative transfer problems.
Spectral Element Method for the Simulation of Unsteady Compressible Flows
Diosady, Laslo Tibor; Murman, Scott M.
2013-01-01
This work uses a discontinuous-Galerkin spectral-element method (DGSEM) to solve the compressible Navier-Stokes equations [1{3]. The inviscid ux is computed using the approximate Riemann solver of Roe [4]. The viscous fluxes are computed using the second form of Bassi and Rebay (BR2) [5] in a manner consistent with the spectral-element approximation. The method of lines with the classical 4th-order explicit Runge-Kutta scheme is used for time integration. Results for polynomial orders up to p = 15 (16th order) are presented. The code is parallelized using the Message Passing Interface (MPI). The computations presented in this work are performed using the Sandy Bridge nodes of the NASA Pleiades supercomputer at NASA Ames Research Center. Each Sandy Bridge node consists of 2 eight-core Intel Xeon E5-2670 processors with a clock speed of 2.6Ghz and 2GB per core memory. On a Sandy Bridge node the Tau Benchmark [6] runs in a time of 7.6s.
Domain decomposition solvers for nonlinear multiharmonic finite element equations
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.
Nonlinear dynamic analysis using Petrov-Galerkin natural element method
International Nuclear Information System (INIS)
Lee, Hong Woo; Cho, Jin Rae
2004-01-01
According to our previous study, it is confirmed that the Petrov-Galerkin Natural Element Method (PG-NEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin Natural Element Method (BG-NEM). This paper is an extension of PG-NEM to two-dimensional nonlinear dynamic problem. For the analysis, a constant average acceleration method and a linearized total Lagrangian formulation is introduced with the PG-NEM. At every time step, the grid points are updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates the nonlinear dynamic problem
Spectral response of multi-element silicon detectors
Energy Technology Data Exchange (ETDEWEB)
Ludewigt, B.A.; Rossington, C.S.; Chapman, K. [Univ. of California, Berkeley, CA (United States)
1997-04-01
Multi-element silicon strip detectors, in conjunction with integrated circuit pulse-processing electronics, offer an attractive alternative to conventional lithium-drifted silicon Si(Li) and high purity germanium detectors (HPGe) for high count rate, low noise synchrotron x-ray fluorescence applications. One of the major differences between the segmented Si detectors and the commercially available single-element Si(Li) or HPGe detectors is that hundreds of elements can be fabricated on a single Si substrate using standard silicon processing technologies. The segmentation of the detector substrate into many small elements results in very low noise performance at or near, room temperature, and the count rate of the detector is increased many-fold due to the multiplication in the total number of detectors. Traditionally, a single channel of detector with electronics can handle {approximately}100 kHz count rates while maintaining good energy resolution; the segmented detectors can operate at greater than MHz count rates merely due to the multiplication in the number of channels. One of the most critical aspects in the development of the segmented detectors is characterizing the charge sharing and charge loss that occur between the individual detector strips, and determining how these affect the spectral response of the detectors.
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
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.
Efficient Hybrid-Spectral Model for Fully Nonlinear Numerical Wave Tank
DEFF Research Database (Denmark)
Christiansen, Torben; Bingham, Harry B.; Engsig-Karup, Allan Peter
2013-01-01
A new hybrid-spectral solution strategy is proposed for the simulation of the fully nonlinear free surface equations based on potential flow theory. A Fourier collocation method is adopted horisontally for the discretization of the free surface equations. This is combined with a modal Chebyshev Tau...... method in the vertical for the discretization of the Laplace equation in the fluid domain, which yields a sparse and spectrally accurate Dirichletto-Neumann operator. The Laplace problem is solved with an efficient Defect Correction method preconditioned with a spectral discretization of the linearised...... wave problem, ensuring fast convergence and optimal scaling with the problem size. Preliminary results for very nonlinear waves show expected convergence rates and a clear advantage of using spectral schemes....
Spectral methods for a nonlinear initial value problem involving pseudo differential operators
International Nuclear Information System (INIS)
Pasciak, J.E.
1982-01-01
Spectral methods (Fourier methods) for approximating the solution of a nonlinear initial value problem involving pseudo differential operators are defined and analyzed. A semidiscrete approximation to the nonlinear equation based on an L 2 projection is described. The semidiscrete L 2 approximation is shown to be a priori stable and convergent under sufficient decay and smoothness assumptions on the initial data. It is shown that the semidiscrete method converges with infinite order, that is, higher order decay and smoothness assumptions imply higher order error bounds. Spectral schemes based on spacial collocation are also discussed
Comparison of modal spectral and non-linear time history analysis of a piping system
International Nuclear Information System (INIS)
Gerard, R.; Aelbrecht, D.; Lafaille, J.P.
1987-01-01
A typical piping system of the discharge line of the chemical and volumetric control system, outside the containment, between the penetration and the heat exchanger, an operating power plant was analyzed using four different methods: Modal spectral analysis with 2% constant damping, modal spectral analysis using ASME Code Case N411 (PVRC damping), linear time history analysis, non-linear time history analysis. This paper presents an estimation of the conservatism of the linear methods compared to the non-linear analysis. (orig./HP)
Directory of Open Access Journals (Sweden)
Woo-Young Jung
2015-04-01
Full Text Available For the solution of geometrically nonlinear analysis of plates and shells, the formulation of a nonlinear nine-node refined first-order shear deformable element-based Lagrangian shell element is presented. Natural co-ordinate-based higher order transverse shear strains are used in present shell element. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, a refined first-order shear deformation theory for thin and thick shells, which results in parabolic through-thickness distribution of the transverse shear strains from the formulation based on the third-order shear deformation theory, is proposed. This formulation eliminates the need for shear correction factors in the first-order theory. To avoid difficulties resulting from large increments of the rotations, a scheme of attached reference system is used for the expression of rotations of shell normal. Numerical examples demonstrate that the present element behaves reasonably satisfactorily either for the linear or for geometrically nonlinear analysis of thin and thick plates and shells with large displacement but small strain. Especially, the nonlinear results of slit annular plates with various loads provided the benchmark to test the accuracy of related numerical solutions.
Nonlinear effects of high temperature on buckling of structural elements
International Nuclear Information System (INIS)
Iyengar, N.G.R.
1975-01-01
Structural elements used in nuclear reactors are subjected to high temperatures. Since with increase in temperature there is a gradual fall in the elastic modulus and the stress-strain relationship is nonlinear at these operating load levels, a realistic estimate of the buckling load should include this nonlinearity. In this paper the buckling loads for uniform columns with circular and rectangular cross-sections and different boundary conditions under high temperature environment are estimated. The stress-strain relationship for the material has been assumed to follow inverse Ramberg-Osgood law. In view of the fact that no closed form solutions are possible, approximate methods like perturbation and Galerkin techniques are used. Further, the solution for general value for 'm' is quite involved. Results have been obtained with values for 'm' as 3 and 5. Studies reveal that the influence of material nonlinearity on the buckling load is of the softening type, and it increases with increase in the value of 'm'. The nonlinear effects are more for clamped boundaries than for simply supported boundaries. For the first mode analysis both the methods are powerful. It is, however, felt that for higher modes the Galerkin method might be better in view of its simplicity. This investigation may be considered as a step towards a more general solution
Finite element solution of quasistationary nonlinear magnetic field
International Nuclear Information System (INIS)
Zlamal, Milos
1982-01-01
The computation of quasistationary nonlinear two-dimensional magnetic field leads to the following problem. There is given a bounded domain OMEGA and an open nonempty set R included in OMEGA. We are looking for the magnetic vector potential u(x 1 , x 2 , t) which satisifies: 1) a certain nonlinear parabolic equation and an initial condition in R: 2) a nonlinear elliptic equation in S = OMEGA - R which is the stationary case of the above mentioned parabolic equation; 3) a boundary condition on delta OMEGA; 4) u as well as its conormal derivative are continuous accross the common boundary of R and S. This problem is formulated in two equivalent abstract ways. There is constructed an approximate solution completely discretized in space by a generalized Galerkin method (straight finite elements are a special case) and by backward A-stable differentiation methods in time. Existence and uniqueness of a weak solution is proved as well as a weak and strong convergence of the approximate solution to this solution. There are also derived error bounds for the solution of the two-dimensional nonlinear magnetic field equations under the assumption that the exact solution is sufficiently smooth
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.
NONLINEAR SPECTRAL IMAGING OF ELASTIC CARTILAGE IN RABBIT EARS
Directory of Open Access Journals (Sweden)
JING CHEN
2013-07-01
Full Text Available Elastic cartilage in the rabbit external ear is an important animal model with attractive potential value for researching the physiological and pathological states of cartilages especially during wound healing. In this work, nonlinear optical microscopy based on two-photon excited fluorescence and second harmonic generation were employed for imaging and quantifying the intact elastic cartilage. The morphology and distribution of main components in elastic cartilage including cartilage cells, collagen and elastic fibers were clearly observed from the high-resolution two-dimensional nonlinear optical images. The areas of cell nuclei, a parameter related to the pathological changes of normal or abnormal elastic cartilage, can be easily quantified. Moreover, the three-dimensional structure of chondrocytes and matrix were displayed by constructing three-dimensional image of cartilage tissue. At last, the emission spectra from cartilage were obtained and analyzed. We found that the different ratio of collagen over elastic fibers can be used to locate the observed position in the elastic cartilage. The redox ratio based on the ratio of nicotinamide adenine dinucleotide (NADH over flavin adenine dinucleotide (FAD fluorescence can also be calculated to analyze the metabolic state of chondrocytes in different regions. Our results demonstrated that this technique has the potential to provide more accurate and comprehensive information for the physiological states of elastic cartilage.
A mixed finite element method for nonlinear diffusion equations
Burger, Martin; Carrillo, José
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.
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.
A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis
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.
Superconducting nanowires as nonlinear inductive elements for qubits
Ku, Jaseung; Manucharyan, Vladimir; Bezryadin, Alexey
2011-03-01
We report microwave transmission measurements of superconducting Fabry-Perot resonators, having a superconducting nanowire placed at a supercurrent antinode. As the plasma oscillation is excited, the supercurrent is forced to flow through the nanowire. The microwave transmission of the resonator-nanowire device shows a nonlinear resonance behavior, significantly dependent on the amplitude of the supercurrent oscillation. We show that such amplitude-dependent response is due to the nonlinearity of the current-phase relationship of the nanowire. The results are explained within a nonlinear oscillator model of the Duffing oscillator, in which the nanowire acts as a purely inductive element, in the limit of low temperatures and low amplitudes. The low-quality factor sample exhibits a ``crater'' at the resonance peak at higher driving power, which is due to dissipation. We observe a hysteretic bifurcation behavior of the transmission response to frequency sweep in a sample with a higher quality factor. The Duffing model is used to explain the Duffing bistability diagram. NSF DMR-1005645, DOE DO-FG02-07ER46453.
Nonlinear magnetohydrodynamics simulation using high-order finite elements
International Nuclear Information System (INIS)
Plimpton, Steven James; Schnack, D.D.; Tarditi, A.; Chu, M.S.; Gianakon, T.A.; Kruger, S.E.; Nebel, R.A.; Barnes, D.C.; Sovinec, C.R.; Glasser, A.H.
2005-01-01
A conforming representation composed of 2D finite elements and finite Fourier series is applied to 3D nonlinear non-ideal magnetohydrodynamics using a semi-implicit time-advance. The self-adjoint semi-implicit operator and variational approach to spatial discretization are synergistic and enable simulation in the extremely stiff conditions found in high temperature plasmas without sacrificing the geometric flexibility needed for modeling laboratory experiments. Growth rates for resistive tearing modes with experimentally relevant Lundquist number are computed accurately with time-steps that are large with respect to the global Alfven time and moderate spatial resolution when the finite elements have basis functions of polynomial degree (p) two or larger. An error diffusion method controls the generation of magnetic divergence error. Convergence studies show that this approach is effective for continuous basis functions with p (ge) 2, where the number of test functions for the divergence control terms is less than the number of degrees of freedom in the expansion for vector fields. Anisotropic thermal conduction at realistic ratios of parallel to perpendicular conductivity (x(parallel)/x(perpendicular)) is computed accurately with p (ge) 3 without mesh alignment. A simulation of tearing-mode evolution for a shaped toroidal tokamak equilibrium demonstrates the effectiveness of the algorithm in nonlinear conditions, and its results are used to verify the accuracy of the numerical anisotropic thermal conduction in 3D magnetic topologies.
Spectral dependence of third-order nonlinear optical properties in InN
International Nuclear Information System (INIS)
Ahn, H.; Lee, M.-T.; Chang, Y.-M.
2014-01-01
We report on the nonlinear optical properties of InN measured in a wide near-infrared spectral range with the femtosecond Z-scan technique. The above-bandgap nonlinear absorption in InN is found to originate from the saturation of absorption by the band-state-filling and its cross-section increases drastically near the bandgap energy. With below-bandgap excitation, the nonlinear absorption undergoes a transition from saturation absorption (SA) to reverse-SA (RSA), attributed to the competition between SA of band-tail states and two-photon-related RSA. The measured large nonlinear refractive index of the order of 10 −10 cm 2 /W indicates InN as a potential material for all-optical switching and related applications
Guo, Tong; Chen, Zhuo; Li, Minghui; Wu, Juhong; Fu, Xing; Hu, Xiaotang
2018-04-20
Based on white-light spectral interferometry and the Linnik microscopic interference configuration, the nonlinear phase components of the spectral interferometric signal were analyzed for film thickness measurement. The spectral interferometric signal was obtained using a Linnik microscopic white-light spectral interferometer, which includes the nonlinear phase components associated with the effective thickness, the nonlinear phase error caused by the double-objective lens, and the nonlinear phase of the thin film itself. To determine the influence of the effective thickness, a wavelength-correction method was proposed that converts the effective thickness into a constant value; the nonlinear phase caused by the effective thickness can then be determined and subtracted from the total nonlinear phase. A method for the extraction of the nonlinear phase error caused by the double-objective lens was also proposed. Accurate thickness measurement of a thin film can be achieved by fitting the nonlinear phase of the thin film after removal of the nonlinear phase caused by the effective thickness and by the nonlinear phase error caused by the double-objective lens. The experimental results demonstrated that both the wavelength-correction method and the extraction method for the nonlinear phase error caused by the double-objective lens improve the accuracy of film thickness measurements.
A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems
Directory of Open Access Journals (Sweden)
S. S. Motsa
2013-01-01
Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.
Discrete conservation properties for shallow water flows using mixed mimetic spectral elements
Lee, D.; Palha, A.; Gerritsma, M.
2018-01-01
A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of calculus with respect to the standard Lagrange basis functions in
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael
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.
Spectral transformations in the regime of pulse self-trapping in a nonlinear photonic crystal
International Nuclear Information System (INIS)
Novitsky, Denis V.
2011-01-01
We consider the interaction of a femtosecond light pulse with a one-dimensional photonic crystal with relaxing cubic nonlinearity in the regime of self-trapping. By use of numerical simulations, it is shown that, under certain conditions, the spectra of reflected and transmitted light possess the properties of narrowband (quasimonochromatic) or wideband (continuumlike) radiation. It is remarkable that these spectral features appear due to a significant frequency shift and occur inside a photonic band gap of the structure under investigation.
Directory of Open Access Journals (Sweden)
S. S. Motsa
2014-01-01
Full Text Available This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs. The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Motsa, S S; Magagula, V M; Sibanda, P
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Incompressible spectral-element method: Derivation of equations
Deanna, Russell G.
1993-01-01
A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang Jin; Seo, Jeong Moon
2000-08-01
The main goal of this research is to establish a methodology of finite element analysis of containment building predicting not only global behaviour but also local failure mode. In this report, we summerize some existing numerical analysis techniques to be improved for containment building. In other words, a complete description of the standard degenerated shell finite element formulation is provided for nonlinear stress analysis of nuclear containment structure. A shell finite element is derived using the degenerated solid concept which does not rely on a specific shell theory. Reissner-Mindlin assumptions are adopted to consider the transverse shear deformation effect. In order to minimize the sensitivity of the constitutive equation to structural types, microscopic material model is adopted. The four solution algorithms based on the standard Newton-Raphson method are discussed. Finally, two numerical examples are carried out to test the performance of the adopted shell medel.
International Nuclear Information System (INIS)
Lee, Sang Jin; Seo, Jeong Moon
2000-08-01
The main goal of this research is to establish a methodology of finite element analysis of containment building predicting not only global behaviour but also local failure mode. In this report, we summerize some existing numerical analysis techniques to be improved for containment building. In other words, a complete description of the standard degenerated shell finite element formulation is provided for nonlinear stress analysis of nuclear containment structure. A shell finite element is derived using the degenerated solid concept which does not rely on a specific shell theory. Reissner-Mindlin assumptions are adopted to consider the transverse shear deformation effect. In order to minimize the sensitivity of the constitutive equation to structural types, microscopic material model is adopted. The four solution algorithms based on the standard Newton-Raphson method are discussed. Finally, two numerical examples are carried out to test the performance of the adopted shell medel
A mass and energy conserving spectral element atmospheric dynamical core on the cubed-sphere grid
International Nuclear Information System (INIS)
Taylor, M A; Edwards, J; Thomas, S; Nair, R
2007-01-01
We present results from a conservative formulation of the spectral element method applied to global atmospheric circulation modeling. Exact local conservation of both mass and energy is obtained via a new compatible formulation of the spectral element method. Compatibility insures that the key integral property of the divergence and gradient operators required to show conservation also hold in discrete form. The spectral element method is used on a cubed-sphere grid to discretize the horizontal directions on the sphere. It can be coupled to any conservative vertical/radial discretization. The accuracy and conservation properties of the method are illustrated using a baroclinic instability test case
Chiang, C. K.; Xue, David Y.; Mei, Chuh
1993-04-01
A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.
Energy Technology Data Exchange (ETDEWEB)
Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr. [Los Alamos National Lab., NM (United States)
1993-11-01
Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime.
International Nuclear Information System (INIS)
Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr.
1993-01-01
Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime
Taneja, Ankur; Higdon, Jonathan
2018-01-01
A high-order spectral element discontinuous Galerkin method is presented for simulating immiscible two-phase flow in petroleum reservoirs. The governing equations involve a coupled system of strongly nonlinear partial differential equations for the pressure and fluid saturation in the reservoir. A fully implicit method is used with a high-order accurate time integration using an implicit Rosenbrock method. Numerical tests give the first demonstration of high order hp spatial convergence results for multiphase flow in petroleum reservoirs with industry standard relative permeability models. High order convergence is shown formally for spectral elements with up to 8th order polynomials for both homogeneous and heterogeneous permeability fields. Numerical results are presented for multiphase fluid flow in heterogeneous reservoirs with complex geometric or geologic features using up to 11th order polynomials. Robust, stable simulations are presented for heterogeneous geologic features, including globally heterogeneous permeability fields, anisotropic permeability tensors, broad regions of low-permeability, high-permeability channels, thin shale barriers and thin high-permeability fractures. A major result of this paper is the demonstration that the resolution of the high order spectral element method may be exploited to achieve accurate results utilizing a simple cartesian mesh for non-conforming geological features. Eliminating the need to mesh to the boundaries of geological features greatly simplifies the workflow for petroleum engineers testing multiple scenarios in the face of uncertainty in the subsurface geology.
Espath, L. F R; Braun, Alexandre Luis; Awruch, Armando Miguel; Dalcin, Lisandro
2015-01-01
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Huang, K.M. [Wuhan Univ. (China). School of Electronic Information; Chinese Academey of Sciences, Hefei (China). Key Lab. of Geospace Environment; Embry Riddle Aeronautical Univ., Daytona Beach, FL (United States). Dept. of Physical Science; Ministry of Education, Wuhan (China). Key Lab. of Geospace Environment and Geodesy; State Observatory for Atmospheric Remote Sensing, Wuhan (China); Liu, A.Z.; Li, Z. [Embry Riddle Aeronautical Univ., Daytona Beach, FL (United States). Dept. of Physical Science; Zhang, S.D.; Yi, F. [Wuhan Univ. (China). School of Electronic Information; Ministry of Education, Wuhan (China). Key Lab. of Geospace Environment and Geodesy; State Observatory for Atmospheric Remote Sensing, Wuhan (China)
2012-07-01
Nonlinear interactions of gravity waves are studied with a two-dimensional, fully nonlinear model. The energy exchanges among resonant and near-resonant triads are examined in order to understand the spectral energy transfer through interactions. The results show that in both resonant and near-resonant interactions, the energy exchange between two high frequency waves is strong, but the energy transfer from large to small vertical scale waves is rather weak. This suggests that the energy cascade toward large vertical wavenumbers through nonlinear interaction is inefficient, which is different from the rapid turbulence cascade. Because of considerable energy exchange, nonlinear interactions can effectively spread high frequency spectrum, and play a significant role in limiting wave amplitude growth and transferring energy into higher altitudes. In resonant interaction, the interacting waves obey the resonant matching conditions, and resonant excitation is reversible, while near-resonant excitation is not so. Although near-resonant interaction shows the complexity of match relation, numerical experiments show an interesting result that when sum and difference near-resonant interactions occur between high and low frequency waves, the wave vectors tend to approximately match in horizontal direction, and the frequency of the excited waves is also close to the matching value. (orig.)
A fast conservative spectral solver for the nonlinear Boltzmann collision operator
International Nuclear Information System (INIS)
Gamba, Irene M.; Haack, Jeffrey R.; Hu, Jingwei
2014-01-01
We present a conservative spectral method for the fully nonlinear Boltzmann collision operator based on the weighted convolution structure in Fourier space developed by Gamba and Tharkabhushnanam. This method can simulate a broad class of collisions, including both elastic and inelastic collisions as well as angularly dependent cross sections in which grazing collisions play a major role. The extension presented in this paper consists of factorizing the convolution weight on quadrature points by exploiting the symmetric nature of the particle interaction law, which reduces the computational cost and memory requirements of the method to O(M 2 N 4 logN) from the O(N 6 ) complexity of the original spectral method, where N is the number of velocity grid points in each velocity dimension and M is the number of quadrature points in the factorization, which can be taken to be much smaller than N. We present preliminary numerical results
Tomar, S.K.
2002-01-01
It is well known that elliptic problems when posed on non-smooth domains, develop singularities. We examine such problems within the framework of spectral element methods and resolve the singularities with exponential accuracy.
Special function solutions of a spectral problem for a nonlinear quantum oscillator
International Nuclear Information System (INIS)
Schulze-Halberg, A; Morris, J R
2012-01-01
We construct exact solutions of a spectral problem involving the Schrödinger equation for a nonlinear, one-parameter oscillator potential. In contrast to a previous analysis of the problem (Carinena et al 2007 Ann. Phys. 322 434–59), where solutions were given through a Rodrigues-type formula, our approach leads to closed-form representations of the solutions in terms of special functions, not containing any derivative operators. We show normalizability and orthogonality of our solutions, as well as correct reduction of the problem to the harmonic oscillator model, if the parameter in the potential gets close to zero. (paper)
Directory of Open Access Journals (Sweden)
Z. Pashazadeh Atabakan
2013-01-01
Full Text Available Spectral homotopy analysis method (SHAM as a modification of homotopy analysis method (HAM is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.
Non-linear finite element analysis in structural mechanics
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.
International Nuclear Information System (INIS)
Olson, R.; Scott, P.; Wilkowski, G.M.
1992-01-01
As part of the US NRC's Degraded Piping Program, the concept of using a nonlinear spring element to simulate the response of cracked pipe in dynamic finite element pipe evaluations was initially proposed. The nonlinear spring element is used to represent the moment versus rotation response of the cracked pipe section. The moment-rotation relationship for the crack size and material of interest is determined from either J-estimation scheme analyses or experimental data. In this paper, a number of possible approaches for modeling the nonlinear stiffness of the cracked pipe section are introduced. One approach, modeling the cracked section moment rotation response with a series of spring-slider elements, is discussed in detail. As part of this discussion, results from a series of finite element predictions using the spring-slider nonlinear spring element are compared with the results from a series of dynamic cracked pipe system experiments from the International Piping Integrity Research Group (IPIRG) program
Near-fault earthquake ground motion prediction by a high-performance spectral element numerical code
International Nuclear Information System (INIS)
Paolucci, Roberto; Stupazzini, Marco
2008-01-01
Near-fault effects have been widely recognised to produce specific features of earthquake ground motion, that cannot be reliably predicted by 1D seismic wave propagation modelling, used as a standard in engineering applications. These features may have a relevant impact on the structural response, especially in the nonlinear range, that is hard to predict and to be put in a design format, due to the scarcity of significant earthquake records and of reliable numerical simulations. In this contribution a pilot study is presented for the evaluation of seismic ground-motions in the near-fault region, based on a high-performance numerical code for 3D seismic wave propagation analyses, including the seismic fault, the wave propagation path and the near-surface geological or topographical irregularity. For this purpose, the software package GeoELSE is adopted, based on the spectral element method. The set-up of the numerical benchmark of 3D ground motion simulation in the valley of Grenoble (French Alps) is chosen to study the effect of the complex interaction between basin geometry and radiation mechanism on the variability of earthquake ground motion
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
Ervin, Vincent J.; Jenkins, Eleanor W.; Sun, Shuyu
2011-01-01
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
International Nuclear Information System (INIS)
Ostachowicz, W; Kudela, P
2010-01-01
A Spectral Element Method is used for wave propagation modelling. A 3D solid spectral element is derived with shape functions based on Lagrange interpolation and Gauss-Lobatto-Legendre points. This approach is applied for displacement approximation suited for fundamental modes of Lamb waves as well as potential distribution in piezoelectric transducers. The novelty is the model geometry extension from flat to curved elements for application in shell-like structures. Exemplary visualisations of waves excited by the piezoelectric transducers in curved shell structure made of aluminium alloy are presented. Simple signal analysis of wave interaction with crack is performed. The crack is modelled by separation of appropriate nodes between elements. An investigation of influence of the crack length on wave propagation signals is performed. Additionally, some aspects of the spectral element method implementation are discussed.
Spectral/hp element methods: Recent developments, applications, and perspectives
DEFF Research Database (Denmark)
Xu, Hui; Cantwell, Chris; Monteserin, Carlos
2018-01-01
regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral...... is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain...
Sokolov, Alexei V; Naveira, Lucas M; Poudel, Milan P; Strohaber, James; Trendafilova, Cynthia S; Buck, William C; Wang, Jieyu; Strycker, Benjamin D; Wang, Chao; Schuessler, Hans; Kolomenskii, Alexandre; Kattawar, George W
2010-01-20
We study propagation of short laser pulses through water and use a spectral hole filling technique to essentially perform a sensitive balanced comparison of absorption coefficients for pulses of different duration. This study is motivated by an alleged violation of the Bouguer-Lambert-Beer law at low light intensities, where the pulse propagation is expected to be linear, and by a possible observation of femtosecond optical precursors in water. We find that at low intensities, absorption of laser light is determined solely by its spectrum and does not directly depend on the pulse duration, in agreement with our earlier work and in contradiction to some work of others. However, as the laser fluence is increased, interaction of light with water becomes nonlinear, causing energy exchange among the pulse's spectral components and resulting in peak-intensity dependent (and therefore pulse-duration dependent) transmission. For 30 fs pulses at 800 nm center wavelength, we determine the onset of nonlinear propagation effects to occur at a peak value of about 0.12 mJ/cm(2) of input laser energy fluence.
Nonlinear signaling on biological networks: The role of stochasticity and spectral clustering
Hernandez-Hernandez, Gonzalo; Myers, Jesse; Alvarez-Lacalle, Enrique; Shiferaw, Yohannes
2017-03-01
Signal transduction within biological cells is governed by networks of interacting proteins. Communication between these proteins is mediated by signaling molecules which bind to receptors and induce stochastic transitions between different conformational states. Signaling is typically a cooperative process which requires the occurrence of multiple binding events so that reaction rates have a nonlinear dependence on the amount of signaling molecule. It is this nonlinearity that endows biological signaling networks with robust switchlike properties which are critical to their biological function. In this study we investigate how the properties of these signaling systems depend on the network architecture. Our main result is that these nonlinear networks exhibit bistability where the network activity can switch between states that correspond to a low and high activity level. We show that this bistable regime emerges at a critical coupling strength that is determined by the spectral structure of the network. In particular, the set of nodes that correspond to large components of the leading eigenvector of the adjacency matrix determines the onset of bistability. Above this transition the eigenvectors of the adjacency matrix determine a hierarchy of clusters, defined by its spectral properties, which are activated sequentially with increasing network activity. We argue further that the onset of bistability occurs either continuously or discontinuously depending upon whether the leading eigenvector is localized or delocalized. Finally, we show that at low network coupling stochastic transitions to the active branch are also driven by the set of nodes that contribute more strongly to the leading eigenvector. However, at high coupling, transitions are insensitive to network structure since the network can be activated by stochastic transitions of a few nodes. Thus this work identifies important features of biological signaling networks that may underlie their biological
Stability estimates for hp spectral element methods for elliptic ...
Indian Academy of Sciences (India)
... parallel preconditioners and error estimates for the solution of the minimization problem which are nearly optimal as the condition number of the preconditioned system is polylogarithmic in , the number of processors and the number of degrees of freedom in each variable on each element. Moreover if the data is analytic ...
Domain decomposition solvers for nonlinear multiharmonic finite element equations
Copeland, D. M.; Langer, U.
2010-01-01
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
A finite element model for nonlinear shells of revolution
International Nuclear Information System (INIS)
Cook, W.A.
1979-01-01
A shell-of-revolution model was developed to analyze impact problems associated with the safety analysis of nuclear material shipping containers. The nonlinear shell theory presented by Eric Reissner in 1972 was used to develop our model. Reissner's approach includes transverse shear deformation and moments turning about the middle surface normal. With these features, this approach is valid for both thin and thick shells. His theory is formulated in terms of strain and stress resultants that refer to the undeformed geometry. This nonlinear shell model is developed using the virtual work principle associated with Reissner's equilibrium equations. First, the virtual work principle is modified for incremental loading; then it is linearized by assuming that the nonlinear portions of the strains are known. By iteration, equilibrium is then approximated for each increment. A benefit of this approach is that this iteration process makes it possible to use nonlinear material properties. (orig.)
Directory of Open Access Journals (Sweden)
Xingjian Dong
2014-02-01
Full Text Available An efficient spectral element (SE with electric potential degrees of freedom (DOF is proposed to investigate the static electromechanical responses of a piezoelectric bimorph for its actuator and sensor functions. A sublayer model based on the piecewise linear approximation for the electric potential is used to describe the nonlinear distribution of electric potential through the thickness of the piezoelectric layers. An equivalent single layer (ESL model based on first-order shear deformation theory (FSDT is used to describe the displacement field. The Legendre orthogonal polynomials of order 5 are used in the element interpolation functions. The validity and the capability of the present SE model for investigation of global and local responses of the piezoelectric bimorph are confirmed by comparing the present solutions with those obtained from coupled 3-D finite element (FE analysis. It is shown that, without introducing any higher-order electric potential assumptions, the current method can accurately describe the distribution of the electric potential across the thickness even for a rather thick bimorph. It is revealed that the effect of electric potential is significant when the bimorph is used as sensor while the effect is insignificant when the bimorph is used as actuator, and therefore, the present study may provide a better understanding of the nonlinear induced electric potential for bimorph sensor and actuator.
International Nuclear Information System (INIS)
Cook, W.A.
1978-10-01
Nuclear Material shipping containers have shells of revolution as a basic structural component. Analytically modeling the response of these containers to severe accident impact conditions requires a nonlinear shell-of-revolution model that accounts for both geometric and material nonlinearities. Present models are limited to large displacements, small rotations, and nonlinear materials. This report discusses a first approach to developing a finite element nonlinear shell of revolution model that accounts for these nonlinear geometric effects. The approach uses incremental loads and a linear shell model with equilibrium iterations. Sixteen linear models are developed, eight using the potential energy variational principle and eight using a mixed variational principle. Four of these are suitable for extension to nonlinear shell theory. A nonlinear shell theory is derived, and a computational technique used in its solution is presented
PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual
Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.
1977-01-01
The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.
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.
Oral, Elif; Gélis, Céline; Bonilla, Luis Fabián; Delavaud, Elise
2017-12-01
Numerical modelling of seismic wave propagation, considering soil nonlinearity, has become a major topic in seismic hazard studies when strong shaking is involved under particular soil conditions. Indeed, when strong ground motion propagates in saturated soils, pore pressure is another important parameter to take into account when successive phases of contractive and dilatant soil behaviour are expected. Here, we model 1-D seismic wave propagation in linear and nonlinear media using the spectral element numerical method. The study uses a three-component (3C) nonlinear rheology and includes pore-pressure excess. The 1-D-3C model is used to study the 1987 Superstition Hills earthquake (ML 6.6), which was recorded at the Wildlife Refuge Liquefaction Array, USA. The data of this event present strong soil nonlinearity involving pore-pressure effects. The ground motion is numerically modelled for different assumptions on soil rheology and input motion (1C versus 3C), using the recorded borehole signals as input motion. The computed acceleration-time histories show low-frequency amplification and strong high-frequency damping due to the development of pore pressure in one of the soil layers. Furthermore, the soil is found to be more nonlinear and more dilatant under triaxial loading compared to the classical 1C analysis, and significant differences in surface displacements are observed between the 1C and 3C approaches. This study contributes to identify and understand the dominant phenomena occurring in superficial layers, depending on local soil properties and input motions, conditions relevant for site-specific studies.
Non-linear spectral splitting of Rydberg sodium in external fields
International Nuclear Information System (INIS)
Gao Wei; Yang Hai-Feng; Cheng Hong; Zhang Shan-Shan; Liu Hong-Ping; Liu Dan-Feng
2015-01-01
We have studied highly excited sodium in various electric fields, parallel electric and magnetic fields, with one σ and π photon irradiation, and even in a magnetic field with a complex laser polarization configuration. The σ spectra shows a simple linear Stark effect with the applied electric field, while the π spectra exhibits a strong non-linear dependence on the electric field. The π transitions in parallel fields show a similar behavior to that in a pure electric field but the spectra get more smooth due to the magnetic field. The diamagnetic spectrum with laser polarization angles between 0 and π/2 proves that it can be reproduced by simple linear combination of π and σ components, indicating there is no interference between the π and σ channels. A full quantum calculation considering the quantum defects accounts for all the observations. The quantum defects, especially for the channel np, play an important role in the spectral profile. (paper)
Spectral Analysis of Large Finite Element Problems by Optimization Methods
Directory of Open Access Journals (Sweden)
Luca Bergamaschi
1994-01-01
Full Text Available Recently an efficient method for the solution of the partial symmetric eigenproblem (DACG, deflated-accelerated conjugate gradient was developed, based on the conjugate gradient (CG minimization of successive Rayleigh quotients over deflated subspaces of decreasing size. In this article four different choices of the coefficient βk required at each DACG iteration for the computation of the new search direction Pk are discussed. The “optimal” choice is the one that yields the same asymptotic convergence rate as the CG scheme applied to the solution of linear systems. Numerical results point out that the optimal βk leads to a very cost effective algorithm in terms of CPU time in all the sample problems presented. Various preconditioners are also analyzed. It is found that DACG using the optimal βk and (LLT−1 as a preconditioner, L being the incomplete Cholesky factor of A, proves a very promising method for the partial eigensolution. It appears to be superior to the Lanczos method in the evaluation of the 40 leftmost eigenpairs of five finite element problems, and particularly for the largest problem, with size equal to 4560, for which the speed gain turns out to fall between 2.5 and 6.0, depending on the eigenpair level.
The spectral transform as a tool for solving nonlinear discrete evolution equations
International Nuclear Information System (INIS)
Levi, D.
1979-01-01
In this contribution we study nonlinear differential difference equations which became important to the description of an increasing number of problems in natural science. Difference equations arise for instance in the study of electrical networks, in statistical problems, in queueing problems, in ecological problems, as computer models for differential equations and as models for wave excitation in plasma or vibrations of particles in an anharmonic lattice. We shall first review the passages necessary to solve linear discrete evolution equations by the discrete Fourier transfrom, then, starting from the Zakharov-Shabat discretized eigenvalue, problem, we shall introduce the spectral transform. In the following part we obtain the correlation between the evolution of the potentials and scattering data through the Wronskian technique, giving at the same time many other properties as, for example, the Baecklund transformations. Finally we recover some of the important equations belonging to this class of nonlinear discrete evolution equations and extend the method to equations with n-dependent coefficients. (HJ)
Energy Technology Data Exchange (ETDEWEB)
Heasler, Patrick G.; Posse, Christian; Hylden, Jeff L.; Anderson, Kevin K.
2007-06-13
This paper presents a nonlinear Bayesian regression algorithm for the purpose of detecting and estimating gas plume content from hyper-spectral data. Remote sensing data, by its very nature, is collected under less controlled conditions than laboratory data. As a result, the physics-based model that is used to describe the relationship between the observed remotesensing spectra, and the terrestrial (or atmospheric) parameters that we desire to estimate, is typically littered with many unknown "nuisance" parameters (parameters that we are not interested in estimating, but also appear in the model). Bayesian methods are well-suited for this context as they automatically incorporate the uncertainties associated with all nuisance parameters into the error estimates of the parameters of interest. The nonlinear Bayesian regression methodology is illustrated on realistic simulated data from a three-layer model for longwave infrared (LWIR) measurements from a passive instrument. This shows that this approach should permit more accurate estimation as well as a more reasonable description of estimate uncertainty.
Ye, W; Bel-Brunon, A; Catheline, S; Combescure, A; Rochette, M
2018-01-01
In this study, visco-hyperelastic Landau's model, which is widely used in acoustical physic field, is introduced into a finite element formulation. It is designed to model the nonlinear behaviour of finite amplitude shear waves in soft solids, typically, in biological tissues. This law is used in finite element models based on elastography, experiments reported in Jacob et al, the simulations results show a good agreement with the experimental study: It is observed in both that a plane shear wave generates only odd harmonics and a nonplane wave generates both odd and even harmonics in the spectral domain. In the second part, a parametric study is performed to analyse the influence of different factors on the generation of odd harmonics of plane wave. A quantitative relation is fitted between the odd harmonic amplitudes and the non-linear elastic parameter of Landau's model, which provides a practical guideline to identify the non-linearity of homogeneous tissues using elastography experiment. Copyright © 2017 John Wiley & Sons, Ltd.
Masè, Michela; Cristoforetti, Alessandro; Avogaro, Laura; Tessarolo, Francesco; Piccoli, Federico; Caola, Iole; Pederzolli, Carlo; Graffigna, Angelo; Ravelli, Flavia
2015-01-01
The assessment of collagen structure in cardiac pathology, such as atrial fibrillation (AF), is essential for a complete understanding of the disease. This paper introduces a novel methodology for the quantitative description of collagen network properties, based on the combination of nonlinear optical microscopy with a spectral approach of image processing and analysis. Second-harmonic generation (SHG) microscopy was applied to atrial tissue samples from cardiac surgery patients, providing label-free, selective visualization of the collagen structure. The spectral analysis framework, based on 2D-FFT, was applied to the SHG images, yielding a multiparametric description of collagen fiber orientation (angle and anisotropy indexes) and texture scale (dominant wavelength and peak dispersion indexes). The proof-of-concept application of the methodology showed the capability of our approach to detect and quantify differences in the structural properties of the collagen network in AF versus sinus rhythm patients. These results suggest the potential of our approach in the assessment of collagen properties in cardiac pathologies related to a fibrotic structural component.
Advance elements of optoisolation circuits nonlinearity applications in engineering
Aluf, Ofer
2017-01-01
This book on advanced optoisolation circuits for nonlinearity applications in engineering addresses two separate engineering and scientific areas, and presents advanced analysis methods for optoisolation circuits that cover a broad range of engineering applications. The book analyzes optoisolation circuits as linear and nonlinear dynamical systems and their limit cycles, bifurcation, and limit cycle stability by using Floquet theory. Further, it discusses a broad range of bifurcations related to optoisolation systems: cusp-catastrophe, Bautin bifurcation, Andronov-Hopf bifurcation, Bogdanov-Takens (BT) bifurcation, fold Hopf bifurcation, Hopf-Hopf bifurcation, Torus bifurcation (Neimark-Sacker bifurcation), and Saddle-loop or Homoclinic bifurcation. Floquet theory helps as to analyze advance optoisolation systems. Floquet theory is the study of the stability of linear periodic systems in continuous time. Another way to describe Floquet theory, it is the study of linear systems of differential equations with p...
Superconducting Nanowires as Nonlinear Inductive Elements for Qubits
Ku, Jaseung; Manucharyan, Vladimir; Bezryadin, Alexey
2010-01-01
We report microwave transmission measurements of superconducting Fabry-Perot resonators (SFPR), having a superconducting nanowire placed at a supercurrent antinode. As the plasma oscillation is excited, the supercurrent is forced to flow through the nanowire. The microwave transmission of the resonator-nanowire device shows a nonlinear resonance behavior, significantly dependent on the amplitude of the supercurrent oscillation. We show that such amplitude-dependent response is due to the nonl...
Elements of nonlinear time series analysis and forecasting
De Gooijer, Jan G
2017-01-01
This book provides an overview of the current state-of-the-art of nonlinear time series analysis, richly illustrated with examples, pseudocode algorithms and real-world applications. Avoiding a “theorem-proof” format, it shows concrete applications on a variety of empirical time series. The book can be used in graduate courses in nonlinear time series and at the same time also includes interesting material for more advanced readers. Though it is largely self-contained, readers require an understanding of basic linear time series concepts, Markov chains and Monte Carlo simulation methods. The book covers time-domain and frequency-domain methods for the analysis of both univariate and multivariate (vector) time series. It makes a clear distinction between parametric models on the one hand, and semi- and nonparametric models/methods on the other. This offers the reader the option of concentrating exclusively on one of these nonlinear time series analysis methods. To make the book as user friendly as possible...
DEFF Research Database (Denmark)
Lillieholm, Mads; Corcoran, B.; Galili, Michael
2017-01-01
We characterize the performance of 4× spectral magnification based on four-wave mixing in optimized nonlinear fibres, for 4/8/16-QAM formats, and report >19-nm operational bandwidth. Predominantly OSNR penalties of ~1 dB per bit/QAM-symbol from aberrations non-intrinsic to time lenses are observed....
Nonlinear Finite Element Analysis of Shells with Large Aspect Ratio
Chang, T. Y.; Sawamiphakdi, K.
1984-01-01
A higher order degenerated shell element with nine nodes was selected for large deformation and post-buckling analysis of thick or thin shells. Elastic-plastic material properties are also included. The post-buckling analysis algorithm is given. Using a square plate, it was demonstrated that the none-node element does not have shear locking effect even if its aspect ratio was increased to the order 10 to the 8th power. Two sample problems are given to illustrate the analysis capability of the shell element.
Material model for non-linear finite element analyses of large concrete structures
Engen, Morten; Hendriks, M.A.N.; Øverli, Jan Arve; Åldstedt, Erik; Beushausen, H.
2016-01-01
A fully triaxial material model for concrete was implemented in a commercial finite element code. The only required input parameter was the cylinder compressive strength. The material model was suitable for non-linear finite element analyses of large concrete structures. The importance of including
Stochastic Finite Element Analysis of Non-Linear Structures Modelled by Plasticity Theory
DEFF Research Database (Denmark)
Frier, Christian; Sørensen, John Dalsgaard
2003-01-01
A Finite Element Reliability Method (FERM) is introduced to perform reliability analyses on two-dimensional structures in plane stress, modeled by non-linear plasticity theory. FERM is a coupling between the First Order Reliability Method (FORM) and the Finite Element Method (FEM). FERM can be us...
Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics
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
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.
Nonlinear Finite Element Analysis of a General Composite Shell
1988-12-01
for (t) in Equation (B.15) (Appendix B) and writes it as a function of displacements for I the nonlinear problem one obtains [8] 3 29 (*(a)) - [K(a...linked to the main program before execution. Isubroutine upress(t,pa,pb,iunit, ielt ,x,y,z,live,press) c c Pressure distribution subroutine for c...then compiled and linked to the main program before execution. I SUBROUTINE UPRESS(T,PA,PB,IUNIT, IELT ,X,Y,Z,LIVE,PRESS) C c Pressure distribution
High-precision solution to the moving load problem using an improved spectral element method
Wen, Shu-Rui; Wu, Zhi-Jing; Lu, Nian-Li
2018-02-01
In this paper, the spectral element method (SEM) is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem. In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases. Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.
Spectral element model for 2-D electrostatic fields in a linear synchronous motor
van Beek, T.A.; Curti, M.; Jansen, J.W.; Gysen, B.L.J.; Paulides, J.J.H.; Lomonova, E.A.
2017-01-01
This paper presents a fast and accurate 2-D spectral element model for analyzing electric field distributions in linear synchronous motors. The electric field distribution is derived using the electric scalar potential for static cases. The spatial potential and electric field distributions obtained
Application of Least-Squares Spectral Element Methods to Polynomial Chaos
Vos, P.E.J.; Gerritsma, M.I.
2006-01-01
This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.
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.
Finite elements for non-linear analysis of pipelines
International Nuclear Information System (INIS)
Benjamim, A.C.; Ebecken, N.F.F.
1982-01-01
The application of a three-dimensional lagrangian formulation for the great dislocations analysis and great rotation of pipelines systems is studied. This formulation is derived from the soil mechanics and take into account the shear stress effects. Two finite element models are implemented. The first, of right axis, uses as interpolation functions the conventional gantry functions, defined in relation to mobile coordinates. The second, of curve axis and variable cross sections, is obtained from the degeneration of the three-dimensional isoparametric element, and uses as interpolation functions third degree polynomials. (E.G.) [pt
Muravyov, Alexander A.
1999-01-01
In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.
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...
Nonlinear nonstationary analysis with the finite element method
International Nuclear Information System (INIS)
Vaz, L.E.
1981-01-01
In this paper, after some introductory remarks on numerical methods for the integration of initial value problems, the applicability of the finite element method for transient diffusion analysis as well as dynamic and inelastic analysis is discussed, and some examples are presented. (RW) [de
Wavelet-based spectral finite element dynamic analysis for an axially moving Timoshenko beam
Mokhtari, Ali; Mirdamadi, Hamid Reza; Ghayour, Mostafa
2017-08-01
In this article, wavelet-based spectral finite element (WSFE) model is formulated for time domain and wave domain dynamic analysis of an axially moving Timoshenko beam subjected to axial pretension. The formulation is similar to conventional FFT-based spectral finite element (SFE) model except that Daubechies wavelet basis functions are used for temporal discretization of the governing partial differential equations into a set of ordinary differential equations. The localized nature of Daubechies wavelet basis functions helps to rule out problems of SFE model due to periodicity assumption, especially during inverse Fourier transformation and back to time domain. The high accuracy of WSFE model is then evaluated by comparing its results with those of conventional finite element and SFE results. The effects of moving beam speed and axial tensile force on vibration and wave characteristics, and static and dynamic stabilities of moving beam are investigated.
On the Possibility of Using Nonlinear Elements for Landau Damping in High-Intensity Beams
Energy Technology Data Exchange (ETDEWEB)
Alexahin, Y. [Fermilab; Gianfelice-Wendt, E. [Fermilab; Lebedev, V. [Fermilab; Valishev, A. [Fermilab
2016-09-30
Direct space-charge force shifts incoherent tunes downwards from the coherent ones breaking the Landau mechanism of coherent oscillations damping at high beam intensity. To restore it nonlinear elements can be employed which move back tunes of large amplitude particles. In the present report we consider the possibility of creating a “nonlinear integrable optics” insertion in the Fermilab Recycler to host either octupoles or hollow electron lens for this purpose. For comparison we also consider the classic scheme with distributed octupole families. It is shown that for the Proton Improvement Plan II (PIP II) parameters the required nonlinear tune shift can be created without destroying the dynamic aperture.
Finite element modeling of nonlinear piezoelectric energy harvesters with magnetic interaction
International Nuclear Information System (INIS)
Upadrashta, Deepesh; Yang, Yaowen
2015-01-01
Piezoelectric energy harvesting from ambient vibrations is a potential technology for powering wireless sensors and low power electronic devices. The conventional linear harvesters suffer from narrow operational bandwidth. Many attempts have been made especially using the magnetic interaction to broaden the bandwidth of harvesters. The finite element (FE) modeling has been used only for analyzing the linear harvesters in the literature. The main difficulties in extending the FE modeling to analyze the nonlinear harvesters involving magnetic interaction are developing the mesh needed for magnetic interaction in dynamic problems and the high demand on computational resource needed for solving the coupled electrical–mechanical–magnetic problem. In this paper, an innovative method is proposed to model the magnetic interaction without inclusion of the magnetic module. The magnetic force is modeled using the nonlinear spring element available in ANSYS finite element analysis (FEA) package, thus simplifying the simulation of nonlinear piezoelectric energy harvesters as an electromechanically coupled problem. Firstly, an FE model of a monostable nonlinear harvester with cantilever configuration is developed and the results are validated with predictions from the theoretical model. Later, the proposed technique of FE modeling is extended to a complex 2-degree of freedom nonlinear energy harvester for which an accurate analytical model is difficult to derive. The performance predictions from FEA are compared with the experimental results. It is concluded that the proposed modeling technique is able to accurately analyze the behavior of nonlinear harvesters with magnetic interaction. (paper)
Mittal, Ankita; Girimaji, Sharath
2017-11-01
We examine the effect of compressible spectral energy transfer in the nonlinear regime of transition to turbulence of hypersonic boundary layers. The nature of spectral energy transfer between perturbation modes is profoundly influenced by two compressibility mechanisms. First and foremost, the emergence of nonlinear pressure-dilatation mechanism leads to kinetic-internal energy exchange within the perturbation field. Such interchange is absent in incompressible flow as pressure merely reorients the perturbation amplitude vector while conserving kinetic energy. Secondly, the nature of triadic interactions also changes due to variability in density. In this work, we demonstrate that the efficiency of nonlinear spectral energy transfer is diminished in compressible boundary layers. Emergence of new perturbation modes or `broad-banding' of the perturbation field is significantly delayed in comparison to incompressible boundary layer undergoing transition. A significant amount of perturbation energy is transformed to internal energy and thus unavailable for `tripping' the flow into turbulent state. These factors profoundly change the nature of the nonlinear stage of transition in compressible boundary layer leading to delayed onset of full-fledged turbulence.
Siminos, Evangelos; Bénisti, Didier; Gremillet, Laurent
2011-05-01
We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, N. When the advection term in the Vlasov equation is dominant, the convergence with N of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced by Crawford and Hislop [Ann. Phys. (NY) 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the advection term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic Bernstein-Greene-Kruskal mode with multiple phase-space vortices, compare our results with numerical simulations of the Vlasov-Poisson system, and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed. © 2011 American Physical Society
Non-Linear Three Dimensional Finite Elements for Composite Concrete Structures
Directory of Open Access Journals (Sweden)
O. Kohnehpooshi
Full Text Available Abstract The current investigation focused on the development of effective and suitable modelling of reinforced concrete component with and without strengthening. The modelling includes physical and constitutive models. New interface elements have been developed, while modified constitutive law have been applied and new computational algorithm is utilised. The new elements are the Truss-link element to model the interaction between concrete and reinforcement bars, the interface element between two plate bending elements and the interface element to represent the interfacial behaviour between FRP, steel plates and concrete. Nonlinear finite-element (FE codes were developed with pre-processing. The programme was written using FORTRAN language. The accuracy and efficiency of the finite element programme were achieved by analyzing several examples from the literature. The application of the 3D FE code was further enhanced by carrying out the numerical analysis of the three dimensional finite element analysis of FRP strengthened RC beams, as well as the 3D non-linear finite element analysis of girder bridge. Acceptable distributions of slip, deflection, stresses in the concrete and FRP plate have also been found. These results show that the new elements are effective and appropriate to be used for structural component modelling.
Research of carbon composite material for nonlinear finite element method
Kim, Jung Ho; Garg, Mohit; Kim, Ji Hoon
2012-04-01
Works on the absorption of collision energy in the structural members are carried out widely with various material and cross-sections. And, with ever increasing safety concerns, they are presently applied in various fields including railroad trains, air crafts and automobiles. In addition to this, problem of lighting structural members became important subject by control of exhaust gas emission, fuel economy and energy efficiency. CFRP(Carbon Fiber Reinforced Plastics) usually is applying the two primary structural members because of different result each design parameter as like stacking thickness, stacking angle, moisture absorption ect. We have to secure the data for applying primary structural members. But it always happens to test design parameters each for securing the data. So, it has much more money and time. We can reduce the money and the time, if can ensure the CFRP material properties each design parameters. In this study, we experiment the coupon test each tension, compression and shear using CFRP prepreg sheet and simulate non-linear analyze at the sources - test result, Caron longitudinal modulus and matrix poisson's ratio using GENOAMQC is specialized at Composite analysis. And then we predict the result that specimen manufacture changing stacking angle and experiment in such a way of test method using GENOA-MCQ.
McGill, Matthew J. (Inventor); Scott, Vibart S. (Inventor); Marzouk, Marzouk (Inventor)
2001-01-01
A holographic optical element transforms a spectral distribution of light to image points. The element comprises areas, each of which acts as a separate lens to image the light incident in its area to an image point. Each area contains the recorded hologram of a point source object. The image points can be made to lie in a line in the same focal plane so as to align with a linear array detector. A version of the element has been developed that has concentric equal areas to match the circular fringe pattern of a Fabry-Perot interferometer. The element has high transmission efficiency, and when coupled with high quantum efficiency solid state detectors, provides an efficient photon-collecting detection system. The element may be used as part of the detection system in a direct detection Doppler lidar system or multiple field of view lidar system.
Spectral element method for elastic and acoustic waves in frequency domain
Energy Technology Data Exchange (ETDEWEB)
Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min; Zhuang, Mingwei [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Na, E-mail: liuna@xmu.edu.cn [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Qing Huo, E-mail: qhliu@duke.edu [Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708 (United States)
2016-12-15
Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.
International Nuclear Information System (INIS)
Bauer, M.; Weitkamp, C.
1977-01-01
The strongest spectra lines of the 85 stable chemical elements have been compiled and plotted along with lines from other elements that may interfere in applications like spectroscopic multielement analysis. For each line a wavelength range of +- 0.25 A.U. around the line of interest has been considered. The tables contain the wavelength, intensity and assignment to an ionization state of the emitting atom, the plots visualize the lines with a doppler broadening corresponding to 8,000 K. (orig.) [de
Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures
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.
FINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NON-LINEAR VARYING WEB DEPTH
Directory of Open Access Journals (Sweden)
Q. A. HASAN
2017-11-01
Full Text Available The paper presents Finite Element Analysis to determine the ultimate shear capacity of tapered composite plate girder. The effect of degree of taper on the ultimate shear capacity of tapered steel-concrete composite plate girder with a nonlinear varying web depth, effect of slenderness ratio on the ultimate shear capacity, and effect of flange stiffness on the ductility were considered as the parametric studies. Effect of concrete slab on the ultimate shear capacity of tapered plate girders was also considered and it was found to be so effective on the ultimate shear capacity of the tapered plate girder compared with the steel one. The accuracy of the finite element method is established by comparing the finite element with the results existing in the literature. The study was conducted using nonlinear finite element modelling with computer software LUSAS 14.7.
Multiscale finite element methods for high-contrast problems using local spectral basis functions
Efendiev, Yalchin
2011-02-01
In this paper we study multiscale finite element methods (MsFEMs) using spectral multiscale basis functions that are designed for high-contrast problems. Multiscale basis functions are constructed using eigenvectors of a carefully selected local spectral problem. This local spectral problem strongly depends on the choice of initial partition of unity functions. The resulting space enriches the initial multiscale space using eigenvectors of local spectral problem. The eigenvectors corresponding to small, asymptotically vanishing, eigenvalues detect important features of the solutions that are not captured by initial multiscale basis functions. Multiscale basis functions are constructed such that they span these eigenfunctions that correspond to small, asymptotically vanishing, eigenvalues. We present a convergence study that shows that the convergence rate (in energy norm) is proportional to (H/Λ*)1/2, where Λ* is proportional to the minimum of the eigenvalues that the corresponding eigenvectors are not included in the coarse space. Thus, we would like to reach to a larger eigenvalue with a smaller coarse space. This is accomplished with a careful choice of initial multiscale basis functions and the setup of the eigenvalue problems. Numerical results are presented to back-up our theoretical results and to show higher accuracy of MsFEMs with spectral multiscale basis functions. We also present a hierarchical construction of the eigenvectors that provides CPU savings. © 2010.
International Nuclear Information System (INIS)
Ruas, V.
1982-09-01
A class of simplicial finite elements for solving incompressible elasticity problems in n-dimensional space, n=2 or 3, is presented. An asymmetric structure of the shape functions with respect to the centroid of the simplex, renders them particularly stable in the large strain case, in which the incompressibility condition is nonlinear. It is proved that under certain assembling conditions of the elements, there exists a solution to the corresponding discrete problems. Numerical examples illustrate the efficiency of the method. (Author) [pt
Spectral interference of zirconium on 24 analyte elements using CCD based ICP-AES technique
International Nuclear Information System (INIS)
Adya, V.C.; Sengupta, Arijit; Godbole, S.V.
2014-01-01
In the present studies, the spectral interference of zirconium on different analytical lines of 24 critical analytes using CCD based ICP-AES technique is described. Suitable analytical lines for zirconium were identified along with their detection limits. The sensitivity and the detection limits of analytical channels for different elements in presence of Zr matrix were calculated. Subsequently analytical lines with least interference from Zr and better detection limits were selected for their determinations. (author)
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.
Co-simulation coupling spectral/finite elements for 3D soil/structure interaction problems
Zuchowski, Loïc; Brun, Michael; De Martin, Florent
2018-05-01
The coupling between an implicit finite elements (FE) code and an explicit spectral elements (SE) code has been explored for solving the elastic wave propagation in the case of soil/structure interaction problem. The coupling approach is based on domain decomposition methods in transient dynamics. The spatial coupling at the interface is managed by a standard coupling mortar approach, whereas the time integration is dealt with an hybrid asynchronous time integrator. An external coupling software, handling the interface problem, has been set up in order to couple the FE software Code_Aster with the SE software EFISPEC3D.
The spectral element approach for the solution of neutron transport problems
International Nuclear Information System (INIS)
Barbarino, A.; Dulla, S.; Ravetto, P.; Mund, E.H.
2011-01-01
In this paper a possible application of the Spectral Element Method to neutron transport problems is presented. The basic features of the numerical scheme on the one-dimensional diffusion equation are illustrated. Then, the AN model for neutron transport is introduced, and the basic steps for the construction of a bi-dimensional solver are described. The AN equations are chosen for their structure, involving a system of coupled elliptic-type equations. Some calculations are carried out on typical benchmark problems and results are compared with the Finite Element Method, in order to evaluate their performances. (author)
The Spectral/hp-Finite Element Method for Partial Differential Equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter
2009-01-01
dimensions. In the course the chosen programming environment is Matlab, however, this is by no means a necessary requirement. The mathematical level needed to grasp the details of this set of notes requires an elementary background in mathematical analysis and linear algebra. Each chapter is supplemented......This set of lecture notes provides an elementary introduction to both the classical Finite Element Method (FEM) and the extended Spectral/$hp$-Finite Element Method for solving Partial Differential Equations (PDEs). Many problems in science and engineering can be formulated mathematically...
Energy Technology Data Exchange (ETDEWEB)
Fischer, P.F. [Brown Univ., Providence, RI (United States)
1996-12-31
Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We seek to improve existing spectral element iterative methods for the pressure solve in order to overcome the slow convergence frequently observed in the presence of highly refined grids or high-aspect ratio elements.
Energy Technology Data Exchange (ETDEWEB)
Borhan, H; Ahmadian, M T [Sharif University of Technology, Center of Excellence for Design, Robotics and Automation, School of Mechanical Engineering, PO Box 11365-9567, Tehran (Iran, Islamic Republic of)
2006-04-01
In this paper, a complete nonlinear finite element model for coupled-domain MEMS devices with electrostatic actuation and squeeze film effect is developed. For this purpose, a corotational finite element formulation for the dynamic analysis of planer Euler beams is employed. In this method, the internal nodal forces due to deformation and intrinsic residual stresses, the inertial nodal forces, and the damping effect of squeezed air film are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory using d'Alamber and virtual work principles. An incremental-iterative method based on the Newmark direct integration procedure and the Newton-Raphson algorithm is used to solve the nonlinear dynamic equilibrium equations. Numerical examples are presented and compared with experimental findings which indicate properly good agreement.
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
International Nuclear Information System (INIS)
Pontaza, J.P.; Reddy, J.N.
2003-01-01
We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier-Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L 2 least-squares functional and L 2 error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier-Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation
International Nuclear Information System (INIS)
Hawileh, Rami A.; El-Maaddawy, Tamer A.; Naser, Mohannad Z.
2012-01-01
Highlights: ► A 3D nonlinear FE model is developed of RC deep beams with web openings. ► We used cohesion elements to simulate bond. ► The developed FE model is suitable for analysis of such complex structures. -- Abstract: This paper aims to develop 3D nonlinear finite element (FE) models for reinforced concrete (RC) deep beams containing web openings and strengthened in shear with carbon fiber reinforced polymer (CFRP) composite sheets. The web openings interrupted the natural load path either fully or partially. The FE models adopted realistic materials constitutive laws that account for the nonlinear behavior of materials. In the FE models, solid elements for concrete, multi-layer shell elements for CFRP and link elements for steel reinforcement were used to simulate the physical models. Special interface elements were implemented in the FE models to simulate the interfacial bond behavior between the concrete and CFRP composites. A comparison between the FE results and experimental data published in the literature demonstrated the validity of the computational models in capturing the structural response for both unstrengthened and CFRP-strengthened deep beams with openings. The developed FE models can serve as a numerical platform for performance prediction of RC deep beams with openings strengthened in shear with CFRP composites.
Non-linear finite element analyses applicable for the design of large reinforced concrete structures
Engen, M; Hendriks, M.A.N.; Øverli, Jan Arve; Åldstedt, Erik
2017-01-01
In order to make non-linear finite element analyses applicable during assessments of the ultimate load capacity or the structural reliability of large reinforced concrete structures, there is need for an efficient solution strategy with a low modelling uncertainty. A solution strategy comprises
Modal representation of geometrically nonlinear behavior by the finite element method
International Nuclear Information System (INIS)
Nagy, D.A.
1977-01-01
A method is presented for representing mild geometrically nonlinear static behavior of thin-type structures, within the finite element method, in terms of linear elastic and linear (bifurcation) buckling analysis results for structural loading or geometry situations which violate the idealized restrictive (perfect) interpretation of linear behavior up to bifurcation. (Auth.)
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 fibe...
Nonlinear finite element analysis of reinforced and prestressed concrete shells with edge beams
International Nuclear Information System (INIS)
Srinivasa Rao, P.; Duraiswamy, S.
1994-01-01
The structural design of reinforced and prestressed concrete shells demands the application of nonlinear finite element analysis (NFEM) procedures to ensure safety and serviceability. In this paper the details of a comprehensive NFEM program developed are presented. The application of the program is highlighted by solving two numerical problems and comparing the results with experimental results. (author). 20 refs., 15 figs
The Superconvergence of Mixed Finite Element Methods for Nonlinear Hyperbolic Equations
Institute of Scientific and Technical Information of China (English)
YanpingCHEN; YunqingHUANG
1998-01-01
Imprioved L2-error estimates are computed for mixed finte element methods for second order nonlinear hyperbolic equations.Superconvergence results,L∞ in time and discrete L2 in space,are derived for both the solution and gradients on the rectangular domain.Results are given for the continuous-time case.
COYOTE: a finite element computer program for nonlinear heat conduction problems
International Nuclear Information System (INIS)
Gartling, D.K.
1978-06-01
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
Finite Element Model for Nonlinear Analysis of Reinforced Concrete Beams and Plane Frames
Directory of Open Access Journals (Sweden)
R.S.B. STRAMANDINOLI
Full Text Available Abstract In this work, a two-dimensional finite element (FE model for physical and geometric nonlinear analysis of reinforced concrete beams and plane frames, developed by the authors, is presented. The FE model is based on the Euler-Bernoulli Beam Theory, in which shear deformations are neglected. The bar elements have three nodes with a total of seven degrees of freedom. Three Gauss-points are utilized for the element integration, with the element section discretized into layers at each Gauss point (Fiber Model. It is assumed that concrete and reinforcing bars are perfectly bonded, and each section layer is assumed to be under a uniaxial stress-state. Nonlinear constitutive laws are utilized for both concrete and reinforcing steel layers, and a refined tension-stiffening model, developed by the authors, is included. The Total Lagrangean Formulation is adopted for geometric nonlinear consideration and several methods can be utilized to achieve equilibrium convergence of the nonlinear equations. The developed model is implemented into a computer program named ANEST/CA, which is validated by comparison with some tests on RC beams and plane frames, showing an excellent correlation between numerical and experimental results.
Knaus, Helene; Blab, Gerhard A; Agronskaia, Alexandra V; van den Heuvel, Dave J; Gerritsen, Hans C; Wösten, Han A B
2013-10-01
Label-free nonlinear spectral imaging microscopy (NLSM) records two-photon-excited fluorescence emission spectra of endogenous fluorophores within the specimen. Here, NLSM is introduced as a novel, minimally invasive method to analyze the metabolic state of fungal hyphae by monitoring the autofluorescence of NAD(P)H and flavin adenine dinucleotide (FAD). Moreover, the presence of melanin was analyzed by NLSM. NAD(P)H, FAD, and melanin were used as biomarkers for freshness of mushrooms of Agaricus bisporus (white button mushroom) that had been stored at 4°C for 0 to 17 days. During this period, the mushrooms did not show changes in morphology or color detectable by eye. In contrast, FAD/NAD(P)H and melanin/NAD(P)H ratios increased over time. For instance, these ratios increased from 0.92 to 2.02 and from 0.76 to 1.53, respectively, at the surface of mushroom caps that had been harvested by cutting the stem. These ratios were lower under the skin than at the surface of fresh mushrooms (0.78 versus 0.92 and 0.41 versus 0.76, respectively), indicative of higher metabolism and lower pigment formation within the fruiting body. Signals were different not only between tissues of the mushroom but also between neighboring hyphae. These data show that NLSM can be used to determine the freshness of mushrooms and to monitor the postharvest browning process at an early stage. Moreover, these data demonstrate the potential of NLSM to address a broad range of fundamental and applied microbiological processes.
Spectral element method for band-structure calculations of 3D phononic crystals
International Nuclear Information System (INIS)
Shi, Linlin; Liu, Na; Zhou, Jianyang; Zhou, Yuanguo; Wang, Jiamin; Liu, Qing Huo
2016-01-01
The spectral element method (SEM) is a special kind of high-order finite element method (FEM) which combines the flexibility of a finite element method with the accuracy of a spectral method. In contrast to the traditional FEM, the SEM exhibits advantages in the high-order accuracy as the error decreases exponentially with the increase of interpolation degree by employing the Gauss–Lobatto–Legendre (GLL) polynomials as basis functions. In this study, the spectral element method is developed for the first time for the determination of band structures of 3D isotropic/anisotropic phononic crystals (PCs). Based on the Bloch theorem, we present a novel, intuitive discretization formulation for Navier equation in the SEM scheme for periodic media. By virtue of using the orthogonal Legendre polynomials, the generalized eigenvalue problem is converted to a regular one in our SEM implementation to improve the efficiency. Besides, according to the specific geometry structure, 8-node and 27-node hexahedral elements as well as an analytic mesh have been used to accurately capture curved PC models in our SEM scheme. To verify its accuracy and efficiency, this study analyses the phononic-crystal plates with square and triangular lattice arrangements, and the 3D cubic phononic crystals consisting of simple cubic (SC), bulk central cubic (BCC) and faced central cubic (FCC) lattices with isotropic or anisotropic scatters. All the numerical results considered demonstrate that SEM is superior to the conventional FEM and can be an efficient alternative method for accurate determination of band structures of 3D phononic crystals. (paper)
Element-specific spectral imaging of multiple contrast agents: a phantom study
Panta, R. K.; Bell, S. T.; Healy, J. L.; Aamir, R.; Bateman, C. J.; Moghiseh, M.; Butler, A. P. H.; Anderson, N. G.
2018-02-01
This work demonstrates the feasibility of simultaneous discrimination of multiple contrast agents based on their element-specific and energy-dependent X-ray attenuation properties using a pre-clinical photon-counting spectral CT. We used a photon-counting based pre-clinical spectral CT scanner with four energy thresholds to measure the X-ray attenuation properties of various concentrations of iodine (9, 18 and 36 mg/ml), gadolinium (2, 4 and 8 mg/ml) and gold (2, 4 and 8 mg/ml) based contrast agents, calcium chloride (140 and 280 mg/ml) and water. We evaluated the spectral imaging performances of different energy threshold schemes between 25 to 82 keV at 118 kVp, based on K-factor and signal-to-noise ratio and ranked them. K-factor was defined as the X-ray attenuation in the K-edge containing energy range divided by the X-ray attenuation in the preceding energy range, expressed as a percentage. We evaluated the effectiveness of the optimised energy selection to discriminate all three contrast agents in a phantom of 33 mm diameter. A photon-counting spectral CT using four energy thresholds of 27, 33, 49 and 81 keV at 118 kVp simultaneously discriminated three contrast agents based on iodine, gadolinium and gold at various concentrations using their K-edge and energy-dependent X-ray attenuation features in a single scan. A ranking method to evaluate spectral imaging performance enabled energy thresholds to be optimised to discriminate iodine, gadolinium and gold contrast agents in a single spectral CT scan. Simultaneous discrimination of multiple contrast agents in a single scan is likely to open up new possibilities of improving the accuracy of disease diagnosis by simultaneously imaging multiple bio-markers each labelled with a nano-contrast agent.
The spectral element method for static neutron transport in AN approximation. Part I
International Nuclear Information System (INIS)
Barbarino, A.; Dulla, S.; Mund, E.H.; Ravetto, P.
2013-01-01
Highlights: ► Spectral elements methods (SEMs) are extended for the neutronics of nuclear reactor cores. ► The second-order, A N formulation of neutron trasport is adopted. ► Results for classical benchmark cases in 2D are presented and compared to finite elements. ► The advantages of SEM in terms of precision and convergence rate are illustrated. ► SEM consitutes a promising approach for the solution of neutron transport problems. - Abstract: Spectral elements methods provide very accurate solutions of elliptic problems. In this paper we apply the method to the A N (i.e. SP 2N−1 ) approximation of neutron transport. Numerical results for classical benchmark cases highlight its performance in comparison with finite element computations, in terms of accuracy per degree of freedom and convergence rate. All calculations presented in this paper refer to two-dimensional problems. The method can easily be extended to three-dimensional cases. The results illustrate promising features of the method for more complex transport problems
A spectral element-FCT method for the compressible Euler equations
International Nuclear Information System (INIS)
Giannakouros, J.; Karniadakis, G.E.
1994-01-01
A new algorithm based on spectral element discretizations and flux-corrected transport concepts is developed for the solution of the Euler equations of inviscid compressible fluid flow. A conservative formulation is proposed based on one- and two-dimensional cell-averaging and reconstruction procedures, which employ a staggered mesh of Gauss-Chebyshev and Gauss-Lobatto-Chebyshev collocation points. Particular emphasis is placed on the construction of robust boundary and interfacial conditions in one- and two-dimensions. It is demonstrated through shock-tube problems and two-dimensional simulations that the proposed algorithm leads to stable, non-oscillatory solutions of high accuracy. Of particular importance is the fact that dispersion errors are minimal, as show through experiments. From the operational point of view, casting the method in a spectral element formulation provides flexibility in the discretization, since a variable number of macro-elements or collocation points per element can be employed to accomodate both accuracy and geometric requirements
An efficient formulation for linear and geometric non-linear membrane elements
Directory of Open Access Journals (Sweden)
Mohammad Rezaiee-Pajand
Full Text Available Utilizing the straingradient notation process and the free formulation, an efficient way of constructing membrane elements will be proposed. This strategy can be utilized for linear and geometric non-linear problems. In the suggested formulation, the optimization constraints of insensitivity to distortion, rotational invariance and not having parasitic shear error are employed. In addition, the equilibrium equations will be established based on some constraints among the strain states. The authors' technique can easily separate the rigid body motions, and those belong to deformational motions. In this article, a novel triangular element, named SST10, is formulated. This element will be used in several plane problems having irregular mesh and complicated geometry with linear and geometrically nonlinear behavior. The numerical outcomes clearly demonstrate the efficiency of the new formulation.
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.
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang Jin; Lee, Hong Pyo; Seo, Jeong Moon [Korea Atomic Energy Research Institute, Taejeon (Korea)
2002-03-01
The maim goal of this research is to develop a nonlinear finite element analysis program NUCAS to accurately predict global and local failure modes of containment building subjected to internal pressure. In this report, we describe the techniques we developed throught this research. An adequate model to the analysis of containment building such as microscopic material model is adopted and it applied into the development Reissner-Mindlin degenerated shell element. To avoid finite element deficiencies, the substitute strains based on the assumed strain method is used in the shell formulation. Arc-length control method is also adopted to fully trace the peak load-displacement path due to crack formation. In addition, a benchmark test suite is developed to investigate the performance of NUCAS and proposed as the future benchmark tests for nonlinear analysis of reinforced concrete. Finally, the input format of NUCAS and the examples of input/output file are described. 39 refs., 65 figs., 8 tabs. (Author)
Nonlinear transfer of elements from soil to plants: impact on radioecological modeling
Energy Technology Data Exchange (ETDEWEB)
Tuovinen, Tiina S.; Kolehmainen, Mikko; Roivainen, Paeivi; Kumlin, Timo; Makkonen, Sari; Holopainen, Toini; Juutilainen, Jukka [University of Eastern Finland, Department of Environmental and Biological Sciences, P.O. Box 1627, Kuopio (Finland)
2016-08-15
In radioecology, transfer of radionuclides from soil to plants is typically described by a concentration ratio (CR), which assumes linearity of transfer with soil concentration. Nonlinear uptake is evidenced in many studies, but it is unclear how it should be taken into account in radioecological modeling. In this study, a conventional CR-based linear model, a nonlinear model derived from observed uptake into plants, and a new simple model based on the observation that nonlinear uptake leads to a practically constant concentration in plant tissues are compared. The three models were used to predict transfer of {sup 234}U, {sup 59}Ni and {sup 210}Pb into spruce needles. The predictions of the nonlinear and the new model were essentially similar. In contrast, plant radionuclide concentration was underestimated by the linear model when the total element concentration in soil was relatively low, but within the range commonly observed in nature. It is concluded that the linear modeling could easily be replaced by a new approach that more realistically reflects the true processes involved in the uptake of elements into plants. The new modeling approach does not increase the complexity of modeling in comparison with CR-based linear models, and data needed for model parameters (element concentrations) are widely available. (orig.)
Studies of biaxial mechanical properties and nonlinear finite element modeling of skin.
Shang, Xituan; Yen, Michael R T; Gaber, M Waleed
2010-06-01
The objective of this research is to conduct mechanical property studies of skin from two individual but potentially connected aspects. One is to determine the mechanical properties of the skin experimentally by biaxial tests, and the other is to use the finite element method to model the skin properties. Dynamic biaxial tests were performed on 16 pieces of abdominal skin specimen from rats. Typical biaxial stress-strain responses show that skin possesses anisotropy, nonlinearity and hysteresis. To describe the stress-strain relationship in forms of strain energy function, the material constants of each specimen were obtained and the results show a high correlation between theory and experiments. Based on the experimental results, a finite element model of skin was built to model the skin's special properties including anisotropy and nonlinearity. This model was based on Arruda and Boyce's eight-chain model and Bischoff et al.'s finite element model of skin. The simulation results show that the isotropic, nonlinear eight-chain model could predict the skin's anisotropic and nonlinear responses to biaxial loading by the presence of an anisotropic prestress state.
International Nuclear Information System (INIS)
Kapuria, S; Yaqoob Yasin, M
2013-01-01
In this work, we present an electromechanically coupled efficient layerwise finite element model for the static response of piezoelectric laminated composite and sandwich plates, considering the nonlinear behavior of piezoelectric materials under strong electric field. The nonlinear model is developed consistently using a variational principle, considering a rotationally invariant second order nonlinear constitutive relationship, and full electromechanical coupling. In the piezoelectric layer, the electric potential is approximated to have a quadratic variation across the thickness, as observed from exact three dimensional solutions, and the equipotential condition of electroded piezoelectric surfaces is modeled using the novel concept of an electric node. The results predicted by the nonlinear model compare very well with the experimental data available in the literature. The effect of the piezoelectric nonlinearity on the static response and deflection/stress control is studied for piezoelectric bimorph as well as hybrid laminated plates with isotropic, angle-ply composite and sandwich substrates. For high electric fields, the difference between the nonlinear and linear predictions is large, and cannot be neglected. The error in the prediction of the smeared counterpart of the present theory with the same number of primary displacement unknowns is also examined. (paper)
Burgess, A. B. H.; Erler, A. R.; Shepherd, T. G.
2012-04-01
We present spectra, nonlinear interaction terms, and fluxes computed for horizontal wind fields from high-resolution meteorological analyses made available by ECMWF for the International Polar Year. Total kinetic energy spectra clearly show two spectral regimes: a steep spectrum at large scales and a shallow spectrum in the mesoscale. The spectral shallowing appears at ~200 hPa, and is due to decreasing rotational power with height, which results in the shallower divergent spectrum dominating in the mesoscale. The spectra we find are steeper than those observed in aircraft data and GCM simulations. Though the analyses resolve total spherical harmonic wavenumbers up to n = 721, effects of dissipation on the fluxes and spectra are visible starting at about n = 200. We find a weak forward energy cascade and a downscale enstrophy cascade in the mesoscale. Eddy-eddy nonlinear kinetic energy transfers reach maximum amplitudes at the tropopause, and decrease with height thereafter; zonal mean-eddy transfers dominate in the stratosphere. In addition, zonal anisotropy reaches a minimum at the tropopause. Combined with strong eddy-eddy interactions, this suggests flow in the tropopause region is very active and bears the greatest resemblance to isotropic turbulence. We find constant enstrophy flux over a broad range of wavenumbers around the tropopause and in the upper stratosphere. A relatively constant spectral enstrophy flux at the tropopause suggests a turbulent inertial range, and that the enstrophy flux is resolved. A main result of our work is its implications for explaining the shallow mesoscale spectrum observed in aircraft wind measurements, GCM studies, and now meteorological analyses. The strong divergent component in the shallow mesoscale spectrum indicates unbalanced flow, and nonlinear transfers decreasing quickly with height are characteristic of waves, not turbulence. Together with the downscale flux of energ y through the shallow spectral range, these
Energy Technology Data Exchange (ETDEWEB)
Nageshwari, M.; Jayaprakash, P.; Kumari, C. Rathika Thaya [PG & Research Department of Physics, Arignar Anna Govt. Arts College, Cheyyar 604407, Tamil Nadu (India); Vinitha, G. [Department of Physics, School of Advanced Sciences, VIT Chennai, 600127 Tamil Nadu (India); Caroline, M. Lydia, E-mail: lydiacaroline2006@yahoo.co.in [PG & Research Department of Physics, Arignar Anna Govt. Arts College, Cheyyar 604407, Tamil Nadu (India)
2017-04-15
An efficient nonlinear optical semiorganic material L-valinium L-valine chloride (LVVCl) was synthesized and grown-up by means of slow evaporation process. Single crystal XRD evince that LVVCl corresponds to monoclinic system having acentric space group P2{sub 1}. The diverse functional groups existing in LVVCl were discovered with FTIR spectral investigation. The UV-Visible and photoluminescence spectrum discloses the optical and electronic properties respectively for the grown crystal. Several optical properties specifically extinction coefficient, reflectance, linear refractive index, electrical and optical conductivity were also determined. The SEM analysis was also carried out and it portrayed the surface morphology of LVVCl. The calculated value of laser damage threshold was 2.59 GW/cm{sup 2}. The mechanical and dielectric property of LVVCl was investigated employing microhardness and dielectric studies. The second and third order nonlinear optical characteristics of LVVCl was characterized utilizing Kurtz Perry and Z scan technique respectively clearly suggest its suitability in the domain of optics and photonics. - Graphical abstract: Good quality transparent single crystals of L-valinium L-valine chloride single crystal was grown by slow evaporation technique. The grown crystals were analyzed using different instrumentation methods to check its usefulness for the device fabrication. The determination of nonlinear refractive index (n{sub 2}), absorption coefficient (β) and third order nonlinear susceptibility was determined by Z scan technique, highlighted that LVVCl can serve as a promising candidate for opto electronic and nonlinear optical applications.
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...
Guermond, Jean-Luc; Nazarov, Murtazo; Popov, Bojan; Yang, Yong
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.
Modal representation of geometrically nonlinear behavior by the finite element method
International Nuclear Information System (INIS)
Nagy, D.A.
1977-01-01
A method is presented for representing mild geometrically nonlinear static behavior of thin-type structures, within the finite element method, in terms of linear elastic and linear (bifurcation) buckling analysis results for structural loading or geometry situations which violate the idealized restrictive (perfect) interpretation of linear behavior up to bifurcation. Formulation of the finite element displacement method for material linearity but retaining the full, nonlinear strain-displacement relations (geometric nonlinearity) leads to highly nonlinear equations relating the unknown nodal generalized displacements r to the applied loading R. Restriction to small strains alone does not linearize these equations for thin-type structural configurations; only explicitly requiring that all products of displacement gadients be much smaller than the gadients themselves reduces the equations to the familiar linear form Ksub(e)r=R, where Ksub(e) is the elastic stiffness. Assuming then that the solutions r of the linear equations also satisfies the full nonlinear equations (i.e., that the above explicit requirement is satisfied), a second solution to the full equations can be sought for a one-parameter loading path lambdaR, leading to the well-known linear (bifurcation) buckling eigenvalue problem Ksub(e)X=-Ksub(g)XΛ where Ksub(g) is the geometric stiffness, X the matrix whose columns are the eigenvectors (so-called buckling mode shapes) and Λ is a diagonal matrix of eigenvalues lambda(i) (so-called load scale factors). From the viewpoint of the practising structural analyst using finite element software, the method presented here gives broader and deeper significance to an existing linear (bifurcation) buckling analysis capability, in that the additional computations are minimal beyond those already required for a linear static and buckling analysis, and should be easily performable within any well-designed general purpose finite element system
Dynamic analysis of smart composite beams by using the frequency domain spectral element method
Energy Technology Data Exchange (ETDEWEB)
Park, Il Wook; Lee, Usik [Inha Univ., Incheon (Korea, Republic of)
2012-08-15
To excite or measure the dynamic responses of a laminated composite structure for the active controls of vibrations or noises, wafertype piezoelectric transducers are often bonded on the surface of the composite structure to form a multi layer smart composite structure. Thus, for such smart composite structures, it is very important to develop and use a very reliable mathematical and/or computational model for predicting accurate dynamic characteristics. In this paper, the axial-bending coupled equations of motion and boundary conditions are derived for two layer smart composite beams by using the Hamilton's principle with Lagrange multipliers. The spectral element model is then formulated in the frequency domain by using the variation approach. Through some numerical examples, the extremely high accuracy of the present spectral element model is verified by comparing with the solutions by the conventional finite element model provided in this paper. The effects of the lay up of composite laminates and surface bonded wafer type piezoelectric (PZT) layer on the dynamics and wave characteristics of smart composite beams are investigated. The effective constraint forces at the interface between the base beam and PZT layer are also investigated via Lagrange multipliers.
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......, including the non-linear temperature dependent magnetic data described by a three-parameter modified Frohlich equation fitted to the magnetic saturation curve, and solved with an iterative procedure. The numerical calculations are compared with experiments conducted with two types of induction coils, built...... 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...
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.
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.
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
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.
Suppression of Instabilities Generated by an Anti-Damper with a Nonlinear Magnetic Element in IOTA
Energy Technology Data Exchange (ETDEWEB)
Stern, E. [Fermilab
2018-04-01
The Integrable Optics Test Accelerator (IOTA) storage ring is being constructed at Fermilab as a testbed for new accelerator concepts. One important series of experiments tests the use of a novel nonlinear magnetic insert to damp coherent instabilities. To test the damping power of the element, an instability of desired strength may be intentionally excited with an anti-damper. We report on simulations of beam stabilization using the Synergia modeling framework over ranges of driving and damping strengths.
International Nuclear Information System (INIS)
Kojima, O; Isu, T; Ishi-Hayase, J; Sasaki, M; Tsuchiya, M
2007-01-01
We report the enhancement of the nonlinear optical response of the weakly confined excitons with use of spectrally rectangular pulse. The nonlinear optical response was investigated as a function of excitation energy by a degenerate four-wave-mixing (DFWM) technique. In the case that the laser pulse with the controlled spectral shape excites the plural exciton states simultaneously, the DFWM signal intensity is enhanced by a factor of two in comparison with the intensity under the excitation of a single exciton state. This enhancement is caused by the superposition of the nonlinear optical responses from the plural exciton states
ABAQUS/EPGEN - a general purpose finite element code with emphasis on nonlinear applications
International Nuclear Information System (INIS)
Hibbitt, H.D.
1984-01-01
The article contains a summary description of ABAQUS, a finite element program designed for general use in nonlinear as well as linear structural problems, in the context of its application to nuclear structural integrity analysis. The article begins with a discussion of the design criteria and methods upon which the code development has been based. The engineering modelling capabilities, currently implemented in the program - elements, constitutive models and analysis procedures - are then described. Finally, a few demonstration examples are presented, to illustrate some of the program's features that are of interest in structural integrity analysis associated with nuclear power plants. (orig.)
Zhang, Lei; Cao, Ling; Zhao, Laishi; Algeo, Thomas J.; Chen, Zhong-Qiang; Li, Zhihong; Lv, Zhengyi; Wang, Xiangdong
2017-08-01
Conodont apatite has long been used in paleoenvironmental studies, often with minimal evaluation of the influence of diagenesis on measured elemental and isotopic signals. In this study, we evaluate diagenetic influences on conodonts using an integrated set of analytical techniques. A total of 92 points in 19 coniform conodonts from Ordovician marine units of South China were analyzed by micro-laser Raman spectroscopy (M-LRS), laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS), high-resolution X-ray microdiffraction (HXRD), and secondary ion mass spectrometry (SIMS). Each conodont element was analyzed along its full length, including the albid crown, hyaline crown, and basal body, in either a whole specimen (i.e., reflecting the composition of its outer layer) or a split specimen (i.e., reflecting the composition of its interior). In the conodonts of this study, the outer surfaces consist of hydroxyfluorapatite and the interiors of strontian hydroxyfluorapatite. Ionic substitutions resulted in characteristic Raman spectral shifts in the position (SS1) and width (SS2) of the ν1-PO43- stretching band. Although multiple elements were enriched (Sr2+, Mg2+) and depleted (Fe3+, Mn2+, Ca2+) during diagenesis, geochemical modeling constraints and known Raman spectral patterns suggest that Sr uptake was the dominant influence on diagenetic redshifts of SS1. All study specimens show lower SS2 values than modern bioapatite and synthetic apatite, suggesting that band width decreases with time in ancient bioapatite, possibly through an annealing process that produces larger, more uniform crystal domains. Most specimens consist mainly of amorphous or poorly crystalline apatite, which is inferred to represent the original microstructure of conodonts. In a subset of specimens, some tissues (especially albid crown) exhibit an increased degree of crystallinity developed through aggrading neomorphism. However, no systematic relationship was observed between
Chen, Xiao-Li; Guo, Wen-Zhong; Xue, Xu-Zhang; Wang, Li-Chun; Li, Liang; Chen, Fei
2013-08-01
Mineral elements absorption and content of Lactuca sativa under different spectral component conditions were studied by ICP-AES technology. The results showed that: (1) For Lactuca sativa, the average proportion for Ca : Mg : K : Na : P was 5.5 : 2.5 : 2.3 : 1.5 : 1.0, the average proportion for Fe : Mn : Zn : Cu : B was 25.9 : 5.9 : 2.8 : 1.1 : 1.0; (2) The absorptions for K, P, Ca, Mg and B are the largest under the LED treatment R/B = 1 : 2.75, red light from fluorescent lamps and LED can both promote the absorptions of Fe and Cu; (3)The LED treatments exhibiting relatively higher content of mineral elements are R/B = 1 : 2.75 and R/W = 1 : 1 while higher dry matter accumulations are R/B = 1 : 2.75 and B/W = 1 : 1.
Computational Performance of a Parallelized Three-Dimensional High-Order Spectral Element Toolbox
Bosshard, Christoph; Bouffanais, Roland; Clémençon, Christian; Deville, Michel O.; Fiétier, Nicolas; Gruber, Ralf; Kehtari, Sohrab; Keller, Vincent; Latt, Jonas
In this paper, a comprehensive performance review of an MPI-based high-order three-dimensional spectral element method C++ toolbox is presented. The focus is put on the performance evaluation of several aspects with a particular emphasis on the parallel efficiency. The performance evaluation is analyzed with help of a time prediction model based on a parameterization of the application and the hardware resources. A tailor-made CFD computation benchmark case is introduced and used to carry out this review, stressing the particular interest for clusters with up to 8192 cores. Some problems in the parallel implementation have been detected and corrected. The theoretical complexities with respect to the number of elements, to the polynomial degree, and to communication needs are correctly reproduced. It is concluded that this type of code has a nearly perfect speed up on machines with thousands of cores, and is ready to make the step to next-generation petaflop machines.
Directory of Open Access Journals (Sweden)
Huiqing Fang
2016-01-01
Full Text Available Based on geometrically exact beam theory, a hybrid interpolation is proposed for geometric nonlinear spatial Euler-Bernoulli beam elements. First, the Hermitian interpolation of the beam centerline was used for calculating nodal curvatures for two ends. Then, internal curvatures of the beam were interpolated with a second interpolation. At this point, C1 continuity was satisfied and nodal strain measures could be consistently derived from nodal displacement and rotation parameters. The explicit expression of nodal force without integration, as a function of global parameters, was founded by using the hybrid interpolation. Furthermore, the proposed beam element can be degenerated into linear beam element under the condition of small deformation. Objectivity of strain measures and patch tests are also discussed. Finally, four numerical examples are discussed to prove the validity and effectivity of the proposed beam element.
Rahimi Dalkhani, Amin; Javaherian, Abdolrahim; Mahdavi Basir, Hadi
2018-04-01
Wave propagation modeling as a vital tool in seismology can be done via several different numerical methods among them are finite-difference, finite-element, and spectral-element methods (FDM, FEM and SEM). Some advanced applications in seismic exploration benefit the frequency domain modeling. Regarding flexibility in complex geological models and dealing with the free surface boundary condition, we studied the frequency domain acoustic wave equation using FEM and SEM. The results demonstrated that the frequency domain FEM and SEM have a good accuracy and numerical efficiency with the second order interpolation polynomials. Furthermore, we developed the second order Clayton and Engquist absorbing boundary condition (CE-ABC2) and compared it with the perfectly matched layer (PML) for the frequency domain FEM and SEM. In spite of PML method, CE-ABC2 does not add any additional computational cost to the modeling except assembling boundary matrices. As a result, considering CE-ABC2 is more efficient than PML for the frequency domain acoustic wave propagation modeling especially when computational cost is high and high-level absorbing performance is unnecessary.
Design and implementation of a sensitive high-resolution nonlinear spectral imaging microscope
Palero, Jonathan A.; Latouche, Gwendal; de Bruijn, Henriëtte S.; van der Ploeg van den Heuvel, Angélique; Sterenborg, Henricus J. C. M.; Gerritsen, Hans C.
2008-01-01
Live tissue nonlinear microscopy based on multiphoton autofluorescence and second harmonic emission originating from endogenous fluorophores and noncentrosymmetric-structured proteins is rapidly gaining interest in biomedical applications. The advantage of this technique includes high imaging
Discrete conservation properties for shallow water flows using mixed mimetic spectral elements
Lee, D.; Palha, A.; Gerritsma, M.
2018-03-01
A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of calculus with respect to the standard Lagrange basis functions in one dimension. These are used to construct tensor product solution spaces which satisfy the generalized Stokes theorem, as well as the annihilation of the gradient operator by the curl and the curl by the divergence. This allows for the exact conservation of first order moments (mass, vorticity), as well as higher moments (energy, potential enstrophy), subject to the truncation error of the time stepping scheme. The continuity equation is solved in the strong form, such that mass conservation holds point wise, while the momentum equation is solved in the weak form such that vorticity is globally conserved. While mass, vorticity and energy conservation hold for any quadrature rule, potential enstrophy conservation is dependent on exact spatial integration. The method possesses a weak form statement of geostrophic balance due to the compatible nature of the solution spaces and arbitrarily high order spatial error convergence.
Spectral-element Method for 3D Marine Controlled-source EM Modeling
Liu, L.; Yin, C.; Zhang, B., Sr.; Liu, Y.; Qiu, C.; Huang, X.; Zhu, J.
2017-12-01
As one of the predrill reservoir appraisal methods, marine controlled-source EM (MCSEM) has been widely used in mapping oil reservoirs to reduce risk of deep water exploration. With the technical development of MCSEM, the need for improved forward modeling tools has become evident. We introduce in this paper spectral element method (SEM) for 3D MCSEM modeling. It combines the flexibility of finite-element and high accuracy of spectral method. We use Galerkin weighted residual method to discretize the vector Helmholtz equation, where the curl-conforming Gauss-Lobatto-Chebyshev (GLC) polynomials are chosen as vector basis functions. As a kind of high-order complete orthogonal polynomials, the GLC have the characteristic of exponential convergence. This helps derive the matrix elements analytically and improves the modeling accuracy. Numerical 1D models using SEM with different orders show that SEM method delivers accurate results. With increasing SEM orders, the modeling accuracy improves largely. Further we compare our SEM with finite-difference (FD) method for a 3D reservoir model (Figure 1). The results show that SEM method is more effective than FD method. Only when the mesh is fine enough, can FD achieve the same accuracy of SEM. Therefore, to obtain the same precision, SEM greatly reduces the degrees of freedom and cost. Numerical experiments with different models (not shown here) demonstrate that SEM is an efficient and effective tool for MSCEM modeling that has significant advantages over traditional numerical methods.This research is supported by Key Program of National Natural Science Foundation of China (41530320), China Natural Science Foundation for Young Scientists (41404093), and Key National Research Project of China (2016YFC0303100, 2017YFC0601900).
Directory of Open Access Journals (Sweden)
Vahid Reza Afkhami
2017-12-01
Full Text Available In the steel frames, beam-column connections are traditionally assumed to be rigid or pinned, but in the steel frames, most types of beam-column connections are semi-rigid. Recent studies and some new codes, especially EC3 and EC4, include methods and formulas to estimate the resistance and stiffness of the panel zone. Because of weaknesses of EC3 and EC4 in some cases, Bayo et al. proposed a new component-based method (cruciform element method to model internal and external semi-rigid connections that revived and modified EC methods. The nonlinear modelling of structures plays an important role in the analysis and design of structures and nonlinear static analysis is a rather simple and efficient technique for analysis of structures. This paper presents nonlinear static (pushover analysis technique by new nonlinearity factor and Bayo et al. model of two types of semi-rigid connections, end plate connection and top and seat angles connection. Two types of lateral loading, uniform and triangular distributions are considered. Results show that the frames with top and seat angles connection have fewer initial stiffness than frames with semi-rigid connection and P-Δ effect more decreases base shear capacity in the case of top and seat angles connection. P-Δ effect in decrease of base shear capacity increases with the increase of number of stories.
Hamim, Salah Uddin Ahmed
Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain behavior. Thus, theoretically it is possible to extract mechanical properties of a material through nanoindentation. However, due to various nonlinearities associated with nanoindentation the process of interpreting load-displacement data into material properties is difficult. Although, simple elastic behavior can be characterized easily, a method to characterize complicated material behavior such as nonlinear viscoelasticity is still lacking. In this study, a nanoindentation-based material characterization technique is developed to characterize soft materials exhibiting nonlinear viscoelasticity. Nanoindentation experiment was modeled in finite element analysis software (ABAQUS), where a nonlinear viscoelastic behavior was incorporated using user-defined subroutine (UMAT). The model parameters were calibrated using a process called inverse analysis. In this study, a surrogate model-based approach was used for the inverse analysis. The different factors affecting the surrogate model performance are analyzed in order to optimize the performance with respect to the computational cost.
International Nuclear Information System (INIS)
Kulak, R.F.; Belytschko, T.B.
1975-09-01
The formulation of a finite-element procedure for the implicit transient and static analysis of plate/shell type structures in three-dimensional space is described. The triangular plate/shell element can sustain both membrane and bending stresses. Both geometric and material nonlinearities can be treated, and an elastic-plastic material law has been incorporated. The formulation permits the element to undergo arbitrarily large rotations and translations; but, in its present form it is restricted to small strains. The discretized equations of motion are obtained by a stiffness method. An implicit integration algorithm based on trapezoidal integration formulas is used to integrate the discretized equations of motion in time. To ensure numerical stability, an iterative solution procedure with equilibrium checks is used
Energy Technology Data Exchange (ETDEWEB)
Liu, Youshan, E-mail: ysliu@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); Teng, Jiwen, E-mail: jwteng@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); Xu, Tao, E-mail: xutao@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); CAS Center for Excellence in Tibetan Plateau Earth Sciences, Beijing, 100101 (China); Badal, José, E-mail: badal@unizar.es [Physics of the Earth, Sciences B, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza (Spain)
2017-05-01
The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational
Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José
2017-05-01
The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant-Friedrichs-Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational
International Nuclear Information System (INIS)
Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José
2017-01-01
The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational
International Nuclear Information System (INIS)
Marinković, D; Köppe, H; Gabbert, U
2008-01-01
Active piezoelectric thin-walled structures, especially those with a notably higher membrane than bending stiffness, are susceptible to large rotations and transverse deflections. Recent investigations conducted by a number of researchers have shown that the predicted behavior of piezoelectric structures can be significantly influenced by the assumption of large displacements and rotations of the structure, thus demanding a geometrically nonlinear formulation in order to investigate it. This paper offers a degenerated shell element and a simplified formulation that relies on small incremental steps for the geometrically nonlinear analysis of piezoelectric composite structures. A set of purely mechanical static cases is followed by a set of piezoelectric coupled static cases, both demonstrating the applicability of the proposed formulation
Whiteley, J. P.
2017-10-01
Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.
Stupishin, L. U.; Nikitin, K. E.; Kolesnikov, A. G.
2018-02-01
The article is concerned with a methodology of optimal design of geometrically nonlinear (flexible) shells of revolution of minimum weight with strength, stability and strain constraints. The problem of optimal design with constraints is reduced to the problem of unconstrained minimization using the penalty functions method. Stress-strain state of shell is determined within the geometrically nonlinear deformation theory. A special feature of the methodology is the use of a mixed finite-element formulation based on the Galerkin method. Test problems for determining the optimal form and thickness distribution of a shell of minimum weight are considered. The validity of the results obtained using the developed methodology is analyzed, and the efficiency of various optimization algorithms is compared to solve the set problem. The developed methodology has demonstrated the possibility and accuracy of finding the optimal solution.
Automatic endmember selection and nonlinear spectral unmixing of Lunar analog minerals
Rommel, Daniela; Grumpe, Arne; Felder, Marian Patrik; Wöhler, Christian; Mall, Urs; Kronz, Andreas
2017-03-01
While the interpretation of spectral reflectance data has been widely applied to detect the presence of minerals, determining and quantifying the abundances of minerals contained by planetary surfaces is still an open problem. With this paper we address one of the two main questions arising from the spectral unmixing problem. While the mathematical mixture model has been extensively researched, considerably less work has been committed to the selection of endmembers from a possibly huge database or catalog of potential endmembers. To solve the endmember selection problem we define a new spectral similarity measure that is not purely based on the reconstruction error, i.e. the squared difference between the modeled and the measured reflectance spectrum. To select reasonable endmembers, we extend the similarity measure by adding information extracted from the spectral absorption bands. This will allow for a better separation of spectrally similar minerals. Evaluating all possible subsets of a possibly very large catalog that contain at least one endmember leads to an exponential increase in computational complexity, rendering catalogs of 20-30 endmembers impractical. To overcome this computational limitation, we propose the usage of a genetic algorithm that, while initially starting with random subsets, forms new subsets by combining the best subsets and, to some extent, does a local search around the best subsets by randomly adding a few endmembers. A Monte-Carlo simulation based on synthetic mixtures and a catalog size varying from three to eight endmembers demonstrates that the genetic algorithm is expected to require less combinations to be evaluated than an exhaustive search if the catalog comprises 10 or more endmembers. Since the genetic algorithm evaluates some combinations multiple times, we propose a simple modification and store previously evaluated endmember combinations. The resulting algorithm is shown to never require more function evaluations than a
Nonlinear finite element analysis of the plantar fascia due to the windlass mechanism.
Cheng, Hsin-Yi Kathy; Lin, Chun-Li; Chou, Shih-Wei; Wang, Hsien-Wen
2008-08-01
Tightening of plantar fascia by passively dorsiflexing the toes during walking has functional importance. The purpose of this research was to evaluate the influence of big toe dorsiflexion angles upon plantar fascia tension (the windlass effect) with a nonlinear finite element approach. A two-dimensional finite element model of the first ray was constructed for biomechanical analysis. In order to imitate the windlass effect and to evaluate the mechanical responses of the plantar fascia under various conditions, 12 model simulations--three dorsiflexion angles of the big toe (45 degrees, 30 degrees, and 15 degrees), two plantar fascia properties (linear, nonlinear), and two weightbearing conditions (with body weight, without body weight)--were designed and analyzed. Our results demonstrated that nonlinear modeling of the plantar fascia provides a more sophisticated representation of experimental data than the linear one. Nonlinear plantar fascia setting also predicted a higher stress distribution along the fiber directions especially with larger toe dorsiflexion angles (45 degrees>30 degrees>15 degrees). The plantar fascia stress was found higher near the metatarsal insertion and faded as it moved toward the calcaneal insertion. Passively dorsiflexing the big toe imposes tension onto the plantar fascia. Windlass mechanism also occurs during stance phase of walking while the toes begin to dorsiflex. From a biomechanical standpoint, the plantar fascia tension may help propel the body upon its release at the point of push off. A controlled stretch via dorsiflexing the big toe may have a positive effect on treating plantar fasciitis by providing proper guidance for collagen regeneration. The windlass mechanism is also active during the stance phase of walking when the toes begin to dorsiflex.
International Nuclear Information System (INIS)
Lee, Tae Hee; Yoo, Jung Hun; Choi, Hyeong Cheol
2002-01-01
A finite element package is often used as a daily design tool for engineering designers in order to analyze and improve the design. The finite element analysis can provide the responses of a system for given design variables. Although finite element analysis can quite well provide the structural behaviors for given design variables, it cannot provide enough information to improve the design such as design sensitivity coefficients. Design sensitivity analysis is an essential step to predict the change in responses due to a change in design variables and to optimize a system with the aid of the gradient-based optimization techniques. To develop a numerical method of design sensitivity analysis, analytical derivatives that are based on analytical differentiation of the continuous or discrete finite element equations are effective but analytical derivatives are difficult because of the lack of internal information of the commercial finite element package such as shape functions. Therefore, design sensitivity analysis outside of the finite element package is necessary for practical application in an industrial setting. In this paper, the semi-analytic method for design sensitivity analysis is used for the development of the design sensitivity module outside of a commercial finite element package of ANSYS. The direct differentiation method is employed to compute the design derivatives of the response and the pseudo-load for design sensitivity analysis is effectively evaluated by using the design variation of the related internal nodal forces. Especially, we suggest an effective method for stress and nonlinear design sensitivity analyses that is independent of the commercial finite element package is also discussed. Numerical examples are illustrated to show the accuracy and efficiency of the developed method and to provide insights for implementation of the suggested method into other commercial finite element packages
Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics
Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.
2016-01-01
Entropy stable (SS) discontinuous spectral collocation formulations of any order are developed for the compressible Navier-Stokes equations on hexahedral elements. Recent progress on two complementary efforts is presented. The first effort is a generalization of previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Although being more costly to implement, it is shown that the LG operators are significantly more accurate on comparable grids. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort generalizes previous SS work to include the possibility of p-refinement at non-conforming interfaces. A generalization of existing entropy stability machinery is developed to accommodate the nuances of fully multi-dimensional summation-by-parts (SBP) operators. The entropy stability of the compressible Euler equations on non-conforming interfaces is demonstrated using the newly developed LG operators and multi-dimensional interface interpolation operators.
Eiber, Calvin D; Dokos, Socrates; Lovell, Nigel H; Suaning, Gregg J
2017-05-01
The capacity to quickly and accurately simulate extracellular stimulation of neurons is essential to the design of next-generation neural prostheses. Existing platforms for simulating neurons are largely based on finite-difference techniques; due to the complex geometries involved, the more powerful spectral or differential quadrature techniques cannot be applied directly. This paper presents a mathematical basis for the application of a spectral element method to the problem of simulating the extracellular stimulation of retinal neurons, which is readily extensible to neural fibers of any kind. The activating function formalism is extended to arbitrary neuron geometries, and a segmentation method to guarantee an appropriate choice of collocation points is presented. Differential quadrature may then be applied to efficiently solve the resulting cable equations. The capacity for this model to simulate action potentials propagating through branching structures and to predict minimum extracellular stimulation thresholds for individual neurons is demonstrated. The presented model is validated against published values for extracellular stimulation threshold and conduction velocity for realistic physiological parameter values. This model suggests that convoluted axon geometries are more readily activated by extracellular stimulation than linear axon geometries, which may have ramifications for the design of neural prostheses.
Using spectral element method to solve variational inequalities with applications in finance
International Nuclear Information System (INIS)
Moradipour, M.; Yousefi, S.A.
2015-01-01
Under the Black–Scholes model, the value of an American option solves a time dependent variational inequality problem (VIP). In this paper, first we discretize the variational inequality of American option in temporal direction by applying the Rannacher time stepping and achieve a sequence of elliptic variational inequalities. Second we discretize the spatial domain of variational inequalities by using spectral element methods with high order Lagrangian polynomials introduced on Gauss–Legendre–Lobatto points. Also by computing integrals by the Gauss–Legendre–Lobatto quadrature rule we derive a sequence of the linear complementarity problems (LCPs) having a positive definite sparse coefficient matrix. To find the unique solutions of the LCPs, we use the projected successive over-relaxation (PSOR) algorithm. Furthermore we present some existence and uniqueness theorems for the variational inequalities and LCPs. Finally, theoretical results are verified on the relevant numerical examples.
Direct numerical simulation of the Rayleigh-Taylor instability with the spectral element method
International Nuclear Information System (INIS)
Zhang Xu; Tan Duowang
2009-01-01
A novel method is proposed to simulate Rayleigh-Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier-Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh-Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh-Taylor instabilities of turbulent flows. (authors)
Nguyen, Vu-Hieu; Naili, Salah
2013-01-01
This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally graded anisotropic material coupled with fluids. The viscous effects are taken into account. The geometrical configuration mimics the one of axial transmission technique used for evaluating the bone quality. We present a numerical procedure adapted for this purpose which is based on the spectral finite element method (FEM). By using a combined Laplace-Fourier transform, the vibroacoustic problem may be transformed into the frequency-wavenumber domain in which, as radiation conditions may be exactly introduced in the infinite fluid halfspaces, only the heterogeneous solid layer needs to be analysed using FEM. Several numerical tests are presented showing very good performance of the proposed approach. We present some results to study the influence of the frequency on the first arriving signal velocity in (visco)elastic bone plate.
Direct Numerical Simulation of the Rayleigh−Taylor Instability with the Spectral Element Method
International Nuclear Information System (INIS)
Xu, Zhang; Duo-Wang, Tan
2009-01-01
A novel method is proposed to simulate Rayleigh−Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier–Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh−Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh–Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh−Taylor instabilities of turbulent flows. (fundamental areas of phenomenology (including applications))
Jafari, Azadeh; Deville, Michel O.; Fiétier, Nicolas
2008-09-01
This study discusses the capability of the constitutive laws for the matrix logarithm of the conformation tensor (LCT model) within the framework of the spectral elements method. The high Weissenberg number problems (HWNP) usually produce a lack of convergence of the numerical algorithms. Even though the question whether the HWNP is a purely numerical problem or rather a breakdown of the constitutive law of the model has remained somewhat of a mystery, it has been recognized that the selection of an appropriate constitutive equation constitutes a very crucial step although implementing a suitable numerical technique is still important for successful discrete modeling of non-Newtonian flows. The LCT model formulation of the viscoelastic equations originally suggested by Fattal and Kupferman is applied for 2-dimensional (2D) FENE-CR model. The Planar Poiseuille flow is considered as a benchmark problem to test this representation at high Weissenberg number. The numerical results are compared with numerical solution of the standard constitutive equation.
Viner, K.; Reinecke, P. A.; Gabersek, S.; Flagg, D. D.; Doyle, J. D.; Martini, M.; Ryglicki, D.; Michalakes, J.; Giraldo, F.
2016-12-01
NEPTUNE: the Navy Environmental Prediction sysTem Using the NUMA*corE, is a 3D spectral element atmospheric model composed of a full suite of physics parameterizations and pre- and post-processing infrastructure with plans for data assimilation and coupling components to a variety of Earth-system models. This talk will focus on the initial struggles and solutions in adapting NUMA for stable and accurate integration on the sphere using both the deep atmosphere equations and a newly developed shallow-atmosphere approximation, as demonstrated through idealized test cases. In addition, details of the physics-dynamics coupling methodology will be discussed. NEPTUNE results for test cases from the 2016 Dynamical Core Model Intercomparison Project (DCMIP-2016) will be shown and discussed. *NUMA: Nonhydrostatic Unified Model of the Atmosphere; Kelly and Giraldo 2012, JCP
Gopalakrishnan, Srinivasan; Roy Mahapatra, Debiprosad
2008-01-01
The use of composites and Functionally Graded Materials (FGMs) in structural applications has increased. FGMs allow the user to design materials for a specified functionality and have many uses in structural engineering. However, the behaviour of these structures under high-impact loading is not well understood. This book is the first to apply the Spectral Finite Element Method (SFEM) to inhomogeneous and anisotropic structures in a unified and systematic manner. It focuses on some of the problems with this media which were previously thought unmanageable. Types of SFEM for regular and damaged 1-D and 2-D waveguides, solution techniques, methods of detecting the presence of damages and their locations, and methods for controlling the wave propagation responses are discussed. Tables, figures and graphs support the theory and case studies are included. This book is of value to senior undergraduates and postgraduates studying in this field, and researchers and practicing engineers in structural integrity.
A discrete element model for the investigation of the geometrically nonlinear behaviour of solids
Ockelmann, Felix; Dinkler, Dieter
2018-07-01
A three-dimensional discrete element model for elastic solids with large deformations is presented. Therefore, an discontinuum approach is made for solids. The properties of elastic material are transferred analytically into the parameters of a discrete element model. A new and improved octahedron gap-filled face-centred cubic close packing of spheres is split into unit cells, to determine the parameters of the discrete element model. The symmetrical unit cells allow a model with equal shear components in each contact plane and fully isotropic behaviour for Poisson's ratio above 0. To validate and show the broad field of applications of the new model, the pin-pin Euler elastica is presented and investigated. The thin and sensitive structure tends to undergo large deformations and rotations with a highly geometrically nonlinear behaviour. This behaviour of the elastica can be modelled and is compared to reference solutions. Afterwards, an improved more realistic simulation of the elastica is presented which softens secondary buckling phenomena. The model is capable of simulating solids with small strains but large deformations and a strongly geometrically nonlinear behaviour, taking the shear stiffness of the material into account correctly.
Directory of Open Access Journals (Sweden)
Romanas Karkauskas
2011-04-01
Full Text Available The expressions of the finite element method tangent stiffness matrix of geometrically nonlinear constructions are not fully presented in publications. The matrixes of small displacements stiffness are usually presented only. To solve various problems of construction analysis or design and to specify the mode of the real deflection of construction, it is necessary to have a fully described tangent matrix analytical expression. This paper presents a technique of tangent stiffness matrix generation using discrete body total potential energy stationary conditions considering geometrically nonlinear 2D frame element taking account of interelement interaction forces only. The obtained vector-function derivative of internal forces considering nodal displacements is the tangent stiffness matrix. The analytical expressions having nodal displacements of matrixes forming the content of the 2D frame construction element tangent stiffness matrix are presented in the article. The suggested methodology has been checked making symbolical calculations in the medium of MatLAB calculation complex. The analytical expression of the stiffness matrix has been obtained.Article in Lithuanian
Spectral, spatial and temporal control of high-power diode lasers through nonlinear optical feedback
van Voorst, P.D.
2008-01-01
A high-power diode laser offers multi-Watt output power from a small and efficient device, which makes them an interesting source for numerous applications. The spatial and spectral output however, are of reduced quality which limits the applicability. This limited quality is connected to the design
Linear and nonlinear dynamic analysis by boundary element method. Ph.D. Thesis, 1986 Final Report
Ahmad, Shahid
1991-01-01
An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons
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
The design of sheet pile walls by lower bound limit analysis is considered. The design problem involves the determination of the necessary yield moment of the wall, the wall depth and the anchor force such that the structure is able to sustain the given loads. This problem is formulated...... 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....
Assessment of non-linear analysis finite element program (NONSAP) for inelastic analysis
International Nuclear Information System (INIS)
Chang, T.Y.; Prachuktam, S.; Reich, M.
1976-11-01
An assessment on a nonlinear structural analysis finite element program called NONSAP is given with respect to its inelastic analysis capability for pressure vessels and components. The assessment was made from the review of its theoretical basis and bench mark problem runs. It was found that NONSAP has only limited capability for inelastic analysis. However, the program was written flexible enough that it can be easily extended or modified to suit the user's need. Moreover, some of the numerical difficulties in using NONSAP are pointed out
Extensions to a nonlinear finite-element axisymmetric shell model based on Reissner's shell theory
International Nuclear Information System (INIS)
Cook, W.A.
1981-01-01
Extensions to shell analysis not usually associated with shell theory are described in this paper. These extensions involve thick shells, nonlinear materials, a linear normal stress approximation, and a changing shell thickness. A finite element shell-of-revolution model has been developed to analyze nuclear material shipping containers under severe impact conditions. To establish the limits for this shell model, the basic assumptions used in its development were studied; these are listed in this paper. Several extensions were evident from the study of these limits: a thick shell, a plastic hinge, and a linear normal stress
Frost heave modelling of buried pipelines using non-linear Fourier finite elements
International Nuclear Information System (INIS)
Wan, R. G.; You, R.
1998-01-01
Numerical analysis of the response of a three-dimensional soil-pipeline system in a freezing environment using non-linear Fourier finite elements was described as an illustration of the effectiveness of this technique in analyzing plasticity problems. Plastic deformations occur when buried pipeline is under the action of non-uniform frost heave. The three-dimensional frost heave which develops over time including elastoplastic deformations of the soil and pipe are computed. The soil heave profile obtained in the numerical analysis was consistent with experimental findings for similar configurations. 8 refs., 8 figs
Karaton, Muhammet
2014-01-01
A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched.
2014-12-18
liquid. Since the diffusive nature of the relaxation follows the Debye –Stokes–Einstein relation [39], this mechanism is referred to as diffusive...Sigma-Aldrich, 270660, ≥99.9%) are conducted using 1 mm path length , fused silica cuvettes. Using the refractive index measurements of [46], we find...studies of molecular liquids,” Ann. Rev. Phys. Chem. 31, 523–558 (1980). 38. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic/Elsevier, 2008). 39. P. Debye
Spectral dependence of nonlinear optical absorption of silica glass with copper nanoparticles
International Nuclear Information System (INIS)
Golubev, A N; Nikitin, S I; Smirnov, M A; Stepanov, A L
2011-01-01
The nonlinear optical properties of silica glass with copper nanoparticles synthesized by ion implantation were investigated by z-scan method in nanosecond time scale. The reverse saturation absorption (RSA) at the wavelength range of 450–540 nm and saturation absorption (SA) at 550–585 nm were observed. It was supposed that the two-photon electron absorption from bound of d-states determined the RSA effect and the SA is due to saturation of plasmon excitation.
International Nuclear Information System (INIS)
Koteras, J.R.
1996-01-01
The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region
A time-domain finite element model reduction method for viscoelastic linear and nonlinear systems
Directory of Open Access Journals (Sweden)
Antônio Marcos Gonçalves de Lima
Full Text Available AbstractMany authors have shown that the effective design of viscoelastic systems can be conveniently carried out by using modern mathematical models to represent the frequency- and temperature-dependent behavior of viscoelastic materials. However, in the quest for design procedures of real-word engineering structures, the large number of exact evaluations of the dynamic responses during iterative procedures, combined with the typically high dimensions of large finite element models, makes the numerical analysis very costly, sometimes unfeasible. It is especially true when the viscoelastic materials are used to reduce vibrations of nonlinear systems. As a matter of fact, which the resolution of the resulting nonlinear equations of motion with frequency- and temperature-dependent viscoelastic damping forces is an interesting, but hard-to-solve problem. Those difficulties motivate the present study, in which a time-domain condensation strategy of viscoelastic systems is addressed, where the viscoelastic behavior is modeled by using a four parameter fractional derivative model. After the discussion of various theoretical aspects, the exact and reduced time responses are calculated for a three-layer sandwich plate by considering nonlinear boundary conditions.
Nonlinear finite element formulation for analyzing shape memory alloy cylindrical panels
International Nuclear Information System (INIS)
Mirzaeifar, R; Shakeri, M; Sadighi, M
2009-01-01
In this paper, a general incremental displacement based finite element formulation capable of modeling material nonlinearities based on first-order shear deformation theory (FSDT) is developed for cylindrical shape memory alloy (SMA) shells. The Boyd–Lagoudas phenomenological model with polynomial hardening in conjunction with 3D incremental convex cutting plane explicit algorithm is implemented for preparing the SMA constitutive model in the finite element formulation. Several numerical examples are presented for demonstrating the performance of the proposed formulation in stress, deflection and phase transformation analysis of pseudoelastic behavior of shape memory cylindrical panels with various boundary conditions. Also, it is shown that the presented formulation can be implemented for studying plates and beams with rectangular cross section
FEAST: a two-dimensional non-linear finite element code for calculating stresses
International Nuclear Information System (INIS)
Tayal, M.
1986-06-01
The computer code FEAST calculates stresses, strains, and displacements. The code is two-dimensional. That is, either plane or axisymmetric calculations can be done. The code models elastic, plastic, creep, and thermal strains and stresses. Cracking can also be simulated. The finite element method is used to solve equations describing the following fundamental laws of mechanics: equilibrium; compatibility; constitutive relations; yield criterion; and flow rule. FEAST combines several unique features that permit large time-steps in even severely non-linear situations. The features include a special formulation for permitting many finite elements to simultaneously cross the boundary from elastic to plastic behaviour; accomodation of large drops in yield-strength due to changes in local temperature and a three-step predictor-corrector method for plastic analyses. These features reduce computing costs. Comparisons against twenty analytical solutions and against experimental measurements show that predictions of FEAST are generally accurate to ± 5%
3D airborne EM modeling based on the spectral-element time-domain (SETD) method
Cao, X.; Yin, C.; Huang, X.; Liu, Y.; Zhang, B., Sr.; Cai, J.; Liu, L.
2017-12-01
In the field of 3D airborne electromagnetic (AEM) modeling, both finite-difference time-domain (FDTD) method and finite-element time-domain (FETD) method have limitations that FDTD method depends too much on the grids and time steps, while FETD requires large number of grids for complex structures. We propose a time-domain spectral-element (SETD) method based on GLL interpolation basis functions for spatial discretization and Backward Euler (BE) technique for time discretization. The spectral-element method is based on a weighted residual technique with polynomials as vector basis functions. It can contribute to an accurate result by increasing the order of polynomials and suppressing spurious solution. BE method is a stable tine discretization technique that has no limitation on time steps and can guarantee a higher accuracy during the iteration process. To minimize the non-zero number of sparse matrix and obtain a diagonal mass matrix, we apply the reduced order integral technique. A direct solver with its speed independent of the condition number is adopted for quickly solving the large-scale sparse linear equations system. To check the accuracy of our SETD algorithm, we compare our results with semi-analytical solutions for a three-layered earth model within the time lapse 10-6-10-2s for different physical meshes and SE orders. The results show that the relative errors for magnetic field B and magnetic induction are both around 3-5%. Further we calculate AEM responses for an AEM system over a 3D earth model in Figure 1. From numerical experiments for both 1D and 3D model, we draw the conclusions that: 1) SETD can deliver an accurate results for both dB/dt and B; 2) increasing SE order improves the modeling accuracy for early to middle time channels when the EM field diffuses fast so the high-order SE can model the detailed variation; 3) at very late time channels, increasing SE order has little improvement on modeling accuracy, but the time interval plays
Compatible-strain mixed finite element methods for incompressible nonlinear elasticity
Faghih Shojaei, Mostafa; Yavari, Arash
2018-05-01
We introduce a new family of mixed finite elements for incompressible nonlinear elasticity - compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields. In particular, we define the displacement in H1, the displacement gradient in H (curl), the stress in H (div), and the pressure field in L2. The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces. Next, in a conforming setting, we approximate the solution and the test spaces with some piecewise polynomial subspaces of them. Among these approximation spaces are the tensorial analogues of the Nédélec and Raviart-Thomas finite element spaces of vector fields. This approach results in compatible-strain mixed finite element methods that satisfy both the Hadamard compatibility condition and the continuity of traction at the discrete level independently of the refinement level of the mesh. By considering several numerical examples, we demonstrate that CSFEMs have a good performance for bending problems and for bodies with complex geometries. CSFEMs are capable of capturing very large strains and accurately approximating stress and pressure fields. Using CSFEMs, we do not observe any numerical artifacts, e.g., checkerboarding of pressure, hourglass instability, or locking in our numerical examples. Moreover, CSFEMs provide an efficient framework for modeling heterogeneous solids.
Adegoke, Oluwashina; Dhang, Prasun; Mukhopadhyay, Banibrata; Ramadevi, M. C.; Bhattacharya, Debbijoy
2018-05-01
By analysing the time series of RXTE/PCA data, the non-linear variabilities of compact sources have been repeatedly established. Depending on the variation in temporal classes, compact sources exhibit different non-linear features. Sometimes they show low correlation/fractal dimension, but in other classes or intervals of time they exhibit stochastic nature. This could be because the accretion flow around a compact object is a non-linear general relativistic system involving magnetohydrodynamics. However, the more conventional way of addressing a compact source is the analysis of its spectral state. Therefore, the question arises: What is the connection of non-linearity to the underlying spectral properties of the flow when the non-linear properties are related to the associated transport mechanisms describing the geometry of the flow? This work is aimed at addressing this question. Based on the connection between observed spectral and non-linear (time series) properties of two X-ray binaries: GRS 1915+105 and Sco X-1, we attempt to diagnose the underlying accretion modes of the sources in terms of known accretion classes, namely, Keplerian disc, slim disc, advection dominated accretion flow and general advective accretion flow. We explore the possible transition of the sources from one accretion mode to others with time. We further argue that the accretion rate must play an important role in transition between these modes.
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
A nonlinear finite element model of a piezoelectric tube actuator with hysteresis and creep
International Nuclear Information System (INIS)
Chung, S H; Fung, Eric H K
2010-01-01
Piezoelectric tube actuators are commonly used for nanopositioning in atomic force microscopes (AFMs). However, piezoelectric tube actuators exhibit hysteresis and creep which significantly limit the accuracy of nanopositioning. A finite element model of a piezoelectric tube actuator with hysteresis and creep is important for control purposes, but so far one has not been developed. The purpose of this paper is to present a nonlinear finite element (FE) model with hysteresis and creep for design purposes. Prandtl–Ishlinskii (PI) hysteresis operators and creep operators are adopted into constitutive equations. The nonlinear FE model is formulated using energy approach and Hamilton's principle. The parameters of the PI hysteresis operators and the creep operators are identified by comparing the simulation results and experimental results of other researchers. The working operation of the piezoelectric tube actuator is simulated by the reduced order FE model, and the displacement error due to hysteresis, creep and coupling effect is investigated. An output feedback controller is implemented into the reduced order FE model to show that this model is controllable
Energy Technology Data Exchange (ETDEWEB)
Carella, Alfredo Raul
2012-09-15
Quantifying species transport rates is a main concern in chemical and petrochemical industries. In particular, the design and operation of many large-scale industrial chemical processes is as much dependent on diffusion as it is on reaction rates. However, the existing diffusion models sometimes fail to predict experimentally observed behaviors and their accuracy is usually insufficient for process optimization purposes. Fractional diffusion models offer multiple possibilities for generalizing Flick's law in a consistent manner in order to account for history dependence and nonlocal effects. These models have not been extensively applied to the study of real systems, mainly due to their computational cost and mathematical complexity. A least squares spectral formulation was developed for solving fractional differential equations. The proposed method was proven particularly well-suited for dealing with the numerical difficulties inherent to fractional differential operators. The practical implementation was explained in detail in order to enhance reproducibility, and directions were specified for extending it to multiple dimensions and arbitrarily shaped domains. A numerical framework based on the least-squares spectral element method was developed for studying and comparing anomalous diffusion models in pellets. This simulation tool is capable of solving arbitrary integro-differential equations and can be effortlessly adapted to various problems in any number of dimensions. Simulations of the flow around a cylindrical particle were achieved by extending the functionality of the developed framework. A test case was analyzed by coupling the boundary condition yielded by the fluid model with two families of anomalous diffusion models: hyperbolic diffusion and fractional diffusion. Qualitative guidelines for determining the suitability of diffusion models can be formulated by complementing experimental data with the results obtained from this approach.(Author)
Neurosurgery simulation using non-linear finite element modeling and haptic interaction
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.
International Nuclear Information System (INIS)
Liebe, R.
1978-04-01
This study describes theoretical and experimental investigations of the dynamic deformation behavior of single and clustered fuel elements under local fault conditions in a Fast Breeder Reactor core. In particular an energetic molten-fuel-coolant-interaction (FCI) is assumed in one subassembly with corresponding pressure pulses, which may rupture the wrapper and load the adjacent fuel elements impulsively. Associated coherent structural deformation may exceed tolerable and damage the control rods. To attack the outlined coupled fluid-structure-interaction problem it is assumed, that the loading at the structures is known in space and time, and that there is no feedback from the deformation response. Then current FCI-knowledge and experience from underwater core model explosion tests is utilized to estimate upper limits of relevant pulse characteristics. As a first step the static carrying capacity of the rigid-plastic hexagonal wrapper tube is calculated using the methods of limit analysis. Then for a general dynamic simulation of the complete elastoplastic subassembly response the concept of a discrete nonlinear hinge is introduced. A corresponding physical lumped parameter hinge model is presented, and general equations of motion are derived using D'Alembert's principle. Application to the static and dynamic analysis of a single complete fuel element includes the semiempirical modelling of the fuel-pin bundle by a homogeneous compressible medium. Most important conclusions are concerning the capability of the theoretical models, the failure modes and threshold load levels of single as well as clustered SNR-300 fuel elements and the safety relevant finding, that only limited deformations are found in the first row around the incident element. This shows in agreement with explosion test results that the structured and closely spaced fuel elements constitute an effective, inherent barrier against extreme dynamic loadings. (orig.) [de
Seismoelectric Effects based on Spectral-Element Method for Subsurface Fluid Characterization
Morency, C.
2017-12-01
Present approaches for subsurface imaging rely predominantly on seismic techniques, which alone do not capture fluid properties and related mechanisms. On the other hand, electromagnetic (EM) measurements add constraints on the fluid phase through electrical conductivity and permeability, but EM signals alone do not offer information of the solid structural properties. In the recent years, there have been many efforts to combine both seismic and EM data for exploration geophysics. The most popular approach is based on joint inversion of seismic and EM data, as decoupled phenomena, missing out the coupled nature of seismic and EM phenomena such as seismoeletric effects. Seismoelectric effects are related to pore fluid movements with respect to the solid grains. By analyzing coupled poroelastic seismic and EM signals, one can capture a pore scale behavior and access both structural and fluid properties.Here, we model the seismoelectric response by solving the governing equations derived by Pride and Garambois (1994), which correspond to Biot's poroelastic wave equations and Maxwell's electromagnetic wave equations coupled electrokinetically. We will show that these coupled wave equations can be numerically implemented by taking advantage of viscoelastic-electromagnetic mathematical equivalences. These equations will be solved using a spectral-element method (SEM). The SEM, in contrast to finite-element methods (FEM) uses high degree Lagrange polynomials. Not only does this allow the technique to handle complex geometries similarly to FEM, but it also retains exponential convergence and accuracy due to the use of high degree polynomials. Finally, we will discuss how this is a first step toward full coupled seismic-EM inversion to improve subsurface fluid characterization. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Spectral phase effects on nonlinear resonant photochemistry of 1,3-cyclohexadiene in solution
International Nuclear Information System (INIS)
Carroll, E.C.; Pearson, B.J.; Florean, A.C.; Bucksbaum, P.H.; Sension, Roseanne J.
2006-01-01
We have investigated the ring opening of 1,3-cyclohexadiene to form 1,3,5-cis-hexatriene (Z-HT) using optical pulse shaping to enhance multiphoton excitation. A closed-loop learning algorithm was used to search for an optimal spectral phase function, with the effectiveness or fitness of each optical pulse assessed using the UV absorption spectrum. The learning algorithm was able to identify pulses that increased the formation of Z-HT by as much as a factor of 2 and to identify pulse shapes that decreased solvent fragmentation while leaving the formation of Z-HT essentially unaffected. The highest yields of Z-HT did not occur for the highest peak intensity laser pulses. Rather, negative quadratic phase was identified as an important control parameter in the formation of Z-HT
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...
A study of flow patterns for staggered cylinders at low Reynolds number by spectral element method
Energy Technology Data Exchange (ETDEWEB)
Hsu, Li-Chieh; Chen, Chien-Lin; Ye, Jian-Zhi [National Yunlin University of Science and Technology, Taiwan (China)
2017-06-15
This study investigates the pattern of flow past two staggered array cylinders using the spectral element method by varying the distance between the cylinders and the angle of incidence (α) at low Reynolds numbers (Re = 100-800). Six flow patterns are identified as Shear layer reattachment (SLR), Induced separation (IS), Vortex impingement (VI), Synchronized vortex shedding (SVS), Vortex pairing and enveloping (VPE), and Vortex pairing splitting and enveloping (VPSE). These flow patterns can be transformed from one to another by changing the distance between the cylinders, the angle of incidence, or Re. SLR, IS and VI flow patterns appear in regimes with small angles of incidence (i.e., α ≤ 30° ) and hold only a single von Karman vortex shedding in a wake with one shedding frequency. SVS, VPE and VPSE flow patterns appear in regimes with large angles of incidence (i.e., 30° ≤ α ≤ 50° ) and present two synchronized von Karman vortices. Quantitative analyses and physical interpretation are also conducted to determine the generation mechanisms of the said flow patterns.
International Nuclear Information System (INIS)
Nahavandi, N.; Minuchehr, A.; Zolfaghari, A.; Abbasi, M.
2015-01-01
Highlights: • Powerful hp-SEM refinement approach for P N neutron transport equation has been presented. • The method provides great geometrical flexibility and lower computational cost. • There is a capability of using arbitrary high order and non uniform meshes. • Both posteriori and priori local error estimation approaches have been employed. • High accurate results are compared against other common adaptive and uniform grids. - Abstract: In this work we presented the adaptive hp-SEM approach which is obtained from the incorporation of Spectral Element Method (SEM) and adaptive hp refinement. The SEM nodal discretization and hp adaptive grid-refinement for even-parity Boltzmann neutron transport equation creates powerful grid refinement approach with high accuracy solutions. In this regard a computer code has been developed to solve multi-group neutron transport equation in one-dimensional geometry using even-parity transport theory. The spatial dependence of flux has been developed via SEM method with Lobatto orthogonal polynomial. Two commonly error estimation approaches, the posteriori and the priori has been implemented. The incorporation of SEM nodal discretization method and adaptive hp grid refinement leads to high accurate solutions. Coarser meshes efficiency and significant reduction of computer program runtime in comparison with other common refining methods and uniform meshing approaches is tested along several well-known transport benchmarks
Energy Technology Data Exchange (ETDEWEB)
Del Coz Diaz, J.J.; Rodriguez, A. Martin; Martinez-Luengas, A. Lozano; Biempica, C. Betegon [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Nieto, P.J. Garcia [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain)
2006-06-15
The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown. [Author].
Energy Technology Data Exchange (ETDEWEB)
Diaz del Coz, J.J. [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain)]. E-mail: juanjo@constru.uniovi.es; Nieto, P.J. Garcia [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain); Rodriguez, A. Martin [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Martinez-Luengas, A. Lozano [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Biempica, C. Betegon [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain)
2006-06-15
The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown.
International Nuclear Information System (INIS)
Diaz del Coz, J.J.; Nieto, P.J. Garcia; Rodriguez, A. Martin; Martinez-Luengas, A. Lozano; Biempica, C. Betegon
2006-01-01
The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown
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....
A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics
Brovont, Aaron D.
The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.
Nonlinear dynamics of laser systems with elements of a chaos: Advanced computational code
Buyadzhi, V. V.; Glushkov, A. V.; Khetselius, O. Yu; Kuznetsova, A. A.; Buyadzhi, A. A.; Prepelitsa, G. P.; Ternovsky, V. B.
2017-10-01
A general, uniform chaos-geometric computational approach to analysis, modelling and prediction of the non-linear dynamics of quantum and laser systems (laser and quantum generators system etc) with elements of the deterministic chaos is briefly presented. The approach is based on using the advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunov’s exponents analysis, and surrogate data method, prediction models etc There are firstly presented the numerical data on the topological and dynamical invariants (in particular, the correlation, embedding, Kaplan-York dimensions, the Lyapunov’s exponents, Kolmogorov’s entropy and other parameters) for laser system (the semiconductor GaAs/GaAlAs laser with a retarded feedback) dynamics in a chaotic and hyperchaotic regimes.
A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems
Gambolati, Giuseppe; Teatini, Pietro
1996-01-01
A new quasi three-dimensional finite element model of groundwater flow is developed for highly compressible multiaquifer systems where aquitard permeability and elastic storage are dependent on hydraulic drawdown. The model is solved by a block iterative strategy, which is naturally suggested by the geological structure of the porous medium and can be shown to be mathematically equivalent to a block Gauss-Seidel procedure. As such it can be generalized into a block overrelaxation procedure and greatly accelerated by the use of the optimum overrelaxation factor. Results for both linear and nonlinear multiaquifer systems emphasize the excellent computational performance of the model and indicate that convergence in leaky systems can be improved up to as much as one order of magnitude.
Energy Technology Data Exchange (ETDEWEB)
Johnson, J. M., E-mail: jared.johnson@ttu.edu; Reale, D. V.; Garcia, R. S.; Cravey, W. H.; Neuber, A. A.; Dickens, J. C.; Mankowski, J. J. [Center for Pulsed Power and Power Electronics Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, Texas 79409 (United States); Krile, J. T. [Department of Electromagnetics and Sensor Systems, Naval Surface Warfare Center - Dahlgren Division, Dahlgren, Virginia 22448 (United States)
2016-05-15
In this paper, a solid-state four element array gyromagnetic nonlinear transmission line high power microwave system is presented as well as a detailed description of its subsystems and general output capabilities. This frequency agile S-band source is easily adjusted from 2-4 GHz by way of a DC driven biasing magnetic field and is capable of generating electric fields of 7.8 kV/m at 10 m correlating to 4.2 MW of RF power with pulse repetition frequencies up to 1 kHz. Beam steering of the array at angles of ±16.7° is also demonstrated, and the associated general radiation pattern is detailed.
Spectral-element Seismic Wave Propagation on CUDA/OpenCL Hardware Accelerators
Peter, D. B.; Videau, B.; Pouget, K.; Komatitsch, D.
2015-12-01
Seismic wave propagation codes are essential tools to investigate a variety of wave phenomena in the Earth. Furthermore, they can now be used for seismic full-waveform inversions in regional- and global-scale adjoint tomography. Although these seismic wave propagation solvers are crucial ingredients to improve the resolution of tomographic images to answer important questions about the nature of Earth's internal processes and subsurface structure, their practical application is often limited due to high computational costs. They thus need high-performance computing (HPC) facilities to improving the current state of knowledge. At present, numerous large HPC systems embed many-core architectures such as graphics processing units (GPUs) to enhance numerical performance. Such hardware accelerators can be programmed using either the CUDA programming environment or the OpenCL language standard. CUDA software development targets NVIDIA graphic cards while OpenCL was adopted by additional hardware accelerators, like e.g. AMD graphic cards, ARM-based processors as well as Intel Xeon Phi coprocessors. For seismic wave propagation simulations using the open-source spectral-element code package SPECFEM3D_GLOBE, we incorporated an automatic source-to-source code generation tool (BOAST) which allows us to use meta-programming of all computational kernels for forward and adjoint runs. Using our BOAST kernels, we generate optimized source code for both CUDA and OpenCL languages within the source code package. Thus, seismic wave simulations are able now to fully utilize CUDA and OpenCL hardware accelerators. We show benchmarks of forward seismic wave propagation simulations using SPECFEM3D_GLOBE on CUDA/OpenCL GPUs, validating results and comparing performances for different simulations and hardware usages.
Peter, Daniel; Videau, Brice; Pouget, Kevin; Komatitsch, Dimitri
2015-04-01
Improving the resolution of tomographic images is crucial to answer important questions on the nature of Earth's subsurface structure and internal processes. Seismic tomography is the most prominent approach where seismic signals from ground-motion records are used to infer physical properties of internal structures such as compressional- and shear-wave speeds, anisotropy and attenuation. Recent advances in regional- and global-scale seismic inversions move towards full-waveform inversions which require accurate simulations of seismic wave propagation in complex 3D media, providing access to the full 3D seismic wavefields. However, these numerical simulations are computationally very expensive and need high-performance computing (HPC) facilities for further improving the current state of knowledge. During recent years, many-core architectures such as graphics processing units (GPUs) have been added to available large HPC systems. Such GPU-accelerated computing together with advances in multi-core central processing units (CPUs) can greatly accelerate scientific applications. There are mainly two possible choices of language support for GPU cards, the CUDA programming environment and OpenCL language standard. CUDA software development targets NVIDIA graphic cards while OpenCL was adopted mainly by AMD graphic cards. In order to employ such hardware accelerators for seismic wave propagation simulations, we incorporated a code generation tool BOAST into an existing spectral-element code package SPECFEM3D_GLOBE. This allows us to use meta-programming of computational kernels and generate optimized source code for both CUDA and OpenCL languages, running simulations on either CUDA or OpenCL hardware accelerators. We show here applications of forward and adjoint seismic wave propagation on CUDA/OpenCL GPUs, validating results and comparing performances for different simulations and hardware usages.
Nonlinear finite element analysis of liquid sloshing in complex vehicle motion scenarios
Nicolsen, Brynne; Wang, Liang; Shabana, Ahmed
2017-09-01
The objective of this investigation is to develop a new total Lagrangian continuum-based liquid sloshing model that can be systematically integrated with multibody system (MBS) algorithms in order to allow for studying complex motion scenarios. The new approach allows for accurately capturing the effect of the sloshing forces during curve negotiation, rapid lane change, and accelerating and braking scenarios. In these motion scenarios, the liquid experiences large displacements and significant changes in shape that can be captured effectively using the finite element (FE) absolute nodal coordinate formulation (ANCF). ANCF elements are used in this investigation to describe complex mesh geometries, to capture the change in inertia due to the change in the fluid shape, and to accurately calculate the centrifugal forces, which for flexible bodies do not take the simple form used in rigid body dynamics. A penalty formulation is used to define the contact between the rigid tank walls and the fluid. A fully nonlinear MBS truck model that includes a suspension system and Pacejka's brush tire model is developed. Specified motion trajectories are used to examine the vehicle dynamics in three different scenarios - deceleration during straight-line motion, rapid lane change, and curve negotiation. It is demonstrated that the liquid sloshing changes the contact forces between the tires and the ground - increasing the forces on certain wheels and decreasing the forces on other wheels. In cases of extreme sloshing, this dynamic behavior can negatively impact the vehicle stability by increasing the possibility of wheel lift and vehicle rollover.
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
Energy Technology Data Exchange (ETDEWEB)
Kirsanov, N. Yu.; Latukhina, N. V., E-mail: natalat@yandex.ru; Lizunkova, D. A.; Rogozhina, G. A. [Samara National Research University (Russian Federation); Stepikhova, M. V. [Russian Academy of Sciences, Institute for Physics of Microstructures (Russian Federation)
2017-03-15
The spectral characteristics of the specular reflectance, photosensitivity, and photoluminescence (PL) of multilayer structures based on porous silicon with rare-earth-element (REE) ions are investigated. It is shown that the photosensitivity of these structures in the wavelength range of 0.4–1.0 μm is higher than in structures free of REEs. The structures with Er{sup 3+} ions exhibit a luminescence response at room temperature in the spectral range from 1.1 to 1.7 μm. The PL spectrum of the erbium impurity is characterized by a fine line structure, which is determined by the splitting of the {sup 4}I{sub 15/2} multiplet of the Er{sup 3+} ion. It is shown that the structures with a porous layer on the working surface have a much lower reflectance in the entire spectral range under study (0.2–1.0 μm).
Antoine, Xavier; Levitt, Antoine; Tang, Qinglin
2017-08-01
We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial discretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii Equation (GPE). We first start by reviewing the classical gradient flow (also known as imaginary time (IMT)) method which considers the problem from the PDE standpoint, leading to numerically solve a dissipative equation. Based on this IMT equation, we analyze the forward Euler (FE), Crank-Nicolson (CN) and the classical backward Euler (BE) schemes for linear problems and recognize classical power iterations, allowing us to derive convergence rates. By considering the alternative point of view of minimization problems, we propose the preconditioned steepest descent (PSD) and conjugate gradient (PCG) methods for the GS computation of the GPE. We investigate the choice of the preconditioner, which plays a key role in the acceleration of the convergence process. The performance of the new algorithms is tested in 1D, 2D and 3D. We conclude that the PCG method outperforms all the previous methods, most particularly for 2D and 3D fast rotating BECs, while being simple to implement.
Sabeerali, C. T.; Ajayamohan, R. S.; Giannakis, Dimitrios; Majda, Andrew J.
2017-11-01
An improved index for real-time monitoring and forecast verification of monsoon intraseasonal oscillations (MISOs) is introduced using the recently developed nonlinear Laplacian spectral analysis (NLSA) technique. Using NLSA, a hierarchy of Laplace-Beltrami (LB) eigenfunctions are extracted from unfiltered daily rainfall data from the Global Precipitation Climatology Project over the south Asian monsoon region. Two modes representing the full life cycle of the northeastward-propagating boreal summer MISO are identified from the hierarchy of LB eigenfunctions. These modes have a number of advantages over MISO modes extracted via extended empirical orthogonal function analysis including higher memory and predictability, stronger amplitude and higher fractional explained variance over the western Pacific, Western Ghats, and adjoining Arabian Sea regions, and more realistic representation of the regional heat sources over the Indian and Pacific Oceans. Real-time prediction of NLSA-derived MISO indices is demonstrated via extended-range hindcasts based on NCEP Coupled Forecast System version 2 operational output. It is shown that in these hindcasts the NLSA MISO indices remain predictable out to ˜3 weeks.
Quasi-static earthquake cycle simulation based on nonlinear viscoelastic finite element analyses
Agata, R.; Ichimura, T.; Hyodo, M.; Barbot, S.; Hori, T.
2017-12-01
To explain earthquake generation processes, simulation methods of earthquake cycles have been studied. For such simulations, the combination of the rate- and state-dependent friction law at the fault plane and the boundary integral method based on Green's function in an elastic half space is widely used (e.g. Hori 2009; Barbot et al. 2012). In this approach, stress change around the fault plane due to crustal deformation can be computed analytically, while the effects of complex physics such as mantle rheology and gravity are generally not taken into account. To consider such effects, we seek to develop an earthquake cycle simulation combining crustal deformation computation based on the finite element (FE) method with the rate- and state-dependent friction law. Since the drawback of this approach is the computational cost associated with obtaining numerical solutions, we adopt a recently developed fast and scalable FE solver (Ichimura et al. 2016), which assumes use of supercomputers, to solve the problem in a realistic time. As in the previous approach, we solve the governing equations consisting of the rate- and state-dependent friction law. In solving the equations, we compute stress changes along the fault plane due to crustal deformation using FE simulation, instead of computing them by superimposing slip response function as in the previous approach. In stress change computation, we take into account nonlinear viscoelastic deformation in the asthenosphere. In the presentation, we will show simulation results in a normative three-dimensional problem, where a circular-shaped velocity-weakening area is set in a square-shaped fault plane. The results with and without nonlinear viscosity in the asthenosphere will be compared. We also plan to apply the developed code to simulate the post-earthquake deformation of a megathrust earthquake, such as the 2011 Tohoku earthquake. Acknowledgment: The results were obtained using the K computer at the RIKEN (Proposal number
International Nuclear Information System (INIS)
Lasche, G.P.; Coldwell, R.L.
2001-01-01
and of the sources in the spectrum. (To quantify absolute activities, of course, detector sensitivity, time, and distance must be known). However, with the inclusion of these additional parameters, the values of all the coefficients become strongly dependent upon each other value in a highly nonlinear way, and the solution becomes much more difficult. In the continuum fit in which the knots and coefficients of the Splines are optimized, the optimization problem is highly nonlinear from the start. The greatest challenge in this approach lies in finding the true minimum of chi-square on a multidimensional surface that may contain many local minima. Also, the problems with inversion of large sparse matrices must be overcome. These problems were solved by Coldwell with the development of the RobFit code. Efficient convergence to the vector for the true minimum on the multidimensional chi-square surface is accomplished with Newton-Raphson techniques used to estimate the best Marquardt parameter to add to the diagonal elements of the inversion matrix for the next step in the search. Stability with large, sparse matrix inversion is achieved with Cholesky minimization and numerical techniques to remedy apparent singularities resulting from numerical truncation. Although it requires knowledgeable interactive operation for best results and is computationally intensive, nuclear spectral analysis with nonlinear robust fitting has been shown to be capable of exceptional sensitivity in detecting weak radionuclides in the presence of strong interference and in noisy spectra, sparse spectra, and low-resolution spectra. This increased sensitivity is due to the simultaneous optimization of all the data for all the free variables of the analysis and the iterative construction of a well-determined continuum spanning the entire spectrum. (authors)
DEFF Research Database (Denmark)
Larsen, Jon Steffen; Santos, Ilmar
2015-01-01
An efficient finite element scheme for solving the non-linear Reynolds equation for compressible fluid coupled to compliant structures is presented. The method is general and fast and can be used in the analysis of airfoil bearings with simplified or complex foil structure models. To illustrate...
Bazhenov V.A.; Sacharov A.S.; Guliar A. I.; Pyskunov S.O.; Maksymiuk Y.V.
2014-01-01
Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.
FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE NONLINEAR CALCULATIONS OF PLATES AND SHELLS
Directory of Open Access Journals (Sweden)
Bazhenov V.A.
2014-06-01
Full Text Available Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.
Energy Technology Data Exchange (ETDEWEB)
Li, Mao; Qiu, Zihua; Liang, Chunlei; Sprague, Michael; Xu, Min
2017-01-13
In the present study, a new spectral difference (SD) method is developed for viscous flows on meshes with a mixture of triangular and quadrilateral elements. The standard SD method for triangular elements, which employs Lagrangian interpolating functions for fluxes, is not stable when the designed accuracy of spatial discretization is third-order or higher. Unlike the standard SD method, the method examined here uses vector interpolating functions in the Raviart-Thomas (RT) spaces to construct continuous flux functions on reference elements. Studies have been performed for 2D wave equation and Euler equa- tions. Our present results demonstrated that the SDRT method is stable and high-order accurate for a number of test problems by using triangular-, quadrilateral-, and mixed- element meshes.
DEFF Research Database (Denmark)
Damkilde, Lars; Pedersen, Ronnie
2012-01-01
This paper describes a new triangular plane element which can be considered as a linear strain triangular element (LST) extended with incompatible displacement modes. The extended element will have a full cubic interpolation of strains and stresses. The extended LST-element is connected with other...... elements similar to the LST-element i.e. through three corner nodes and three mid-side nodes. The incompatible modes are associated with two displacement gradients at each mid-side node and displacements in the central node. The element passes the patch test and converges to the exact solution. The element...... often show a very slow convergence, and the numerical solutions will in general overestimate the bearing capacity and underestimate the displacements. The examples show that the extended incompatible element behaves much better than the corresponding compatible elements especially for coarse meshes....
Karaoǧlu, Haydar; Romanowicz, Barbara
2018-06-01
We present a global upper-mantle shear wave attenuation model that is built through a hybrid full-waveform inversion algorithm applied to long-period waveforms, using the spectral element method for wavefield computations. Our inversion strategy is based on an iterative approach that involves the inversion for successive updates in the attenuation parameter (δ Q^{-1}_μ) and elastic parameters (isotropic velocity VS, and radial anisotropy parameter ξ) through a Gauss-Newton-type optimization scheme that employs envelope- and waveform-type misfit functionals for the two steps, respectively. We also include source and receiver terms in the inversion steps for attenuation structure. We conducted a total of eight iterations (six for attenuation and two for elastic structure), and one inversion for updates to source parameters. The starting model included the elastic part of the relatively high-resolution 3-D whole mantle seismic velocity model, SEMUCB-WM1, which served to account for elastic focusing effects. The data set is a subset of the three-component surface waveform data set, filtered between 400 and 60 s, that contributed to the construction of the whole-mantle tomographic model SEMUCB-WM1. We applied strict selection criteria to this data set for the attenuation iteration steps, and investigated the effect of attenuation crustal structure on the retrieved mantle attenuation structure. While a constant 1-D Qμ model with a constant value of 165 throughout the upper mantle was used as starting model for attenuation inversion, we were able to recover, in depth extent and strength, the high-attenuation zone present in the depth range 80-200 km. The final 3-D model, SEMUCB-UMQ, shows strong correlation with tectonic features down to 200-250 km depth, with low attenuation beneath the cratons, stable parts of continents and regions of old oceanic crust, and high attenuation along mid-ocean ridges and backarcs. Below 250 km, we observe strong attenuation in the
Directory of Open Access Journals (Sweden)
Teeraphot Supaviriyakit
2017-11-01
Full Text Available This paper presents a nonlinear finite element analysis of non-seismically detailed RC beam column connections under reversed cyclic load. The test of half-scale nonductile reinforced concrete beam-column joints was conducted. The tested specimens represented those of the actual mid-rise reinforced concrete frame buildings designed according to the non-seismic provisions of the ACI building code. The test results show that specimens representing small and medium column tributary area failed in brittle joint shear while specimen representing large column tributary area failed by ductile flexure though no ductile reinforcement details were provided. The nonlinear finite element analysis was applied to simulate the behavior of the specimens. The finite element analysis employs the smeared crack approach for modeling beam, column and joint, and employs the discrete crack approach for modeling the interface between beam and joint face. The nonlinear constitutive models of reinforced concrete elements consist of coupled tension-compression model to model normal force orthogonal and parallel to the crack and shear transfer model to capture the shear sliding mechanism. The FEM shows good comparison with test results in terms of load-displacement relations, hysteretic loops, cracking process and the failure mode of the tested specimens. The finite element analysis clarifies that the joint shear failure was caused by the collapse of principal diagonal concrete strut.
Kong, Liang; Gu, Zexu; Li, Tao; Wu, Junjie; Hu, Kaijin; Liu, Yanpu; Zhou, Hongzhi; Liu, Baolin
2009-01-01
A nonlinear finite element method was applied to examine the effects of implant diameter and length on the maximum von Mises stresses in the jaw, and to evaluate the maximum displacement of the implant-abutment complex in immediate-loading models. The implant diameter (D) ranged from 3.0 to 5.0 mm and implant length (L) ranged from 6.0 to 16.0 mm. The results showed that the maximum von Mises stress in cortical bone was decreased by 65.8% under a buccolingual load with an increase in D. In cancellous bone, it was decreased by 71.5% under an axial load with an increase in L. The maximum displacement in the implant-abutment complex decreased by 64.8% under a buccolingual load with an increase in D. The implant was found to be more sensitive to L than to D under axial loads, while D played a more important role in enhancing its stability under buccolingual loads. When D exceeded 4.0 mm and L exceeded 11.0 mm, both minimum stress and displacement were obtained. Therefore, these dimensions were the optimal biomechanical selections for immediate-loading implants in type B/2 bone.
Explicit nonlinear finite element geometric analysis of parabolic leaf springs under various loads.
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.
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.
Khan, Sabeel M.; Sunny, D. A.; Aqeel, M.
2017-09-01
Nonlinear dynamical systems and their solutions are very sensitive to initial conditions and therefore need to be approximated carefully. In this article, we present and analyze nonlinear solution characteristics of the periodically forced Chen system with the application of a variational method based on the concept of finite time-elements. Our approach is based on the discretization of physical time space into finite elements where each time-element is mapped to a natural time space. The solution of the system is then determined in natural time space using a set of suitable basis functions. The numerical algorithm is presented and implemented to compute and analyze nonlinear behavior at different time-step sizes. The obtained results show an excellent agreement with the classical RK-4 and RK-5 methods. The accuracy and convergence of the method is shown by comparing numerically computed results with the exact solution for a test problem. The presented method has shown a great potential in dealing with the solutions of nonlinear dynamical systems and thus can be utilized in delineating different features and characteristics of their solutions.
International Nuclear Information System (INIS)
Saitoh, Ayumu; Matsui, Nobuyuki; Itoh, Taku; Kamitani, Atsushi; Nakamura, Hiroaki
2011-01-01
A new method has been proposed for implementing essential boundary conditions to the Element-Free Galerkin Method (EFGM) without using the Lagrange multiplier. Furthermore, the performance of the proposed method has been investigated for a nonlinear Poisson problem. The results of computations show that, as interpolation functions become closer to delta functions, the accuracy of the solution is improved on the boundary. In addition, the accuracy of the proposed method is higher than that of the conventional EFGM. Therefore, it might be concluded that the proposed method is useful for solving the nonlinear Poisson problem. (author)
Aglitskiy, Yefim; Weaver, J. L.; Karasik, M.; Serlin, V.; Obenschain, S. P.; Ralchenko, Yu.
2014-10-01
The spectra of multi-charged ions of Hf, Ta, W, Pt, Au and Bi have been studied on Nike krypton-fluoride laser facility with the help of two kinds of X-ray spectrometers. First, survey instrument covering a spectral range from 0.5 to 19.5 angstroms which allows simultaneous observation of both M- and N- spectra of above mentioned elements with high spectral resolution. Second, an imaging spectrometer with interchangeable spherically bent Quartz crystals that added higher efficiency, higher spectral resolution and high spatial resolution to the qualities of the former one. Multiple spectral lines with X-ray energies as high as 4 keV that belong to the isoelectronic sequences of Fe, Co, Ni, Cu and Zn were identified with the help of NOMAD package developed by Dr. Yu. Ralchenko and colleagues. In our continuous effort to support DOE-NNSA's inertial fusion program, this campaign covered a wide range of plasma conditions that result in production of relatively energetic X-rays. Work supported by the US DOE/NNSA.
Stability Estimates for h-p Spectral Element Methods for Elliptic Problems
Dutt, Pravir; Tomar, S.K.; Kumar, B.V. Rathish
2002-01-01
In a series of papers of which this is the first we study how to solve elliptic problems on polygonal domains using spectral methods on parallel computers. To overcome the singularities that arise in a neighborhood of the corners we use a geometrical mesh. With this mesh we seek a solution which
Integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell
Vakhnenko, Oleksiy O.
2018-05-01
Developing the idea of increasing the number of structural elements in the unit cell of a quasi-one-dimensional lattice as applied to the semi-discrete integrable systems of nonlinear Schrödinger type, we construct the zero-curvature representation for the general integrable nonlinear system on a lattice with three structural elements in the unit cell. The integrability of the obtained general system permits to find explicitly a number of local conservation laws responsible for the main features of system dynamics and in particular for the so-called natural constraints separating the field variables into the basic and the concomitant ones. Thus, considering the reduction to the semi-discrete integrable system of nonlinear Schrödinger type, we revealed the essentially nontrivial impact of concomitant fields on the Poisson structure and on the whole Hamiltonian formulation of system dynamics caused by the nonzero background values of these fields. On the other hand, the zero-curvature representation of a general nonlinear system serves as an indispensable key to the dressing procedure of system integration based upon the Darboux transformation of the auxiliary linear problem and the implicit Bäcklund transformation of field variables. Due to the symmetries inherent to the six-component semi-discrete integrable nonlinear Schrödinger system with attractive-type nonlinearities, the Darboux-Bäcklund dressing scheme is shown to be simplified considerably, giving rise to the appropriately parameterized multi-component soliton solution consisting of six basic and four concomitant components.
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.
International Nuclear Information System (INIS)
Biffle, J.H.
1991-01-01
1 - Description of program or function: JAC is a two-dimensional finite element program for solving large deformation, temperature dependent, quasi-static mechanics problems with the nonlinear conjugate gradient (CG) technique. Either plane strain or axisymmetric geometry may be used with material descriptions which include temperature dependent elastic-plastic, temperature dependent secondary creep, and isothermal soil models. The nonlinear effects examined include material and geometric nonlinearities due to large rotations, large strains, and surface which slide relative to one another. JAC is vectorized to perform efficiently on the Cray1 computer. A restart capability is included. 2 - Method of solution: The nonlinear conjugate gradient method is employed in a two-dimensional plane strain or axisymmetric setting with various techniques for accelerating convergence. Sliding interface conditions are also implemented. A four-node Lagrangian uniform strain element is used with orthogonal hourglass viscosity to control the zero energy modes. Three sets of continuum equations are needed - kinematic statements, constitutive equations, and equations of equilibrium - to describe the deformed configuration of the body. 3 - Restrictions on the complexity of the problem - Maxima of: 10 load and solution control functions, 4 materials. The strain rate is assumed constant over a time interval. Current large rotation theory is applicable to a maximum shear strain of 1.0. JAC should be used with caution for large shear strains. Problem size is limited only by available memory
Directory of Open Access Journals (Sweden)
Vladimir P. Agapov
2017-01-01
Full Text Available Abstract. Objectives Modern building codes prescribe the calculation of building structures taking into account the nonlinearity of deformation. To achieve this goal, the task is to develop a methodology for calculating prestressed reinforced concrete beams, taking into account physical and geometric nonlinearity. Methods The methodology is based on nonlinear calculation algorithms implemented and tested in the computation complex PRINS (a program for calculating engineering constructions for other types of construction. As a tool for solving this problem, the finite element method is used. Non-linear calculation of constructions is carried out by the PRINS computational complex using the stepwise iterative method. In this case, an equation is constructed and solved at the loading step, using modified Lagrangian coordinates. Results The basic formulas necessary for both the formation and the solution of a system of nonlinear algebraic equations by the stepwise iteration method are given, taking into account the loading, unloading and possible additional loading. A method for simulating prestressing is described by setting the temperature action on the reinforcement and stressing steel rod. Different approaches to accounting for physical and geometric nonlinearity of reinforced concrete beam rods are considered. A calculation example of a flat beam is given, in which the behaviour of the beam is analysed at various stages of its loading up to destruction. Conclusion A program is developed for the calculation of flat and spatially reinforced concrete beams taking into account the nonlinearity of deformation. The program is adapted to the computational complex PRINS and as part of this complex is available to a wide range of engineering, scientific and technical specialists.
International Nuclear Information System (INIS)
Wang, Lin; Liu, Xiongwei; Renevier, Nathalie; Stables, Matthew; Hall, George M.
2014-01-01
Due to the increasing size and flexibility of large wind turbine blades, accurate and reliable aeroelastic modelling is playing an important role for the design of large wind turbines. Most existing aeroelastic models are linear models based on assumption of small blade deflections. This assumption is not valid anymore for very flexible blade design because such blades often experience large deflections. In this paper, a novel nonlinear aeroelastic model for large wind turbine blades has been developed by combining BEM (blade element momentum) theory and mixed-form formulation of GEBT (geometrically exact beam theory). The nonlinear aeroelastic model takes account of large blade deflections and thus greatly improves the accuracy of aeroelastic analysis of wind turbine blades. The nonlinear aeroelastic model is implemented in COMSOL Multiphysics and validated with a series of benchmark calculation tests. The results show that good agreement is achieved when compared with experimental data, and its capability of handling large deflections is demonstrated. Finally the nonlinear aeroelastic model is applied to aeroelastic modelling of the parked WindPACT 1.5 MW baseline wind turbine, and reduced flapwise deflection from the nonlinear aeroelastic model is observed compared to the linear aeroelastic code FAST (Fatigue, Aerodynamics, Structures, and Turbulence). - Highlights: • A novel nonlinear aeroelastic model for wind turbine blades is developed. • The model takes account of large blade deflections and geometric nonlinearities. • The model is reliable and efficient for aeroelastic modelling of wind turbine blades. • The accuracy of the model is verified by a series of benchmark calculation tests. • The model provides more realistic aeroelastic modelling than FAST (Fatigue, Aerodynamics, Structures, and Turbulence)
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.
Huang, Xin; Yin, Chang-Chun; Cao, Xiao-Yue; Liu, Yun-He; Zhang, Bo; Cai, Jing
2017-09-01
The airborne electromagnetic (AEM) method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element (SE) method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell's equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic
Rudianto, Indra; Sudarmaji
2018-04-01
We present an implementation of the spectral-element method for simulation of two-dimensional elastic wave propagation in fully heterogeneous media. We have incorporated most of realistic geological features in the model, including surface topography, curved layer interfaces, and 2-D wave-speed heterogeneity. To accommodate such complexity, we use an unstructured quadrilateral meshing technique. Simulation was performed on a GPU cluster, which consists of 24 core processors Intel Xeon CPU and 4 NVIDIA Quadro graphics cards using CUDA and MPI implementation. We speed up the computation by a factor of about 5 compared to MPI only, and by a factor of about 40 compared to Serial implementation.
Nguyen, Vu-Hieu; Naili, Salah
2012-08-01
This paper deals with the modeling of guided waves propagation in in vivo cortical long bone, which is known to be anisotropic medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic material by using Biot's theory formulated in high frequency domain. A hybrid spectral/finite element formulation has been developed to find the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed in two fluid halfspaces. The numerical technique is based on a combined Laplace-Fourier transform, which allows to obtain a reduced dimension problem in the frequency-wavenumber domain. In the spectral domain, as radiation conditions representing infinite fluid halfspaces may be exactly introduced, only the heterogeneous solid layer needs to be analyzed by using finite element method. Several numerical tests are presented showing very good performance of the proposed procedure. A preliminary study on the first arrived signal velocities computed by using equivalent elastic and poroelastic models will be presented. Copyright © 2012 John Wiley & Sons, Ltd.
Smith, J. A.; Peter, D. B.; Tromp, J.; Komatitsch, D.; Lefebvre, M. P.
2015-12-01
We present both SPECFEM3D_Cartesian and SPECFEM3D_GLOBE open-source codes, representing high-performance numerical wave solvers simulating seismic wave propagation for local-, regional-, and global-scale application. These codes are suitable for both forward propagation in complex media and tomographic imaging. Both solvers compute highly accurate seismic wave fields using the continuous Galerkin spectral-element method on unstructured meshes. Lateral variations in compressional- and shear-wave speeds, density, as well as 3D attenuation Q models, topography and fluid-solid coupling are all readily included in both codes. For global simulations, effects due to rotation, ellipticity, the oceans, 3D crustal models, and self-gravitation are additionally included. Both packages provide forward and adjoint functionality suitable for adjoint tomography on high-performance computing architectures. We highlight the most recent release of the global version which includes improved performance, simultaneous MPI runs, OpenCL and CUDA support via an automatic source-to-source transformation library (BOAST), parallel I/O readers and writers for databases using ADIOS and seismograms using the recently developed Adaptable Seismic Data Format (ASDF) with built-in provenance. This makes our spectral-element solvers current state-of-the-art, open-source community codes for high-performance seismic wave propagation on arbitrarily complex 3D models. Together with these solvers, we provide full-waveform inversion tools to image the Earth's interior at unprecedented resolution.
Energy Technology Data Exchange (ETDEWEB)
Griffith, Daniel Todd; Segalman, Daniel Joseph
2006-10-01
A technique published in SAND Report 2006-1789 ''Model Reduction of Systems with Localized Nonlinearities'' is illustrated in two problems of finite element structural dynamics. That technique, called here the Method of Locally Discontinuous Basis Vectors (LDBV), was devised to address the peculiar difficulties of model reduction of systems having spatially localized nonlinearities. It's illustration here is on two problems of different geometric and dynamic complexity, but each containing localized interface nonlinearities represented by constitutive models for bolted joint behavior. As illustrated on simple problems in the earlier SAND report, the LDBV Method not only affords reduction in size of the nonlinear systems of equations that must be solved, but it also facilitates the use of much larger time steps on problems of joint macro-slip than would be possible otherwise. These benefits are more dramatic for the larger problems illustrated here. The work of both the original SAND report and this one were funded by the LDRD program at Sandia National Laboratories.
International Nuclear Information System (INIS)
Maheshwari, B.K.; Truman, K.Z.; El Naggar, M.H.; Gould, P.L.
2004-01-01
The effects of material nonlinearity of soil and separation at the soil-pile interface on the dynamic behaviour of a single pile and pile groups are investigated. An advanced plasticity-based soil model, hierarchical single surface (HiSS), is incorporated in the finite element formulation. To simulate radiation effects, proper boundary conditions are used. The model and algorithm are verified with analytical results that are available for elastic and elastoplastic soil models. Analyses are performed for seismic excitation and for the load applied on the pile cap. For seismic analysis, both harmonic and transient excitations are considered. For loading on the pile cap, dynamic stiffness of the soil-pile system is derived and the effect of nonlinearity is investigated. The effects of spacing between piles are investigated, and it was found that the effect of soil nonlinearity on the seismic response is very much dependent on the frequency of excitation. For the loading on a pile cap, the nonlinearity increases the response for most of the frequencies of excitation while decreasing the dynamic stiffness of the soil-pile system. (author)
Xiong, S. Y.; Yang, J. G.; Zhuang, J.
2011-10-01
In this work, we use nonlinear spectral imaging based on two-photon excited fluorescence (TPEF) and second harmonic generation (SHG) for analyzing the morphology of collagen and elastin and their biochemical variations in basal cell carcinoma (BCC), squamous cell carcinoma (SCC) and normal skin tissue. It was found in this work that there existed apparent differences among BCC, SCC and normal skin in terms of their thickness of the keratin and epithelial layers, their size of elastic fibers, as well as their distribution and spectral characteristics of collagen. These differences can potentially be used to distinguish BCC and SCC from normal skin, and to discriminate between BCC and SCC, as well as to evaluate treatment responses.
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.
Magnetic modeling of a Linear Synchronous Machine with the spectral element method
Curti, M.; Paulides, J.J.H.; Lomonova, E.
2017-01-01
The field calculus for electrical machines is realized solving subdomain problems. Most often, the latter are solved using either finite element analysis or the semi-analytical solution of a Laplace or Poisson equation obtained by separation of variables. The first option can capture complex
Magnetic modeling of a Linear Synchronous Machine with the spectral element method
Curti, M.; Paulides, J.J.H.; Lomonova, E.
2017-01-01
The field calculus for electrical machines (EMs) is realized solving subdomain problems. Most often, the latter are solved using either finite element analysis (FEA) or the semi-analytical solution of a Laplace or Poisson equation obtained by separation of variables. The first option can capture
International Nuclear Information System (INIS)
Pontaza, J.P.; Reddy, J.N.
2004-01-01
We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier-Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C 0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form. Spectral convergence of the L 2 least-squares functional and L 2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least
Directory of Open Access Journals (Sweden)
Djillali Amar Bouzid
2018-04-01
Full Text Available A nonlinear finite element model is developed to examine the lateral behaviors of monopiles, which support offshore wind turbines (OWTs chosen from five different offshore wind farms in Europe. The simulation is using this model to accurately estimate the natural frequency of these slender structures, as a function of the interaction of the foundations with the subsoil. After a brief introduction to the wind power energy as a reliable alternative in comparison to fossil fuel, the paper focuses on concept of natural frequency as a primary indicator in designing the foundations of OWTs. Then the range of natural frequencies is provided for a safe design purpose. Next, an analytical expression of an OWT natural frequency is presented as a function of soil-monopile interaction through monopile head springs characterized by lateral stiffness KL, rotational stiffness KR and cross-coupling stiffness KLR, of which the differences are discussed. The nonlinear pseudo three-dimensional finite element vertical slices model has been used to analyze the lateral behaviors of monopiles supporting the OWTs of different wind farm sites considered. Through the monopiles head movements (displacements and rotations, the values of KL, KR and KLR were obtained and substituted in the analytical expression of natural frequency for comparison. The comparison results between computed and measured natural frequencies showed an excellent agreement for most cases. This confirms the convenience of the finite element model used for the accurate estimation of the monopile head stiffness. Keywords: Nonlinear finite element analysis, Vertical slices model, Monopiles under horizontal loading, Natural frequency, Monopile head stiffness, Offshore wind turbines (OWTs
Conjugation of fiber-coupled wide-band light sources and acousto-optical spectral elements
Machikhin, Alexander; Batshev, Vladislav; Polschikova, Olga; Khokhlov, Demid; Pozhar, Vitold; Gorevoy, Alexey
2017-12-01
Endoscopic instrumentation is widely used for diagnostics and surgery. The imaging systems, which provide the hyperspectral information of the tissues accessible by endoscopes, are particularly interesting and promising for in vivo photoluminescence diagnostics and therapy of tumour and inflammatory diseases. To add the spectral imaging feature to standard video endoscopes, we propose to implement acousto-optical (AO) filtration of wide-band illumination of incandescent-lamp-based light sources. To collect maximum light and direct it to the fiber-optic light guide inside the endoscopic probe, we have developed and tested the optical system for coupling the light source, the acousto-optical tunable filter (AOTF) and the light guide. The system is compact and compatible with the standard endoscopic components.
Angela Mihai, L.; Goriely, Alain
2013-01-01
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
Harmonic balance finite element method applications in nonlinear electromagnetics and power systems
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...
Single nano-hole as a new effective nonlinear element for third-harmonic generation
International Nuclear Information System (INIS)
Melentiev, P N; Konstantinova, T V; Afanasiev, A E; Balykin, V I; Kuzin, A A; Baturin, A S; Tausenev, A V; Konyaschenko, A V
2013-01-01
In this letter, we report on a particularly strong optical nonlinearity at the nanometer scale in aluminum. A strong optical nonlinearity of the third order was demonstrated on a single nanoslit. Single nanoslits of different aspect ratio were excited by a laser pulse (120 fs) at the wavelength 1.5 μm, leading predominantly to third-harmonic generation (THG). It has been shown that strong surface plasmon resonance in a nanoslit allows the realization of an effective nanolocalized source of third-harmonic radiation. We show also that a nanoslit in a metal film has a significant advantage in nonlinear processes over its Babinet complementary nanostructure (nanorod): the effective abstraction of heat in a film with a slit makes it possible to use much higher laser radiation intensities. (letter)
Single nano-hole as a new effective nonlinear element for third-harmonic generation
Melentiev, P. N.; Konstantinova, T. V.; Afanasiev, A. E.; Kuzin, A. A.; Baturin, A. S.; Tausenev, A. V.; Konyaschenko, A. V.; Balykin, V. I.
2013-07-01
In this letter, we report on a particularly strong optical nonlinearity at the nanometer scale in aluminum. A strong optical nonlinearity of the third order was demonstrated on a single nanoslit. Single nanoslits of different aspect ratio were excited by a laser pulse (120 fs) at the wavelength 1.5 μm, leading predominantly to third-harmonic generation (THG). It has been shown that strong surface plasmon resonance in a nanoslit allows the realization of an effective nanolocalized source of third-harmonic radiation. We show also that a nanoslit in a metal film has a significant advantage in nonlinear processes over its Babinet complementary nanostructure (nanorod): the effective abstraction of heat in a film with a slit makes it possible to use much higher laser radiation intensities.
Directory of Open Access Journals (Sweden)
Nassim Kernou
2018-01-01
Full Text Available A rational three-dimensional nonlinear finite element model (NLFEAS is used for evaluating the behavior of high strength concrete slabs under monotonic transverse load. The non-linear equations of equilibrium have been solved using the incremental-iterative technique based on the modified Newton-Raphson method. The convergence of the solution was controlled by a load convergence criterion. The validity of the theoretical formulations and the program used was verified, through comparison with results obtained using ANSYS program and with available experimental test results. A parametric study was conducted to investigate the effect of different parameters on the behavior of slabs which was evaluated in terms of loaddeflection characteristics, concrete and steel stresses and strains, and failure mechanisms. Also, punching shear resistance of slabs was numerically evaluated and compared with the prediction specified by some design codes.
Spectral and thermal behaviours of rare earth element complexes with 3,5-dimethoxybenzoic acid
Directory of Open Access Journals (Sweden)
JANUSZ CHRUŚCIEL
2003-10-01
Full Text Available The conditions for the formation of rare earth element 3,5-dimethytoxybenzoates were studied and their quantitative composition and solubilities in water at 293 K were determined. The complexes are anhydrous or hydrated salts and their solubilities are of the orders of 10-5 10-4 mol dm-3. Their FTIR, FIR and X-ray spectra were recorded. The compounds were also characterized by thermogravimetric studies in air and nitrogen atmospheres and by magnetic measurements. All complexes are crystalline compounds. The carboxylate group in these complexes is a bidentate, chelating ligand. On heating in air to 1173 K, the 3,5-dimethoxybenzoates of rare earth elements decompose in various ways. The hydrated complexes first dehydrate to form anhydrous salts which then decompose in air to the oxides of the respective metals while in nitrogen to mixtures of carbon and oxides of the respective metals. The complexes are more stable in air than in nitrogen.
Li, Nianqiang; Susanto, H; Cemlyn, B R; Henning, I D; Adams, M J
2018-02-19
We study the nonlinear dynamics of solitary and optically injected two-element laser arrays with a range of waveguide structures. The analysis is performed with a detailed direct numerical simulation, where high-resolution dynamic maps are generated to identify regions of dynamic instability in the parameter space of interest. Our combined one- and two-parameter bifurcation analysis uncovers globally diverse dynamical regimes (steady-state, oscillation, and chaos) in the solitary laser arrays, which are greatly influenced by static design waveguiding structures, the amplitude-phase coupling factor of the electric field, i.e. the linewidth-enhancement factor, as well as the control parameter, e.g. the pump rate. When external optical injection is introduced to one element of the arrays, we show that the whole system can be either injection-locked simultaneously or display rich, different dynamics outside the locking region. The effect of optical injection is to significantly modify the nature and the regions of nonlinear dynamics from those found in the solitary case. We also show similarities and differences (asymmetry) between the oscillation amplitude of the two elements of the array in specific well-defined regions, which hold for all the waveguiding structures considered. Our findings pave the way to a better understanding of dynamic instability in large arrays of lasers.
Chróścielewski, Jacek; Schmidt, Rüdiger; Eremeyev, Victor A.
2018-05-01
This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.
International Nuclear Information System (INIS)
Schulte, R T; Fritzen, C-P; Moll, J
2010-01-01
During the last decades, guided waves have shown great potential for Structural Health Monitoring (SHM) applications. These waves can be excited and sensed by piezoelectric elements that can be permanently attached onto a structure offering online monitoring capability. However, the setup of wave based SHM systems for complex structures may be very difficult and time consuming. For that reason there is a growing demand for efficient simulation tools providing the opportunity to design wave based SHM systems in a virtual environment. As usually high frequency waves are used, the associated short wavelength leads to the necessity of a very dense mesh, which makes conventional finite elements not well suited for this purpose. Therefore in this contribution a flat shell spectral element approach is presented. By including electromechanical coupling a SHM system can be simulated entirely from actuator voltage to sensor voltage. Besides a comparison to measured data for anisotropic materials including delamination, a numerical example of a more complex, stiffened shell structure with debonding is presented.
Adaptive Kronrod-Patterson integration of non-linear finite-element matrices
DEFF Research Database (Denmark)
Janssen, Hans
2010-01-01
inappropriate discretization. In response, this article develops adaptive integration, based on nested Kronrod-Patterson-Gauss integration schemes: basically, the integration order is adapted to the locally observed grade of non-linearity. Adaptive integration is developed based on a standard infiltration...
Kuindersma, P.I.; Leijtens, X.J.M.; Zantvoort, van J.H.C.; Waardt, de H.
2012-01-01
We characterize integrated InP circuits for high speed ‘all-optical’ signal processing. Single chip circuits act as optical transistors. Transmodulation is performed by non-linear gain sections. Integrated tunable filters give signal equalization in time domain.
Elements of a dialogue between nonlinear models in condensed matter and biophysics
International Nuclear Information System (INIS)
Bishop, A.R.; Lomdahl, P.S.; Kerr, W.C.
1985-01-01
We indicate some of the emerging thematic connections between strongly nonlinear effects in condensed matter and biological materials. These are illustrated with model studies of: (1) structural phase transitions in anisotropic lattices; and (2) finite temperature effects on self-trapped states in vibron-phonon models of α-helix proteins. 13 refs., 8 figs
GPU-based acceleration of computations in nonlinear finite element deformation analysis.
Mafi, Ramin; Sirouspour, Shahin
2014-03-01
The physics of deformation for biological soft-tissue is best described by nonlinear continuum mechanics-based models, which then can be discretized by the FEM for a numerical solution. However, computational complexity of such models have limited their use in applications requiring real-time or fast response. In this work, we propose a graphic processing unit-based implementation of the FEM using implicit time integration for dynamic nonlinear deformation analysis. This is the most general formulation of the deformation analysis. It is valid for large deformations and strains and can account for material nonlinearities. The data-parallel nature and the intense arithmetic computations of nonlinear FEM equations make it particularly suitable for implementation on a parallel computing platform such as graphic processing unit. In this work, we present and compare two different designs based on the matrix-free and conventional preconditioned conjugate gradients algorithms for solving the FEM equations arising in deformation analysis. The speedup achieved with the proposed parallel implementations of the algorithms will be instrumental in the development of advanced surgical simulators and medical image registration methods involving soft-tissue deformation. Copyright © 2013 John Wiley & Sons, Ltd.
High Power, Pulsed, RF Generation from Nonlinear Lumped Element Transmission Lines (NLETLs)
2011-02-05
in order to focus on the primary technology tinder consideration. Their practicality at very high powers and frequencies is questionable due to...also possessed suitably large CXL ratios. Measuring capacitive nonlinearity tinder high voltage proved to be more tricky than first imagi- ned
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...
Sine sweep and steady-state response of simplified solar array models with nonlinear elements
Fey, R.H.B.; van Liempt, F.P.H.
2002-01-01
In this paper the nonlinear dynamic behaviour of two simplified solar array systems is investigated experimentally and numerically. A simplified beam model supported by one snubber (a bilinear spring which can only take compressive forces) is used to investigate the dynamics of the extension arm on
International Nuclear Information System (INIS)
Koch, Stephan
2009-01-01
This thesis is concerned with the numerical simulation of electromagnetic fields in the quasi-static approximation which is applicable in many practical cases. Main emphasis is put on higher-order finite element methods. Quasi-static applications can be found, e.g., in accelerator physics in terms of the design of magnets required for beam guidance, in power engineering as well as in high-voltage engineering. Especially during the first design and optimization phase of respective devices, numerical models offer a cheap alternative to the often costly assembly of prototypes. However, large differences in the magnitude of the material parameters and the geometric dimensions as well as in the time-scales of the electromagnetic phenomena involved lead to an unacceptably long simulation time or to an inadequately large memory requirement. Under certain circumstances, the simulation itself and, in turn, the desired design improvement becomes even impossible. In the context of this thesis, two strategies aiming at the extension of the range of application for numerical simulations based on the finite element method are pursued. The first strategy consists in parallelizing existing methods such that the computation can be distributed over several computers or cores of a processor. As a consequence, it becomes feasible to simulate a larger range of devices featuring more degrees of freedom in the numerical model than before. This is illustrated for the calculation of the electromagnetic fields, in particular of the eddy-current losses, inside a superconducting dipole magnet developed at the GSI Helmholtzzentrum fuer Schwerionenforschung as a part of the FAIR project. As the second strategy to improve the efficiency of numerical simulations, a hybrid discretization scheme exploiting certain geometrical symmetries is established. Using this method, a significant reduction of the numerical effort in terms of required degrees of freedom for a given accuracy is achieved. The
Energy Technology Data Exchange (ETDEWEB)
Zhao, J. S.; Wu, D. J. [Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing (China); Voitenko, Y.; De Keyser, J., E-mail: js_zhao@pmo.ac.cn [Solar-Terrestrial Centre of Excellence, Space Physics Division, Belgian Institute for Space Aeronomy, Ringlaan-3-Avenue Circulaire, B-1180 Brussels (Belgium)
2014-04-20
We study the nonlocal nonlinear coupling and generation of kinetic Alfvén waves (KAWs) and kinetic slow waves (KSWs) by magnetohydrodynamic Alfvén waves (MHD AWs) in conditions typical for the solar wind in the inner heliosphere. This cross-scale process provides an alternative to the turbulent energy cascade passing through many intermediate scales. The nonlinearities we study are proportional to the scalar products of wave vectors and hence are called 'scalar' ones. Despite the strong Landau damping of kinetic waves, we found fast growing KAWs and KSWs at perpendicular wavelengths close to the ion gyroradius. Using the parametric decay formalism, we investigate two independent decay channels for the pump AW: forward decay (involving co-propagating product waves) and backward decay (involving counter-propagating product waves). The growth rate of the forward decay is typically 0.05 but can exceed 0.1 of the pump wave frequency. The resulting spectral transport is nonlocal and anisotropic, sharply increasing perpendicular wavenumbers but not parallel ones. AWs and KAWs propagating against the pump AW grow with about the same rate and contribute to the sunward wave flux in the solar wind. Our results suggest that the nonlocal decay of MHD AWs into KAWs and KSWs is a robust mechanism for the cross-scale spectral transport of the wave energy from MHD to dissipative kinetic scales in the solar wind and similar media.
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.
Spectral Analysis of Rare Earth Elements using Laser-Induced Breakdown Spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Martin, Madhavi Z [ORNL; Fox, Dr. Richard V [Idaho National Laboratory (INL); Miziolek, Andrzej W [United States Army Research Laboratory; DeLucia, Frank C [United States Army Research Laboratory; Andre, Nicolas O [ORNL
2015-01-01
There is growing interest in rapid analysis of rare earth elements (REEs) both due to the need to find new natural sources to satisfy increased demand in their use in various electronic devices, as well as the fact that they are used to estimate actinide masses for nuclear safeguards and nonproliferation. Laser-Induced Breakdown Spectroscopy (LIBS) appears to be a particularly well-suited spectroscopy-based technology to rapidly and accurately analyze the REEs in various matrices at low concentration levels (parts-per-million). Although LIBS spectra of REEs have been reported for a number of years, further work is still necessary in order to be able to quantify the concentrations of various REEs in realworld complex samples. LIBS offers advantages over conventional solution-based radiochemistry in terms of cost, analytical turnaround, waste generation, personnel dose, and contamination risk. Rare earth elements of commercial interest are found in the following three matrix groups: 1) raw ores and unrefined materials, 2) as components in refined products such as magnets, lighting phosphors, consumer electronics (which are mostly magnets and phosphors), catalysts, batteries, etc., and 3) waste/recyclable materials (aka e-waste). LIBS spectra for REEs such as Gd, Nd, and Sm found in rare earth magnets are presented.
Spectral Analysis of Rare Earth Elements using Laser-Induced Breakdown Spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Martin, Madhavi Z [ORNL; Fox, Dr. Richard V [Idaho National Laboratory (INL); Miziolek, Andrzej W [United States Army Research Laboratory; DeLucia, Frank C [United States Army Research Laboratory; Andre, Nicolas O [ORNL
2015-01-01
There is growing interest in rapid analysis of rare earth elements (REEs) both due to the need to find new natural sources to satisfy increased demand in their use in various electronic devices, as well as the fact that they are used to estimate actinide masses for nuclear safeguards and nonproliferation. Laser-Induced Breakdown Spectroscopy (LIBS) appears to be a particularly well-suited spectroscopy-based technology to rapidly and accurately analyze the REEs in various matrices at low concentration levels (parts-per-million). Although LIBS spectra of REEs have been reported for a number of years, further work is still necessary in order to be able to quantify the concentrations of various REEs in real-world complex samples. LIBS offers advantages over conventional solution-based radiochemistry in terms of cost, analytical turnaround, waste generation, personnel dose, and contamination risk. Rare earth elements of commercial interest are found in the following three matrix groups: 1) raw ores and unrefined materials, 2) as components in refined products such as magnets, lighting phosphors, consumer electronics (which are mostly magnets and phosphors), catalysts, batteries, etc., and 3) waste/recyclable materials (aka e-waste). LIBS spectra for REEs such as Gd, Nd, and Sm found in rare earth magnets are presented.
Ryzhenkov, V.; Ivashchenko, V.; Vinuesa, R.; Mullyadzhanov, R.
2016-10-01
We use the open-source code nek5000 to assess the accuracy of high-order spectral element large-eddy simulations (LES) of a turbulent channel flow depending on the spatial resolution compared to the direct numerical simulation (DNS). The Reynolds number Re = 6800 is considered based on the bulk velocity and half-width of the channel. The filtered governing equations are closed with the dynamic Smagorinsky model for subgrid stresses and heat flux. The results show very good agreement between LES and DNS for time-averaged velocity and temperature profiles and their fluctuations. Even the coarse LES grid which contains around 30 times less points than the DNS one provided predictions of the friction velocity within 2.0% accuracy interval.
DEFF Research Database (Denmark)
Yoon, Gil Ho; Joung, Young Soo; Kim, Yoon Young
2005-01-01
The topology design optimization of “three-dimensional geometrically-nonlinear” continuum structures is still a difficult problem not only because of its problem size but also the occurrence of unstable continuum finite elements during the design optimization. To overcome this difficulty, the ele......) stiffness matrix of continuum finite elements. Therefore, any finite element code, including commercial codes, can be readily used for the ECP implementation. The key ideas and characteristics of these methods will be presented in this paper....
Krasilenko, Vladimir G.; Nikolsky, Alexander I.; Lazarev, Alexander A.; Lazareva, Maria V.
2008-03-01
In the paper the actuality of neurophysiologically motivated neuron arrays with flexibly programmable functions and operations with possibility to select required accuracy and type of nonlinear transformation and learning are shown. We consider neurons design and simulation results of multichannel spatio-time algebraic accumulation - integration of optical signals. Advantages for nonlinear transformation and summation - integration are shown. The offered circuits are simple and can have intellectual properties such as learning and adaptation. The integrator-neuron is based on CMOS current mirrors and comparators. The performance: consumable power - 100...500 μW, signal period- 0.1...1ms, input optical signals power - 0.2...20 μW time delays - less 1μs, the number of optical signals - 2...10, integration time - 10...100 of signal periods, accuracy or integration error - about 1%. Various modifications of the neuron-integrators with improved performance and for different applications are considered in the paper.
International Nuclear Information System (INIS)
Esfandiar, Habib; KoraYem, Moharam Habibnejad
2015-01-01
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.
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.
International Nuclear Information System (INIS)
Rensch, H.J.; Wunderlich, W.
1981-01-01
The governing partial differential equations used are valid for small strains and moderate rotations. Plasticity relations are based on J 2 -flow theory. In order to eliminate the circumferential coordinate, the loading as well as the unkown quantities are expanded in Fourier series in the circumferential direction. The nonlinear terms due to moderate rotations and plastic deformations are treated as pseudo load quantities. In this way, the governing equations can be reduced to uncoupled systems of first-order ordinary differential equations in the meridional direction. They are then integrated over a shell segment via a matrix series expansion. The resulting element transfer matrices are transformed into stiffness matrices, and for the analysis of the total structure the finite element method is employed. Thus, arbitrary branching of the shell geometry is possible. Compared to two-dimensional approximations, the major advantage of the semi-analytical procedure is that the structural stiffness matrix usually has a small handwidth, resulting in shorter computer run times. Moreover, its assemblage and triangularization has to be carried out only once bacause all nonlinear effects are treated as initial loads. (orig./HP)
Wu, Zhijing; Li, Fengming; Zhang, Chuanzeng
2018-05-01
Inspired by the hierarchical structures of butterfly wing surfaces, a new kind of lattice structures with a two-order hierarchical periodicity is proposed and designed, and the band-gap properties are investigated by the spectral element method (SEM). The equations of motion of the whole structure are established considering the macro and micro periodicities of the system. The efficiency of the SEM is exploited in the modeling process and validated by comparing the results with that of the finite element method (FEM). Based on the highly accurate results in the frequency domain, the dynamic behaviors of the proposed two-order hierarchical structures are analyzed. An original and interesting finding is the existence of the distinct macro and micro stop-bands in the given frequency domain. The mechanisms for these two types of band-gaps are also explored. Finally, the relations between the hierarchical periodicities and the different types of the stop-bands are investigated by analyzing the parametrical influences.
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.
Lukowski, Michal L.
Optically pumped semiconductor vertical external cavity surface emitting lasers (VECSEL) were first demonstrated in the mid 1990's. Due to the unique design properties of extended cavity lasers VECSELs have been able to provide tunable, high-output powers while maintaining excellent beam quality. These features offer a wide range of possible applications in areas such as medicine, spectroscopy, defense, imaging, communications and entertainment. Nowadays, newly developed VECSELs, cover the spectral regions from red (600 nm) to around 5 microm. By taking the advantage of the open cavity design, the emission can be further expanded to UV or THz regions by the means of intracavity nonlinear frequency generation. The objective of this dissertation is to investigate and extend the capabilities of high-power VECSELs by utilizing novel nonlinear conversion techniques. Optically pumped VECSELs based on GaAs semiconductor heterostructures have been demonstrated to provide exceptionally high output powers covering the 900 to 1200 nm spectral region with diffraction limited beam quality. The free space cavity design allows for access to the high intracavity circulating powers where high efficiency nonlinear frequency conversions and wavelength tuning can be obtained. As an introduction, this dissertation consists of a brief history of the development of VECSELs as well as wafer design, chip fabrication and resonator cavity design for optimal frequency conversion. Specifically, the different types of laser cavities such as: linear cavity, V-shaped cavity and patented T-shaped cavity are described, since their optimization is crucial for transverse mode quality, stability, tunability and efficient frequency conversion. All types of nonlinear conversions such as second harmonic, sum frequency and difference frequency generation are discussed in extensive detail. The theoretical simulation and the development of the high-power, tunable blue and green VECSEL by the means of type I
Finite element modeling of nanotube structures linear and non-linear models
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.
A Non-Linear Finite Element Model for the LHC Main Dipole Coil Cross-Section
Pojer, M; Scandale, Walter
2006-01-01
The production of the dipole magnets for the Large Hadron Collider is at its final stage. Nevertheless, some mechanical instabilities are still observed for which no clear explanation has been found yet. A FE modelization of the dipole cold mass cross-section had already been developed at CERN, mainly for magnetic analysis, taking into account conductor blocks and a frictionless behavior. This paper describes a new ANSYSÂ® model of the dipole coil cross-section, featuring individual turns inside conductor blocks, and implementing friction and the mechanical non-linear behavior of insulated cables. Preliminary results, comparison with measurements performed in industry and ongoing developments are discussed.
A nanohole in a thin metal film as an efficient nonlinear optical element
Energy Technology Data Exchange (ETDEWEB)
Konstantinova, T. V.; Melent' ev, P. N.; Afanas' ev, A. E. [Russian Academy of Sciences, Institute of Spectroscopy (Russian Federation); Kuzin, A. A.; Starikov, P. A.; Baturin, A. S. [Moscow Institute of Physics and Technology (Russian Federation); Tausenev, A. V.; Konyashchenko, A. V. [OOO Avesta-proekt (Russian Federation); Balykin, V. I., E-mail: balykin@isan.tyroitsk.ru [Russian Academy of Sciences, Institute of Spectroscopy (Russian Federation)
2013-07-15
The nonlinear optical properties of single nanoholes and nanoslits fabricated in gold and aluminum nanofilms are studied by third harmonic generation (THG). It is shown that the extremely high third-order optical susceptibility of aluminum and the presence of strong plasmon resonance of a single nanohole in an aluminum film make possible an efficient nanolocalized radiation source at the third harmonic frequency. The THG efficiency for a single nanohole in a thin metal film can be close to unity for an exciting laser radiation intensity on the order of 10{sup 13} W/cm{sup 2}.
A nanohole in a thin metal film as an efficient nonlinear optical element
International Nuclear Information System (INIS)
Konstantinova, T. V.; Melent’ev, P. N.; Afanas’ev, A. E.; Kuzin, A. A.; Starikov, P. A.; Baturin, A. S.; Tausenev, A. V.; Konyashchenko, A. V.; Balykin, V. I.
2013-01-01
The nonlinear optical properties of single nanoholes and nanoslits fabricated in gold and aluminum nanofilms are studied by third harmonic generation (THG). It is shown that the extremely high third-order optical susceptibility of aluminum and the presence of strong plasmon resonance of a single nanohole in an aluminum film make possible an efficient nanolocalized radiation source at the third harmonic frequency. The THG efficiency for a single nanohole in a thin metal film can be close to unity for an exciting laser radiation intensity on the order of 10 13 W/cm 2
Directory of Open Access Journals (Sweden)
Jónas Elíasson
2014-01-01
Full Text Available A finite Fourier transform is used to perform both linear and nonlinear stability analyses of a Darcy-Lapwood system of convective rolls. The method shows how many modes are unstable, the wave number instability band within each mode, the maximum growth rate (most critical wave numbers on each mode, and the nonlinear growth rates for each amplitude as a function of the porous Rayleigh number. Single amplitude controls the nonlinear growth rates and thereby the physical flow rate and fluid velocity, on each mode. They are called the flak amplitudes. A discrete Fourier transform is used for numerical simulations and here frequency combinations appear that the traditional cut-off infinite transforms do not have. The discrete show a stationary solution in the weak instability phase, but when carried past 2 unstable modes they show fluctuating motion where all amplitudes except the flak may be zero on the average. This leads to a flak amplitude scaling process of the heat conduction, producing an eddy heat conduction coefficient where a Nu-RaL relationship is found. It fits better to experiments than previously found solutions but is lower than experiments.
International Nuclear Information System (INIS)
Gupta, A.; Singh, R.K.; Kushwaha, H.S.; Mahajan, S.C.; Kakodkar, A.
1996-01-01
For safety evaluation of nuclear structures a finite element code ULCA (Ultimate Load Capacity Assessment) has been developed. Eight/nine noded isoparametric quadrilateral plate/shell element with reinforcement as a through thickness discrete but integral smeared layer of the element is presented to analyze reinforced and prestressed concrete structures. Various constitutive models such as crushing, cracking in tension, tension stiffening and rebar yielding are studied and effect of these parameters on the reserve strength of structures is brought out through a number of benchmark tests. A global model is used to analyze the prestressed concrete containment wall of a typical 220 MWe Pressurized Heavy Water Reactor (PHWR) up to its ultimate capacity. This demonstrates the adequacy of Indian PHWR containment design to withstand severe accident loads
Arteaga, Santiago Egido
1998-12-01
The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the
International Nuclear Information System (INIS)
Zhidkov, P.E.
1996-01-01
First, the eigenvalue problem on the segment [0,1] for the Sturm-Liouville operator with a potential depending on the spectral parameter with the zero Dirichlet boundary conditions is considered. For this problem, under some hypotheses on the potential, it is proved that the necessary and sufficient condition for an arbitrary system of eigenfunctions, possessing a unique function with n roots in the interval (0,1) for an arbitrary non-negative integer number n, being complete in the space L 2 (0,1) is the linear independence of the functions from this system in the space L 2 (0,1). Then, this result is applied to the investigation of an eigenvalue problem for a nonlinear operator on the Sturm-Liouville type. For this problem, the completeness of the system of its eigenfunctions in the space L 2 (0,1) is proved. (author). 12 refs
Kong, Ming; Liu, Yanqiu; Wang, Hui; Luo, Junshan; Li, Dandan; Zhang, Shengyi; Li, Shengli; Wu, Jieying; Tian, Yupeng
2015-01-01
Four novel Zn(II) terpyridine complexes (ZnLCl2, ZnLBr2, ZnLI2, ZnL(SCN)2) based on carbazole derivative group were designed, synthesized and fully characterized. Their photophysical properties including absorption and one-photon excited fluorescence, two-photon absorption (TPA) and optical power limiting (OPL) were further investigated systematically and interpreted on the basis of theoretical calculations (TD-DFT). The influences of different solvents on the absorption and One-Photon Excited Fluorescence (OPEF) spectral behavior, quantum yields and the lifetime of the chromophores have been investigated in detail. The third-order nonlinear optical (NLO) properties were investigated by open/closed aperture Z-scan measurements using femtosecond pulse laser in the range from 680 to 1080 nm. These results revealed that ZnLCl2 and ZnLBr2 exhibited strong two-photon absorption and ZnLCl2 showed superior optical power limiting property.
A finite element perspective on non-linear FFT-based micromechanical simulations
Zeman, J.; de Geus, T.W.J.; Vondřejc, J.; Peerlings, R.H.J.; Geers, M.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
A finite element perspective on nonlinear FFT-based micromechanical simulations
Zeman, J.; de Geus, T.W.J.; Vondrejc, J.; Peerlings, R.H.J.; Geers, M.G.D.
2017-01-01
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
Geometrically Nonlinear Analysis of Shell Structures Using Flat DKT Shell Elements.
1985-11-22
In general 1r is a curved surface and the exact expressions of f1 e I are not simpler than f e 1. In fact they are theorically identical when the...1982. [23] Zienkiewicz, 0. C., The Finite Element Method (3rd Edition), McGraw-Hill, 1977. [24] Bergan, P. G., Holand , I., Soreide, T. H., "Use of
Nageshwari, M.; Kumari, C. Rathika Thaya; Vinitha, G.; Mohamed, M. Peer; Sudha, S.; Caroline, M. Lydia
2018-03-01
L-Methionine-Succinic acid (2/1) (LMSA), 2C5H11NO2S·C4H6O4, a novel nonlinear optical material which belongs to the class of organic category was grown-up for the first time by the technique of slow evaporation. Purity of LMSA was improved using repetitive recrystallization. LMSA was analyzed by single crystal and powder X-ray diffraction investigation to affirm the crystal structure and crystalline character. The single crystal XRD revealed that LMSA corresponds to the crystal system of triclinic with P1 as space group showing the asymmetric unit consists of a neutral succinic acid molecule and two methionine residues which are crystallographically independent existing in zwitterionic form. The functional groups existing in LMSA was accomplished using Fourier transform infrared spectroscopy. The optical transparency and the band gap energy were identified utilizing UV-Visible spectrum. The optical constants specifically reflectance and extinction coefficient clearly indicate the elevated transparency of LMSA. The thermal analyses affirmed its thermal stability. The luminescence behavior of LMSA has been analyzed by Photoluminescence (PL) spectral study. The mechanical, laser damage threshold and dielectric investigation of LMSA was done to suggest the material for practical applications. The second and third harmonic generation efficacy was confirmed by means of Kurtz-Perry and Z-scan procedure which attest its potentiality in the domain of nonlinear optics.
A New Method for Non-linear and Non-stationary Time Series Analysis:
The Hilbert Spectral Analysis
CERN. Geneva
2000-01-01
A new method for analysing non-linear and non-stationary data has been developed. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero crossing and extreme, and also having symmetric envelopes defined by the local maximal and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to non-linear and non-stationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Classical non-l...
International Nuclear Information System (INIS)
Gambolati, G.; Toffolo, F.; Uliana, F.
1984-01-01
A nonlinear finite element model based on the Dupuit-Boussinesq equation of flow in an unconfined aquifer has been developed and applied to simulate the water table fluctuation under the electronuclear plant of the test site of Trino Vercellese (northwestern Italy) in response to the flood event that occurred in the Po River from March 30 to April 4, 1981. The nonlinearity has been overcome by the aid of an efficient iterative linearization technique wherein the model equations are solved by symbolic factorization, numerical factorization, and backward-forward substitution after an optimal preliminary reordering. The model was run for uniform values of aquifer permeability and specific yield within the typical range evidenced for the Trino sands by the early data in our possession. The results show that the maximum water level elevation below the reactor is almost 3 m lower than the corresponding river flood peak even in the most unfavorable conditions, i.e., with the hydraulic conductivity in the upper range, and is rather insensitive to the specific yield values within the plausible interval. The model allowed for an easy evaluation of the effectiveness of the impermeable protection walls and of a possible secondary aquifer recharge from a minor channel. The modeling approach for the analysis of the water table behavior appears to be a very promising tool to help in the structural design of future electronuclear plants
Ying, Yingzi; Bean, Christopher J.
2014-05-01
Ocean-generated microseisms are faint Earth tremors associated with the interaction between ocean water waves and the solid Earth. The microseism noise recorded as low frequency ground vibrations by seismometers contains significant information about the Earth's interior and the sea states. In this work, we first aim to investigate the forward propagation of microseisms in a deep-ocean environment. We employ a 3D North-East Atlantic geological model and simulate wave propagation in a coupled fluid-solid domain, using a spectral-element method. The aim is to investigate the effects of the continental shelf on microseism wave propagation. A second goal of this work is to perform noise simulation to calculate synthetic ensemble averaged cross-correlations of microseism noise signals with time reversal method. The algorithm can relieve computational cost by avoiding time stacking and get cross-correlations between the designated master station and all the remaining slave stations, at one time. The origins of microseisms are non-uniform, so we also test the effect of simulated noise source distribution on the determined cross-correlations.
Directory of Open Access Journals (Sweden)
Wan-You Li
2014-01-01
Full Text Available A novel hybrid method, which simultaneously possesses the efficiency of Fourier spectral method (FSM and the applicability of the finite element method (FEM, is presented for the vibration analysis of structures with elastic boundary conditions. The FSM, as one type of analytical approaches with excellent convergence and accuracy, is mainly limited to problems with relatively regular geometry. The purpose of the current study is to extend the FSM to problems with irregular geometry via the FEM and attempt to take full advantage of the FSM and the conventional FEM for structural vibration problems. The computational domain of general shape is divided into several subdomains firstly, some of which are represented by the FSM while the rest by the FEM. Then, fictitious springs are introduced for connecting these subdomains. Sufficient details are given to describe the development of such a hybrid method. Numerical examples of a one-dimensional Euler-Bernoulli beam and a two-dimensional rectangular plate show that the present method has good accuracy and efficiency. Further, one irregular-shaped plate which consists of one rectangular plate and one semi-circular plate also demonstrates the capability of the present method applied to irregular structures.
Directory of Open Access Journals (Sweden)
E. D. Resende
2007-09-01
Full Text Available The freezing process is considered as a propagation problem and mathematically classified as an "initial value problem." The mathematical formulation involves a complex situation of heat transfer with simultaneous changes of phase and abrupt variation in thermal properties. The objective of the present work is to solve the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements. This technique has not yet been applied to freezing processes and represents an alternative numerical approach in this area. The results obtained confirmed the good capability of the numerical method, which allows the simulation of the freezing process in approximately one minute of computer time, qualifying its application in a mathematical optimising procedure. The influence of the latent heat released during the crystallisation phenomena was identified by the significant increase in heat load in the early stages of the freezing process.
Townsend, Molly T; Sarigul-Klijn, Nesrin
2016-01-01
Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.
Extensions to a nonlinear finite element axisymmetric shell model based on Reissner's shell theory
International Nuclear Information System (INIS)
Cook, W.A.
1981-01-01
A finite element shell-of-revolution model has been developed to analyze shipping containers under severe impact conditions. To establish the limits for this shell model, I studied the basic assumptions used in its development; these are listed in this paper. Several extensions were evident from the study of these limits: a thick shell, a plastic hinge, and a linear normal stress. (orig./HP)
Jayaprakash, P.; Sangeetha, P.; Kumari, C. Rathika Thaya; Caroline, M. Lydia
2017-08-01
A nonlinear optical bulk single crystal of L-methionine admixtured D-mandelic acid (LMDMA) has been grown by slow solvent evaporation technique using water as solvent at ambient temperature. The crystallized LMDMA single crystal subjected to single crystal X-ray diffraction study confirmed monoclinic system with the acentric space group P21. The FTIR analysis gives information about the modes of vibration in the various functional groups present in LMDMA. The UV-visible spectral analysis assessed the optical quality and linear optical properties such as extinction coefficient, reflectance, refractive index and from which optical conductivity and electric susceptibility were also evaluated. The frequency doubling efficiency was observed using Kurtz Perry powder technique. A multiple shot laser was utilized to evaluate the laser damage threshold energy of the crystal. Discrete thermodynamic properties were carried out by TG-DTA studies. The hardness, Meyer's index, yield strength, elastic stiffness constant, Knoop hardness, fracture toughness and brittleness index were analyzed using Vickers microhardness tester. Layer growth pattern and the surface defect were examined by chemical etching studies using optical microscope. Fluorescence emission spectrum was recorded and lifetime was also studied. The electric field response of crystal was investigated from the dielectric studies at various temperatures at different frequencies. The third-order nonlinear optical response in LMDMA has been investigated using Z-scan technique with He-Ne laser at 632.8 nm and nonlinear parameters such as refractive index (n2), absorption coefficient (β) and susceptibility (χ3) investigated extensively for they are in optical phase conjucation, high-speed optical switches and optical dielectric devices.
Directory of Open Access Journals (Sweden)
Ibrahim Dauda Muhammad
2015-01-01
Full Text Available The single-walled zirconia nanotube is structurally modeled and its Young’s modulus is valued by using the finite element approach. The nanotube was assumed to be a frame-like structure with bonds between atoms regarded as beam elements. The properties of the beam required for input into the finite element analysis were computed by connecting energy equivalence between molecular and continuum mechanics. Simulation was conducted by applying axial tensile strain on one end of the nanotube while the other end was fixed and the corresponding reaction force recorded to compute Young’s modulus. It was found out that Young’s modulus of zirconia nanotubes is significantly affected by some geometrical parameters such as chirality, diameter, thickness, and length. The obtained values of Young’s modulus for a certain range of diameters are in agreement with what was obtained in the few experiments that have been conducted so far. This study was conducted on the cubic phase of zirconia having armchair and zigzag configuration. The optimal diameter and thickness were obtained, which will assist in designing and fabricating bulk nanostructured components containing zirconia nanotubes for various applications.
Li, Lin
2008-12-01
Partial least squares (PLS) regressions were applied to lunar highland and mare soil data characterized by the Lunar Soil Characterization Consortium (LSCC) for spectral estimation of the abundance of lunar soil chemical constituents FeO and Al2O3. The LSCC data set was split into a number of subsets including the total highland, Apollo 16, Apollo 14, and total mare soils, and then PLS was applied to each to investigate the effect of nonlinearity on the performance of the PLS method. The weight-loading vectors resulting from PLS were analyzed to identify mineral species responsible for spectral estimation of the soil chemicals. The results from PLS modeling indicate that the PLS performance depends on the correlation of constituents of interest to their major mineral carriers, and the Apollo 16 soils are responsible for the large errors of FeO and Al2O3 estimates when the soils were modeled along with other types of soils. These large errors are primarily attributed to the degraded correlation FeO to pyroxene for the relatively mature Apollo 16 soils as a result of space weathering and secondary to the interference of olivine. PLS consistently yields very accurate fits to the two soil chemicals when applied to mare soils. Although Al2O3 has no spectrally diagnostic characteristics, this chemical can be predicted for all subset data by PLS modeling at high accuracies because of its correlation to FeO. This correlation is reflected in the symmetry of the PLS weight-loading vectors for FeO and Al2O3, which prove to be very useful for qualitative interpretation of the PLS results. However, this qualitative interpretation of PLS modeling cannot be achieved using principal component regression loading vectors.
International Nuclear Information System (INIS)
Tayal, M.
1987-01-01
Structures often operate at elevated temperatures. Temperature calculations are needed so that the design can accommodate thermally induced stresses and material changes. A finite element computer called FEAT has been developed to calculate temperatures in solids of arbitrary shapes. FEAT solves the classical equation for steady state conduction of heat. The solution is obtained for two-dimensional (plane or axisymmetric) or for three-dimensional problems. Gap elements are use to simulate interfaces between neighbouring surfaces. The code can model: conduction; internal generation of heat; prescribed convection to a heat sink; prescribed temperatures at boundaries; prescribed heat fluxes on some surfaces; and temperature-dependence of material properties like thermal conductivity. The user has a option of specifying the detailed variation of thermal conductivity with temperature. For convenience to the nuclear fuel industry, the user can also opt for pre-coded values of thermal conductivity, which are obtained from the MATPRO data base (sponsored by the U.S. Nuclear Regulatory Commission). The finite element method makes FEAT versatile, and enables it to accurately accommodate complex geometries. The optional link to MATPRO makes it convenient for the nuclear fuel industry to use FEAT, without loss of generality. Special numerical techniques make the code inexpensive to run, for the type of material non-linearities often encounter in the analysis of nuclear fuel. The code, however, is general, and can be used for other components of the reactor, or even for non-nuclear systems. The predictions of FEAT have been compared against several analytical solutions. The agreement is usually better than 5%. Thermocouple measurements show that the FEAT predictions are consistent with measured changes in temperatures in simulated pressure tubes. FEAT was also found to predict well, the axial variations in temperatures in the end-pellets(UO 2 ) of two fuel elements irradiated
Ricoeur, Andreas; Lange, Stephan; Avakian, Artjom
2015-04-01
Magnetoelectric (ME) coupling is an inherent property of only a few crystals exhibiting very low coupling coefficients at low temperatures. On the other hand, these materials are desirable due to many promising applications, e.g. as efficient data storage devices or medical or geophysical sensors. Efficient coupling of magnetic and electric fields in materials can only be achieved in composite structures. Here, ferromagnetic (FM) and ferroelectric (FE) phases are combined e.g. including FM particles in a FE matrix or embedding fibers of the one phase into a matrix of the other. The ME coupling is then accomplished indirectly via strain fields exploiting magnetostrictive and piezoelectric effects. This requires a poling of the composite, where the structure is exposed to both large magnetic and electric fields. The efficiency of ME coupling will strongly depend on the poling process. Besides the alignment of local polarization and magnetization, it is going along with cracking, also being decisive for the coupling properties. Nonlinear ferroelectric and ferromagnetic constitutive equations have been developed and implemented within the framework of a multifield, two-scale FE approach. The models are microphysically motivated, accounting for domain and Bloch wall motions. A second, so called condensed approach is presented which doesn't require the implementation of a spatial discretisation scheme, however still considering grain interactions and residual stresses. A micromechanically motivated continuum damage model is established to simulate degradation processes. The goal of the simulation tools is to predict the different constitutive behaviors, ME coupling properties and lifetime of smart magnetoelectric devices.
Non-linear finite element analyses of wide plate fracture mechanics experiments
International Nuclear Information System (INIS)
Harrop, L.P.; Gibson, S.
1988-06-01
A series of centre-cracked, wide plate fracture mechanics tests is being conducted with plates made from 0.36% carbon steel. This report gives an account of post-test finite element analyses performed to compare with the results of one of these tests (designated CSTP4) and a pre-test analysis of the next test which has a slightly different geometry (CSTP5). The plates are relatively thick (75mm) and have a width of 1.62m. The finite element analyses use a two-dimensional plane stress mesh. The work shows good agreement between the post-test analysis results and the overall experimental results for CSTP4. It is not expected that the analysis results will be accurate within the dimensions of the process zone ahead of the crack tip; the mesh is not sufficient for this. A vital ingredient in attaining the good overall agreement is the representation of the actual stress-strain curve of the material. The predicted response of test CSTP5 is markedly different from that of CSTP4 even though the only change is the increase in the height of the plate. In particular the shape and size of the plastic zone ahead of the crack tip is quite different in the two tests at the same nominal remote applied load. (author)
Islam, Muhammad Rabiul; Sakib-Ul-Alam, Md.; Nazat, Kazi Kaarima; Hassan, M. Munir
2017-12-01
FEA results greatly depend on analysis parameters. MSC NASTRAN nonlinear implicit analysis code has been used in large deformation finite element analysis of pitted marine SM490A steel rectangular plate. The effect of two types actual pit shape on parameters of integrity of structure has been analyzed. For 3-D modeling, a proposed method for simulation of pitted surface by probabilistic corrosion model has been used. The result has been verified with the empirical formula proposed by finite element analysis of steel surface generated with different pitted data where analyses have been carried out by the code of LS-DYNA 971. In the both solver, an elasto-plastic material has been used where an arbitrary stress versus strain curve can be defined. In the later one, the material model is based on the J2 flow theory with isotropic hardening where a radial return algorithm is used. The comparison shows good agreement between the two results which ensures successful simulation with comparatively less energy and time.
Sato, Yuichi; Kajihara, Shinichi; Kaneko, Yoshio
2011-06-01
This paper presents three-dimensional finite element (FE) analyses of an all-frame model of a three-story reinforced concrete (RC) building damaged in the 1999 Taiwan Chi-Chi Earthquake. Non-structural brick walls of the building acted as a seismic resistant element although their contributions were neglected in the design. Hence, the entire structure of a typical frame was modeled and static and dynamic nonlinear analyses were conducted to evaluate the contributions of the brick walls. However, the results of the analyses were considerably overestimated due to coarse mesh discretizations, which were unavoidable due to limited computer resources. This study corrects the overestimations by modifying (1) the tensile strengths and (2) shear stiffness reduction factors of concrete and brick. The results indicate that brick walls improve frame strength although shear failures are caused in columns shortened by spandrel walls. Then, the effectiveness of three types of seismic retrofits is evaluated. The maximum drift of the first floor is reduced by 89.3%, 94.8%, and 27.5% by Steel-confined, Full-RC, and Full-brick models, respectively. Finally, feasibility analyses of models with soils were conducted. The analyses indicated that the soils elongate the natural period of building models although no significant differences were observed.
Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu
2018-04-01
In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.
Efficient Non-Linear Finite Element Implementation of Elasto-Plasticity for Geotechnical Problems
DEFF Research Database (Denmark)
Clausen, Johan
-Coulomb yield criterion and the corresponding plastic potential possess corners and an apex, which causes numerical difficulties. A simple, elegant and efficient solution to these problems is presented in this thesis. The solution is based on a transformation into principal stress space and is valid for all...... linear isotropic plasticity models in which corners and apexes are encountered. The validity and merits of the proposed solution are examined in relation to the Mohr-Coulomb and the Modified Mohr-Coulomb material models. It is found that the proposed method compares well with existing methods......-Brown material. The efficiency and validity are demonstrated by comparing the finite-element results with well-known solutions for simple geometries. A common geotechnical problem is the assessment of slope stability. For slopes with simple geometries and consisting of a linear Mohr-Coulomb material, this can...
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
Tsuboi, S.; Miyoshi, T.; Obayashi, M.; Tono, Y.; Ando, K.
2014-12-01
Recent progress in large scale computing by using waveform modeling technique and high performance computing facility has demonstrated possibilities to perform full-waveform inversion of three dimensional (3D) seismological structure inside the Earth. We apply the adjoint method (Liu and Tromp, 2006) to obtain 3D structure beneath Japanese Islands. First we implemented Spectral-Element Method to K-computer in Kobe, Japan. We have optimized SPECFEM3D_GLOBE (Komatitsch and Tromp, 2002) by using OpenMP so that the code fits hybrid architecture of K-computer. Now we could use 82,134 nodes of K-computer (657,072 cores) to compute synthetic waveform with about 1 sec accuracy for realistic 3D Earth model and its performance was 1.2 PFLOPS. We use this optimized SPECFEM3D_GLOBE code and take one chunk around Japanese Islands from global mesh and compute synthetic seismograms with accuracy of about 10 second. We use GAP-P2 mantle tomography model (Obayashi et al., 2009) as an initial 3D model and use as many broadband seismic stations available in this region as possible to perform inversion. We then use the time windows for body waves and surface waves to compute adjoint sources and calculate adjoint kernels for seismic structure. We have performed several iteration and obtained improved 3D structure beneath Japanese Islands. The result demonstrates that waveform misfits between observed and theoretical seismograms improves as the iteration proceeds. We now prepare to use much shorter period in our synthetic waveform computation and try to obtain seismic structure for basin scale model, such as Kanto basin, where there are dense seismic network and high seismic activity. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We used F-net seismograms of the National Research Institute for Earth Science and Disaster Prevention.
Lasche, George; Coldwell, Robert; Metzger, Robert
2017-09-01
A new application (known as "VRF", or "Visual RobFit") for analysis of high-resolution gamma-ray spectra has been developed using non-linear fitting techniques to fit full-spectrum nuclide shapes. In contrast to conventional methods based on the results of an initial peak-search, the VRF analysis method forms, at each of many automated iterations, a spectrum-wide shape for each nuclide and, also at each iteration, it adjusts the activities of each nuclide, as well as user-enabled parameters of energy calibration, attenuation by up to three intervening or self-absorbing materials, peak width as a function of energy, full-energy peak efficiency, and coincidence summing until no better fit to the data can be obtained. This approach, which employs a new and significantly advanced underlying fitting engine especially adapted to nuclear spectra, allows identification of minor peaks that are masked by larger, overlapping peaks that would not otherwise be possible. The application and method are briefly described and two examples are presented.
Abd El Baky, Hussien
This research work is devoted to theoretical and numerical studies on the flexural behaviour of FRP-strengthened concrete beams. The objectives of this research are to extend and generalize the results of simple experiments, to recommend new design guidelines based on accurate numerical tools, and to enhance our comprehension of the bond performance of such beams. These numerical tools can be exploited to bridge the existing gaps in the development of analysis and modelling approaches that can predict the behaviour of FRP-strengthened concrete beams. The research effort here begins with the formulation of a concrete model and development of FRP/concrete interface constitutive laws, followed by finite element simulations for beams strengthened in flexure. Finally, a statistical analysis is carried out taking the advantage of the aforesaid numerical tools to propose design guidelines. In this dissertation, an alternative incremental formulation of the M4 microplane model is proposed to overcome the computational complexities associated with the original formulation. Through a number of numerical applications, this incremental formulation is shown to be equivalent to the original M4 model. To assess the computational efficiency of the incremental formulation, the "arc-length" numerical technique is also considered and implemented in the original Bazant et al. [2000] M4 formulation. Finally, the M4 microplane concrete model is coded in FORTRAN and implemented as a user-defined subroutine into the commercial software package ADINA, Version 8.4. Then this subroutine is used with the finite element package to analyze various applications involving FRP strengthening. In the first application a nonlinear micromechanics-based finite element analysis is performed to investigate the interfacial behaviour of FRP/concrete joints subjected to direct shear loadings. The intention of this part is to develop a reliable bond--slip model for the FRP/concrete interface. The bond
Sudarmaji; Rudianto, Indra; Eka Nurcahya, Budi
2018-04-01
A strong tectonic earthquake with a magnitude of 5.9 Richter scale has been occurred in Yogyakarta and Central Java on May 26, 2006. The earthquake has caused severe damage in Yogyakarta and the southern part of Central Java, Indonesia. The understanding of seismic response of earthquake among ground shaking and the level of building damage is important. We present numerical modeling of 3D seismic wave propagation around Yogyakarta and the southern part of Central Java using spectral-element method on MPI-GPU (Graphics Processing Unit) computer cluster to observe its seismic response due to the earthquake. The homogeneous 3D realistic model is generated with detailed topography surface. The influences of free surface topography and layer discontinuity of the 3D model among the seismic response are observed. The seismic wave field is discretized using spectral-element method. The spectral-element method is solved on a mesh of hexahedral elements that is adapted to the free surface topography and the internal discontinuity of the model. To increase the data processing capabilities, the simulation is performed on a GPU cluster with implementation of MPI (Message Passing Interface).
Entropy viscosity method for nonlinear conservation laws
Guermond, Jean-Luc
2011-05-01
A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.
Entropy viscosity method for nonlinear conservation laws
Guermond, Jean-Luc; Pasquetti, Richard; Popov, Bojan
2011-01-01
A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.
International Nuclear Information System (INIS)
Biffle, J.H.; Blanford, M.L.
1994-05-01
JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere
International Nuclear Information System (INIS)
Biffle, J.H.
1993-02-01
JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere
Non-linear heat transfer computer code by finite element method
International Nuclear Information System (INIS)
Nagato, Kotaro; Takikawa, Noboru
1977-01-01
The computer code THETA-2D for the calculation of temperature distribution by the two-dimensional finite element method was made for the analysis of heat transfer in a high temperature structure. Numerical experiment was performed for the numerical integration of the differential equation of heat conduction. The Runge-Kutta method of the numerical experiment produced an unstable solution. A stable solution was obtained by the β method with the β value of 0.35. In high temperature structures, the radiative heat transfer can not be neglected. To introduce a term of the radiative heat transfer, a functional neglecting the radiative heat transfer was derived at first. Then, the radiative term was added after the discretion by variation method. Five model calculations were carried out by the computer code. Calculation of steady heat conduction was performed. When estimated initial temperature is 1,000 degree C, reasonable heat blance was obtained. In case of steady-unsteady temperature calculation, the time integral by THETA-2D turned out to be under-estimation for enthalpy change. With a one-dimensional model, the temperature distribution in a structure, in which heat conductivity is dependent on temperature, was calculated. Calculation with a model which has a void inside was performed. Finally, model calculation for a complex system was carried out. (Kato, T.)
Analysis of noncoplanar pressurized laminations in X2 steel pipes by non-linear finite element
Energy Technology Data Exchange (ETDEWEB)
Morales, Alfredo [Instituto Tecnologico de Puebla (Mexico). Dept. de Posgrado; Gonzalez, Jorge L.; Hallen, Jose M. [Instituto Politecnico Nacional (Mexico). Escuela Superior de Ingenieria Quimica e Industrias Extractivas (ESIQIE). Dept. de Ingenieria Metalurgica
2005-07-01
Hydrogen induced cracking is of great interest in the mechanical integrity assessment of sour gas pipelines. Multiple stepwise cracks with internal pressure called laminations are often observed in pipelines and their interaction and coalescence may significantly affect the residual strength of the pipes. In this work, the interacting fields of non coplanar pressurized laminations in the wall of a pipe under pressure are analyzed by non-lineal finite element, considering an isotropic hardening law and the real tensile properties of the X52 steel. The results are presented as the evolution of the stress fields in the interlaminar region as a function of the pressure inside the laminations. It is found that for two approaching stepwise laminations the critical pressure follows a hyperbolic type law, thus the effect of the lamination length is principal for greater lengths and for shorter lengths the effect is minimum. The critical pressure is defined as pressure inside the lamination that causes plastification of the interlaminar region. (author)
International Nuclear Information System (INIS)
Rompotis, Dimitrios
2016-02-01
In this work, a single-shot temporal metrology scheme operating in the vacuum-extreme ultraviolet spectral range has been designed and experimentally implemented. Utilizing an anti-collinear geometry, a second-order intensity autocorrelation measurement of a vacuum ultraviolet pulse can be performed by encoding temporal delay information on the beam propagation coordinate. An ion-imaging time-of-flight spectrometer, offering micrometer resolution has been set-up for this purpose. This instrument enables the detection of a magnified image of the spatial distribution of ions exclusively generated by direct two-photon absorption in the combined counter-propagating pulse focus and thus obtain the second-order intensity autocorrelation measurement on a single-shot basis. Additionally, an intense VUV light source based on high-harmonic generation has been experimentally realized. It delivers intense sub-20 fs Ti:Sa fifth-harmonic pulses utilizing a loose-focusing geometry in a long Ar gas cell. The VUV pulses centered at 161.8 nm reach pulse energies of 1.1 μJ per pulse, while the corresponding pulse duration is measured with a second-order, fringe-resolved autocorrelation scheme to be 18 ± 1 fs on average. Non-resonant, two-photon ionization of Kr and Xe and three-photon ionization of Ne verify the fifth-harmonic pulse intensity and indicate the feasibility of multi-photon VUV pump/VUV probe studies of ultrafast atomic and molecular dynamics. Finally, the extended functionally of the counter-propagating pulse metrology approach is demonstrated by a single-shot VUV pump/VUV probe experiment aiming at the investigation of ultrafast dissociation dynamics of O 2 excited in the Schumann-Runge continuum at 162 nm.
Ishak, Muhammad Ikman; Shafi, Aisyah Ahmad; Rosli, M. U.; Khor, C. Y.; Zakaria, M. S.; Rahim, Wan Mohd Faizal Wan Abd; Jamalludin, Mohd Riduan
2017-09-01
The success of dental implant surgery is majorly dependent on the stability of prosthesis to anchor to implant body as well as the integration of implant body to bone. The attachment between dental implant body and abutment plays a vital role in attributing to the stability of dental implant system. A good connection between implant body cavity to abutment may minimize the complications of abutment loosening and implant fractures as widely reported in clinical findings. The aim of this paper is to investigate the effect of different abutment-implant connections on stress dispersion within the abutment and implant bodies as well as displacement of implant body via three-dimensional (3-D) finite element analysis (FEA). A 3-D model of mandible was reconstructed from computed tomography (CT) image datasets using an image-processing software with the selected region of interest was the left side covering the second premolar, first molar and second molar regions. The bone was modelled as compact (cortical) and porous (cancellous) structures. Besides, three implant bodies and three generic models of abutment with different types of connections - tapered interference fit (TIF), tapered integrated screwed-in (TIS) and screw retention (SR) were created using computer-aided design (CAD) software and all models were then analysed via 3D FEA software. Occlusal forces of 114.6 N, 17.2 N and 23.4 N were applied in the axial, lingual and mesio-distal directions, respectively, on the top surface of first molar crown. All planes of the mandibular bone model were rigidly fixed. The result exhibited that abutment with TIS connection produced the most favourable stress and displacement outcomes as compared to other attachment types. This is due to the existence of integrated screw at the bottom portion of tapered abutment which increases the motion resistance.
Directory of Open Access Journals (Sweden)
Jiajie Fan
2017-07-01
Full Text Available With the expanding application of light-emitting diodes (LEDs, the color quality of white LEDs has attracted much attention in several color-sensitive application fields, such as museum lighting, healthcare lighting and displays. Reliability concerns for white LEDs are changing from the luminous efficiency to color quality. However, most of the current available research on the reliability of LEDs is still focused on luminous flux depreciation rather than color shift failure. The spectral power distribution (SPD, defined as the radiant power distribution emitted by a light source at a range of visible wavelength, contains the most fundamental luminescence mechanisms of a light source. SPD is used as the quantitative inference of an LED’s optical characteristics, including color coordinates that are widely used to represent the color shift process. Thus, to model the color shift failure of white LEDs during aging, this paper first extracts the features of an SPD, representing the characteristics of blue LED chips and phosphors, by multi-peak curve-fitting and modeling them with statistical functions. Then, because the shift processes of extracted features in aged LEDs are always nonlinear, a nonlinear state-space model is then developed to predict the color shift failure time within a self-adaptive particle filter framework. The results show that: (1 the failure mechanisms of LEDs can be identified by analyzing the extracted features of SPD with statistical curve-fitting and (2 the developed method can dynamically and accurately predict the color coordinates, correlated color temperatures (CCTs, and color rendering indexes (CRIs of phosphor-converted (pc-white LEDs, and also can estimate the residual color life.
Fan, Jiajie; Mohamed, Moumouni Guero; Qian, Cheng; Fan, Xuejun; Zhang, Guoqi; Pecht, Michael
2017-07-18
With the expanding application of light-emitting diodes (LEDs), the color quality of white LEDs has attracted much attention in several color-sensitive application fields, such as museum lighting, healthcare lighting and displays. Reliability concerns for white LEDs are changing from the luminous efficiency to color quality. However, most of the current available research on the reliability of LEDs is still focused on luminous flux depreciation rather than color shift failure. The spectral power distribution (SPD), defined as the radiant power distribution emitted by a light source at a range of visible wavelength, contains the most fundamental luminescence mechanisms of a light source. SPD is used as the quantitative inference of an LED's optical characteristics, including color coordinates that are widely used to represent the color shift process. Thus, to model the color shift failure of white LEDs during aging, this paper first extracts the features of an SPD, representing the characteristics of blue LED chips and phosphors, by multi-peak curve-fitting and modeling them with statistical functions. Then, because the shift processes of extracted features in aged LEDs are always nonlinear, a nonlinear state-space model is then developed to predict the color shift failure time within a self-adaptive particle filter framework. The results show that: (1) the failure mechanisms of LEDs can be identified by analyzing the extracted features of SPD with statistical curve-fitting and (2) the developed method can dynamically and accurately predict the color coordinates, correlated color temperatures (CCTs), and color rendering indexes (CRIs) of phosphor-converted (pc)-white LEDs, and also can estimate the residual color life.
Jayaprakash, P.; Mohamed, M. Peer; Caroline, M. Lydia
2017-04-01
An organic nonlinear optical single crystal, D-alanine DL-mandelic acid was synthesized and successfully grown by slow evaporation solution growth technique at ambient temperature using solvent of aqueous solution. The unit cell parameters were assessed from single crystal X-ray diffraction analysis. The presence of diverse functional groups and vibrational modes were identified using Fourier Transform Infra Red and Fourier Transform Raman spectral analyses. The chemical structure of grown crystal has been identified by Nuclear Magnetic Resonance spectroscopic study. Ultraviolet-visible spectral analysis reveal that the crystal has lower cut-off wavelength down to 259 nm, is a key factor to exhibit second harmonic generation signal. The electronic optical band gap and Urbach energy is calculated as 5.31 eV and 0.2425 eV respectively from the UV absorption profile. The diverse optical properties such as, extinction coefficient, reflectance, linear refractive index, optical conductivity was calculated using UV-visible data. The relative second harmonic efficiency of the compound is found to be 0.81 times greater than that of KH2PO4 (KDP). The thermal stability of the grown crystal was studied by thermogravimetric analysis and differential thermal analysis techniques. The luminescence spectrum exhibited two peaks (520 nm, 564 nm) due to the donation of protons from carboxylic acid to amino group. The Vickers microhardness test was carried out employing one of the as-grown hard crystal and there by hardness number (Hv), Meyer's index (n), yield strength (σy), elastic stiffness constant (C11) and Knoop hardness number (HK) were assessed. The dielectric behaviour of the as-grown crystal was analyzed for different temperatures (313 K, 333 K, 353 K, and 373 K) at different frequencies.
Kim, Euiyoung; Cho, Maenghyo
2017-11-01
In most non-linear analyses, the construction of a system matrix uses a large amount of computation time, comparable to the computation time required by the solving process. If the process for computing non-linear internal force matrices is substituted with an effective equivalent model that enables the bypass of numerical integrations and assembly processes used in matrix construction, efficiency can be greatly enhanced. A stiffness evaluation procedure (STEP) establishes non-linear internal force models using polynomial formulations of displacements. To efficiently identify an equivalent model, the method has evolved such that it is based on a reduced-order system. The reduction process, however, makes the equivalent model difficult to parameterize, which significantly affects the efficiency of the optimization process. In this paper, therefore, a new STEP, E-STEP, is proposed. Based on the element-wise nature of the finite element model, the stiffness evaluation is carried out element-by-element in the full domain. Since the unit of computation for the stiffness evaluation is restricted by element size, and since the computation is independent, the equivalent model can be constructed efficiently in parallel, even in the full domain. Due to the element-wise nature of the construction procedure, the equivalent E-STEP model is easily characterized by design parameters. Various reduced-order modeling techniques can be applied to the equivalent system in a manner similar to how they are applied in the original system. The reduced-order model based on E-STEP is successfully demonstrated for the dynamic analyses of non-linear structural finite element systems under varying design parameters.
Shuxia, ZHAO; Lei, ZHANG; Jiajia, HOU; Yang, ZHAO; Wangbao, YIN; Weiguang, MA; Lei, DONG; Liantuan, XIAO; Suotang, JIA
2018-03-01
The chemical composition of alloys directly determines their mechanical behaviors and application fields. Accurate and rapid analysis of both major and minor elements in alloys plays a key role in metallurgy quality control and material classification processes. A quantitative calibration-free laser-induced breakdown spectroscopy (CF-LIBS) analysis method, which carries out combined correction of plasma temperature and spectral intensity by using a second-order iterative algorithm and two boundary standard samples, is proposed to realize accurate composition measurements. Experimental results show that, compared to conventional CF-LIBS analysis, the relative errors for major elements Cu and Zn and minor element Pb in the copper-lead alloys has been reduced from 12%, 26% and 32% to 1.8%, 2.7% and 13.4%, respectively. The measurement accuracy for all elements has been improved substantially.
Directory of Open Access Journals (Sweden)
E. Çelebi
2012-11-01
Full Text Available The objective of this paper focuses primarily on the numerical approach based on two-dimensional (2-D finite element method for analysis of the seismic response of infinite soil-structure interaction (SSI system. This study is performed by a series of different scenarios that involved comprehensive parametric analyses including the effects of realistic material properties of the underlying soil on the structural response quantities. Viscous artificial boundaries, simulating the process of wave transmission along the truncated interface of the semi-infinite space, are adopted in the non-linear finite element formulation in the time domain along with Newmark's integration. The slenderness ratio of the superstructure and the local soil conditions as well as the characteristics of input excitations are important parameters for the numerical simulation in this research. The mechanical behavior of the underlying soil medium considered in this prediction model is simulated by an undrained elasto-plastic Mohr-Coulomb model under plane-strain conditions. To emphasize the important findings of this type of problems to civil engineers, systematic calculations with different controlling parameters are accomplished to evaluate directly the structural response of the vibrating soil-structure system. When the underlying soil becomes stiffer, the frequency content of the seismic motion has a major role in altering the seismic response. The sudden increase of the dynamic response is more pronounced for resonance case, when the frequency content of the seismic ground motion is close to that of the SSI system. The SSI effects under different seismic inputs are different for all considered soil conditions and structural types.
International Nuclear Information System (INIS)
Walter, H.; Mang, H.A.
1991-01-01
A procedure for combining nonlinear short-time behavior of concrete with nonlinear creep compliance functions is presented. It is an important ingredient of a computer code for nonlinear finite element (FE) analysis of prestressed concrete shells, considering creep, shrinkage and ageing of concrete, and relaxation of the prestressing steel. The program was developed at the Institute for Strength of Materials of Technical University of Vienna, Austria. The procedure has resulted from efforts to extend the range of application of a Finite Element program, abbreviated as FESIA, which originally was capable of modeling reinforeced concrete in the context of thin-shell analysis, using nonlinear constitutive relations for both, conrete and steel. The extension encompasses the time-dependent behavior of concrete: Creep, shrinkage and ageing. Creep is modeled with the help of creep compliance functions which may be nonlinear to conform with the short-time constitutive relations. Ageing causes an interdependence between long-time and short-time deformations. The paper contains a description of the physical background of the procedure and hints on the implementation of the algorithm. The focus is on general aspects. Details of the aforementioned computer program are considered only where this is inevitable. (orig.)
International Nuclear Information System (INIS)
Peng, Han Min; Ding, Qing Jun; Hui, Yao; Li, Hua Feng; Zhao, Chun Sheng
2010-01-01
Ionic polymer–metal composites (IPMC) are a class of electroactive polymers (EAP), and they currently attract numerous researchers to study their performance characteristics and applications. However, research on its start-up characteristics still requires more attention. In the IPMC start-up state (the moment of applying an actuation voltage at the very beginning), its mechanical performance is different in the stable working state (working for at least 10 min). Therefore, this paper focuses on three performance relationships of an IPMC strip between its maximal tip deformation and voltage, its maximal stress and voltage, as well as its maximal strain and voltage, both in the two states. Different from other reports, we found that they present nonlinear tendencies in the start-up state rather than linear ones. Therefore, based on the equivalent bimorph beam model, a finite element electromechanical coupling calculation module in the ANSYS software was utilized to simulate these characteristics. Furthermore, a test system is introduced to validate the phenomena. As a whole, these three relationships and the FEA method may be beneficial for providing control strategies effectively to IPMC actuators, especially in their start-up states
Non-linear finite element model to assess the effect of tendon forces on the foot-ankle complex.
Morales-Orcajo, Enrique; Souza, Thales R; Bayod, Javier; Barbosa de Las Casas, Estevam
2017-11-01
A three-dimensional foot finite element model with actual geometry and non-linear behavior of tendons is presented. The model is intended for analysis of the lower limb tendon forces effect in the inner foot structure. The geometry of the model was obtained from computational tomographies and magnetic resonance images. Tendon tissue was characterized with the first order Ogden material model based on experimental data from human foot tendons. Kinetic data was employed to set the load conditions. After model validation, a force sensitivity study of the five major foot extrinsic tendons was conducted to evaluate the function of each tendon. A synergic work of the inversion-eversion tendons was predicted. Pulling from a peroneus or tibialis tendon stressed the antagonist tendons while reducing the stress in the agonist. Similar paired action was predicted for the Achilles tendon with the tibialis anterior. This behavior explains the complex control motion performed by the foot. Furthermore, the stress state at the plantar fascia, the talocrural joint cartilage, the plantar soft tissue and the tendons were estimated in the early and late midstance phase of walking. These estimations will help in the understanding of the functional role of the extrinsic muscle-tendon-units in foot pronation-supination. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Wolf, J.P.; Darbre, G.R.
1985-01-01
The computational procedure of the so-called truncated indirect boundary-element method is derived. The latter, which is non-local in space and time, represents a rigorous generally applicable procedure for taking into account a layered halfspace in a non-linear soil-structure interaction analysis. As an example, the non-linear soil-structure interaction analysis of a structure embedded in a halfspace with partial uplift of the basement and separation of the side wall is investigated. (orig.)
Kardaś, Tomasz M.; Nejbauer, Michał; Wnuk, Paweł; Resan, Bojan; Radzewicz, Czesław; Wasylczyk, Piotr
2017-02-01
Although new optical materials continue to open up access to more and more wavelength bands where femtosecond laser pulses can be generated, light frequency conversion techniques are still indispensable in filling the gaps on the ultrafast spectral scale. With high repetition rate, low pulse energy laser sources (oscillators) tight focusing is necessary for a robust wave mixing and the efficiency of broadband nonlinear conversion is limited by diffraction as well as spatial and temporal walk-off. Here we demonstrate a miniature third harmonic generator (tripler) with conversion efficiency exceeding 30%, producing 246 fs UV pulses via cascaded second order processes within a single laser beam focus. Designing this highly efficient and ultra compact frequency converter was made possible by full 3-dimentional modelling of propagation of tightly focused, broadband light fields in nonlinear and birefringent media.
Directory of Open Access Journals (Sweden)
Wang Peng
2016-01-01
Full Text Available A family of prismatic and hexahedral solid‒shell (SHB elements with their linear and quadratic versions is presented in this paper to model thin 3D structures. Based on reduced integration and special treatments to eliminate locking effects and to control spurious zero-energy modes, the SHB solid‒shell elements are capable of modeling most thin 3D structural problems with only a single element layer, while describing accurately the various through-thickness phenomena. In this paper, the SHB elements are combined with fully 3D behavior models, including orthotropic elastic behavior for composite materials and anisotropic plastic behavior for metallic materials, which allows describing the strain/stress state in the thickness direction, in contrast to traditional shell elements. All SHB elements are implemented into ABAQUS using both standard/quasi-static and explicit/dynamic solvers. Several benchmark tests have been conducted, in order to first assess the performance of the SHB elements in quasi-static and dynamic analyses. Then, deep drawing of a hemispherical cup is performed to demonstrate the capabilities of the SHB elements in handling various types of nonlinearities (large displacements and rotations, anisotropic plasticity, and contact. Compared to classical ABAQUS solid and shell elements, the results given by the SHB elements show good agreement with the reference solutions.
Energy Technology Data Exchange (ETDEWEB)
Azadi, Mohammad [Sharif University of Technology, Tehran (Iran, Islamic Republic of); Azadi, Mahboobeh [Shiraz University, Shiraz (Iran, Islamic Republic of)
2009-10-15
Nonlinear transient heat transfer and thermoelastic stress analyses of a thick-walled FGM cylinder with temperature dependent materials are performed by using the Hermitian transfinite element method. Temperature-dependency of the material properties has not been taken into account in transient thermoelastic analysis, so far. Due to the mentioned dependency, the resulting governing FEM equations of transient heat transfer are highly nonlinear. Furthermore, in all finite element analysis performed so far in the field, Lagrangian elements have been used. To avoid an artificial local heat source at the mutual boundaries of the elements, Hermitian elements are used instead in the present research. Another novelty of the present paper is simultaneous use of the transfinite element method and updating technique. Time variations of the temperature, displacements, and stresses are obtained through a numerical Laplace inversion. Finally, results obtained considering the temperature-dependency of the material properties are compared with those derived based on temperature independency assumption. Furthermore, the temperature distribution and the radial and circumferential stresses are investigated versus time, geometrical parameters and index of power law. Results reveal that the temperature-dependency effect is significant
Pitton, Giuseppe; Heltai, Luca
2018-01-01
Non Uniform Rational B-spline (NURBS) patches are a standard way to describe complex geometries in Computer Aided Design tools, and have gained a lot of popularity in recent years also for the approximation of partial differential equations, via the Isogeometric Analysis (IGA) paradigm. However, spectral accuracy in IGA is limited to relatively small NURBS patch degrees (roughly p
International Nuclear Information System (INIS)
Kraus, H.G.; Jones, J.L.
1986-01-01
The problem of non-linear superconducting magnet and electrical protection circuit system transients is formulated. To enable studying the effects of coil normalization transients, coil distortion (due to imbalanced magnetic forces), internal coil arcs and shorts, and other normal and off-normal circuit element responses, the following capabilities are included: temporal, voltage and current-dependent voltage sources, current sources, resistors, capacitors and inductors. The concept of self-mutual inductance, and the form of the associated inductance matrix, is discussed for internally shorted coils. This is a Kirchhoff's voltage loop law and Kirchhoff's current node law formulation. The non-linear integrodifferential equation set is solved via a unique hybrid finite difference/integral finite element technique. (author)
Rasouli, Zolaikha; Ghavami, Raouf
2016-08-01
Vanillin (VA), vanillic acid (VAI) and syringaldehyde (SIA) are important food additives as flavor enhancers. The current study for the first time is devote to the application of partial least square (PLS-1), partial robust M-regression (PRM) and feed forward neural networks (FFNNs) as linear and nonlinear chemometric methods for the simultaneous detection of binary and ternary mixtures of VA, VAI and SIA using data extracted directly from UV-spectra with overlapped peaks of individual analytes. Under the optimum experimental conditions, for each compound a linear calibration was obtained in the concentration range of 0.61-20.99 [LOD = 0.12], 0.67-23.19 [LOD = 0.13] and 0.73-25.12 [LOD = 0.15] μg mL- 1 for VA, VAI and SIA, respectively. Four calibration sets of standard samples were designed by combination of a full and fractional factorial designs with the use of the seven and three levels for each factor for binary and ternary mixtures, respectively. The results of this study reveal that both the methods of PLS-1 and PRM are similar in terms of predict ability each binary mixtures. The resolution of ternary mixture has been accomplished by FFNNs. Multivariate curve resolution-alternating least squares (MCR-ALS) was applied for the description of spectra from the acid-base titration systems each individual compound, i.e. the resolution of the complex overlapping spectra as well as to interpret the extracted spectral and concentration profiles of any pure chemical species identified. Evolving factor analysis (EFA) and singular value decomposition (SVD) were used to distinguish the number of chemical species. Subsequently, their corresponding dissociation constants were derived. Finally, FFNNs has been used to detection active compounds in real and spiked water samples.
Martin, Roland; Chevrot, Sébastien; Komatitsch, Dimitri; Seoane, Lucia; Spangenberg, Hannah; Wang, Yi; Dufréchou, Grégory; Bonvalot, Sylvain; Bruinsma, Sean
2017-04-01
We image the internal density structure of the Pyrenees by inverting gravity data using an a priori density model derived by scaling a Vp model obtained by full waveform inversion of teleseismic P-waves. Gravity anomalies are computed via a 3-D high-order finite-element integration in the same high-order spectral-element grid as the one used to solve the wave equation and thus to obtain the velocity model. The curvature of the Earth and surface topography are taken into account in order to obtain a density model as accurate as possible. The method is validated through comparisons with exact semi-analytical solutions. We show that the spectral-element method drastically accelerates the computations when compared to other more classical methods. Different scaling relations between compressional velocity and density are tested, and the Nafe-Drake relation is the one that leads to the best agreement between computed and observed gravity anomalies. Gravity data inversion is then performed and the results allow us to put more constraints on the density structure of the shallow crust and on the deep architecture of the mountain range.
Wittek, Adam; Joldes, Grand; Couton, Mathieu; Warfield, Simon K; Miller, Karol
2010-12-01
Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear finite element procedures implemented on a graphics processing unit (GPU). In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian formulation with explicit time stepping and dynamic relaxation. We used patient-specific finite element meshes consisting of hexahedral and non-locking tetrahedral elements, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial finite element solver executed on a personal computer. Copyright © 2010 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Park, Hyung Kui; Hahm, Dea Gi; Choi, In Kil [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2013-10-15
The sensitivity of the concrete strength is relatively higher compared to that of the steel strength. According to changes in the structure of the material, about 6-10% ultimate internal pressure differences occurred. Thirty sets of an FE model considering the material uncertainty of concrete and steel were composed for the internal pressure fragility assessment. From the internal pressure fragility assessment of the target containment building, the median capacity of liner leakage is estimated to be 116 psi. As can be seen from the Fukushima nuclear power plant accident, the containment building is the final protecting shield to prevent radiation leakage. Thus, a structural soundness evaluation for the containment pressure loads owing to a severe accident is very important. Recently, a probabilistic safety assessment has been commonly used to take into account the possible factors of uncertainty in a structural system. An assessment of the internal pressure fragility of the CANDU type containment buildings considering the correlation of structural material variables, and an assessment of the internal pressure fragility of the CANDU type containment buildings using a nonlinear finite element analysis, were also performed. However, for PWR type containment buildings, a fragility assessment has not been performed yet using a nonlinear finite element model (FEM) analysis. In this study, for the Hanul NPP units 3 and 4 containment building, the internal pressure fragility assessment was established using an FEM analysis. To do this, a three-dimensional finite element model, material property values, and a sensitive analysis were developed. A nonlinear finite element analysis of the Hanul NPP units 3 and 4 containment building was performed for a material sensitivity analysis and internal pressure fragility assessment.
International Nuclear Information System (INIS)
Park, Hyung Kui; Hahm, Dea Gi; Choi, In Kil
2013-01-01
The sensitivity of the concrete strength is relatively higher compared to that of the steel strength. According to changes in the structure of the material, about 6-10% ultimate internal pressure differences occurred. Thirty sets of an FE model considering the material uncertainty of concrete and steel were composed for the internal pressure fragility assessment. From the internal pressure fragility assessment of the target containment building, the median capacity of liner leakage is estimated to be 116 psi. As can be seen from the Fukushima nuclear power plant accident, the containment building is the final protecting shield to prevent radiation leakage. Thus, a structural soundness evaluation for the containment pressure loads owing to a severe accident is very important. Recently, a probabilistic safety assessment has been commonly used to take into account the possible factors of uncertainty in a structural system. An assessment of the internal pressure fragility of the CANDU type containment buildings considering the correlation of structural material variables, and an assessment of the internal pressure fragility of the CANDU type containment buildings using a nonlinear finite element analysis, were also performed. However, for PWR type containment buildings, a fragility assessment has not been performed yet using a nonlinear finite element model (FEM) analysis. In this study, for the Hanul NPP units 3 and 4 containment building, the internal pressure fragility assessment was established using an FEM analysis. To do this, a three-dimensional finite element model, material property values, and a sensitive analysis were developed. A nonlinear finite element analysis of the Hanul NPP units 3 and 4 containment building was performed for a material sensitivity analysis and internal pressure fragility assessment
Institute of Scientific and Technical Information of China (English)
朱卫平; 黄黔
2002-01-01
In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinearbehaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite elementare expanded by taking root-mean-square value of circumferential strains of the shells as aperturbation parameter. The load steps and the iteration times are not cs arbitrary andunpredictable as in usual nonlinear analysis. Instead, there are certain relations betweenthe load steps and the displacement increments, and no need of iteration for each loadstep. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander' s nonlinear geometric equations of moderate smallrotation are used, and the shell made of more than one material ply is also considered.
International Nuclear Information System (INIS)
FEHL, DAVID LEE; BIGGS, F.; CHANDLER, GORDON A.; STYGAR, WILLIAM A.
2000-01-01
The generalized method of Backus and Gilbert (BG) is described and applied to the inverse problem of obtaining spectra from a 5-channel, filtered array of x-ray detectors (XRD's). This diagnostic is routinely fielded on the Z facility at Sandia National Laboratories to study soft x-ray photons ((le)2300 eV), emitted by high density Z-pinch plasmas. The BG method defines spectral resolution limits on the system of response functions that are in good agreement with the unfold method currently in use. The resolution so defined is independent of the source spectrum. For noise-free, simulated data the BG approximating function is also in reasonable agreement with the source spectrum (150 eV black-body) and the unfold. This function may be used as an initial trial function for iterative methods or a regularization model
International Nuclear Information System (INIS)
Lawson, K.; Peacock, N.; Gianella, R.
1998-12-01
The derivation of elemental components of radiated powers and impurity concentrations in bulk tokamak plasmas is complex, often requiring a full description of the impurity transport. A novel, empirical method, the Line Intensity Normalization Technique (LINT) has been developed on the JET (Joint European Torus) tokamak to provide routine information about the impurity content of the plasma and elemental components of radiated power (P rad ). The technique employs a few VUV and XUV resonance line intensities to represent the intrinsic impurity elements in the plasma. From a data base comprising these spectral features, the total bolometric measurement of the radiated power and the Z eff measured by visible spectroscopy, separate elemental components of P rad and Z eff are derived. The method, which converts local spectroscopic signals into global plasma parameters, has the advantage of simplicity, allowing large numbers of pulses to be processed, and, in many operational modes of JET, is found to be both reliable and accurate. It relies on normalizing the line intensities to the absolute calibration of the bolometers and visible spectrometers, using coefficients independent of density and temperature. Accuracies of the order of ± 15% can be achieved for the elemental P rad components of the most significant impurities and the impurity concentrations can be determined to within ±30%. Trace elements can be monitored, although with reduced accuracy. The present paper deals with limiter discharges, which have been the main application to date. As a check on the technique and to demonstrate the value of the LINT results, they have been applied to the transport modelling of intrinsic impurities carried out with the SANCO transport code, which uses atomic data from ADAS. The simulations provide independent confirmation of the concentrations empirically derived using the LINT technique. For this analysis, the simple case of the L-mode regime is considered, the chosen
Energy Technology Data Exchange (ETDEWEB)
Fauqueux, S.
2003-02-01
We consider the propagation of elastic waves in unbounded domains. A new formulation of the linear elasticity system as an H (div) - L{sup 2} system enables us to use the 'mixed spectral finite element method', This new method is based on the definition of new spaces of approximation and the use of mass-lumping. It leads to an explicit scheme with reduced storage and provides the same solution as the spectral finite element method. Then, we model unbounded domains by using Perfectly Matched Layers. Instabilities in the PML in the case of particular 2D elastic media are pointed out and investigated. The numerical method is validated and tested in the case of acoustic and elastic realistic models. A plane wave analysis gives results about numerical dispersion and shows that meshes adapted to the physical and geometrical properties of the media are more accurate than the others. Then, an extension of the method to fluid-solid coupling is introduced for 2D seismic propagation. (author)
Nakamura, Yoshinori; Kanbara, Ryo; Ochiai, Kent T; Tanaka, Yoshinobu
2014-10-01
The mechanical evaluation of the function of partial removable dental prostheses with 3-dimensional finite element modeling requires the accurate assessment and incorporation of soft tissue behavior. The differential behaviors of the residual ridge mucosa and periodontal ligament tissues have been shown to exhibit nonlinear displacement. The mathematic incorporation of known values simulating nonlinear soft tissue behavior has not been investigated previously via 3-dimensional finite element modeling evaluation to demonstrate the effect of prosthesis design on the supporting tissues. The purpose of this comparative study was to evaluate the functional differences of 3 different partial removable dental prosthesis designs with 3-dimensional finite element analysis modeling and a simulated patient model incorporating known viscoelastic, nonlinear soft tissue properties. Three different designs of distal extension removable partial dental prostheses were analyzed. The stress distributions to the supporting abutments and soft tissue displacements of the designs tested were calculated and mechanically compared. Among the 3 dental designs evaluated, the RPI prosthesis demonstrated the lowest stress concentrations on the tissue supporting the tooth abutment and also provided wide mucosa-borne areas of support, thereby demonstrating a mechanical advantage and efficacy over the other designs evaluated. The data and results obtained from this study confirmed that the functional behavior of partial dental prostheses with supporting abutments and soft tissues are consistent with the conventional theories of design and clinical experience. The validity and usefulness of this testing method for future applications and testing protocols are shown. Copyright © 2014 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Terry, J.L.; Manning, H.L.; Marmar, E.S.
1986-07-01
Two methods which together allow sensitivity calibration from 20 A to 430 A are described in detail. The first method, useful up to 120 A, uses a low power source to generate Kα x-rays which are alternately viewed by an absolute detector (a proportional counter) and the spectrometer. The second method extends that calibration to 430 A. It relies on the 2:1 brightness ratio of bright doublet lines from impurity ions which have a single outer shell electron and which are present in hot, magnetically confined plasmas. It requires that the absolute sensitivity of the spectrometer be known at one wavelength point, and in practice requires a multi-element spectral detector
Energy Technology Data Exchange (ETDEWEB)
Anufrik, S S; Mostovnikov, V A; Rubinov, A N
1976-03-01
By doubling the generation frequency of an organic dye laser with lamp pumping, radiation is obtained in the spectral region of 285 to 305 nm. Depending on the mode of operation of a given laser the spectral width of the uv-radiation was 0.5 or approximately 0.003 nm. The maximum energy of second harmonic pulses was equal to approximately 0.01 J. (SJR)
Institute of Scientific and Technical Information of China (English)
高夫征
2005-01-01
A finite volume element predictor-correetor method for a class of nonlinear parabolic system of equations is presented and analyzed. Suboptimal L2 error estimate for the finite volume element predictor-corrector method is derived. A numerical experiment shows that the numerical results are consistent with theoretical analysis.
Evidence for bifurcation and universal chaotic behavior in nonlinear semiconducting devices
International Nuclear Information System (INIS)
Testa, J.; Perez, J.; Jeffries, C.
1982-01-01
Bifurcations, chaos, and extensive periodic windows in the chaotic regime are observed for a driven LRC circuit, the capacitive element being a nonlinear varactor diode. Measurements include power spectral analysis; real time amplitude data; phase portraits; and a bifurcation diagram, obtained by sampling methods. The effects of added external noise are studied. These data yield experimental determinations of several of the universal numbers predicted to characterize nonlinear systems having this route to chaos
Matsuura, Yusuke; Kuniyoshi, Kazuki; Suzuki, Takane; Ogawa, Yasufumi; Sukegawa, Koji; Rokkaku, Tomoyuki; Takahashi, Kazuhisa
2014-11-01
Distal radius fracture, which often occurs in the setting of osteoporosis, can lead to permanent deformity and disability. Great effort has been directed toward developing noninvasive methods for evaluating the distal radius strength, with the goal of assessing fracture risk. The aim of this study was to evaluate distal radius strength using a finite element model and to gauge the accuracy of finite element model measurement using cadaver material. Ten wrists were obtained from cadavers with a mean age of 89.5 years at death. CT images of each wrist in an extended position were obtained. CT-based finite element models were prepared with Mechanical Finder software. Fracture on the models was simulated by applying a mechanical load to the palm in a direction parallel to the forearm axis, after which the fracture load and the site at which the fracture began were identified. For comparison, the wrists were fractured using a universal testing machine and the fracture load and the site of fracture were identified. The fracture load was 970.9 N in the finite element model group and 990.0 N in the actual measurement group. The site of the initial fracture was extra-articular to the distal radius in both groups. The finite element model was predictive for distal radius fracture when compared to the actual measurement. In this study, a finite element model for evaluation of distal radius strength was validated and can be used to predict fracture risk. We conclude that a finite element model is useful for the evaluation of distal radius strength. Knowing distal radius strength might avoid distal radius fracture because appropriate antiosteoporotic treatment can be initiated.
International Nuclear Information System (INIS)
Luehrmann, L.; Noseck, U.
1996-03-01
While the verification report on CHET1 primarily focused on aspects such as the correctness of algorithms with respect to the modeling of advection, dispersion and diffusion, the report in hand is intended to primarily deal with nonlinear sorption and numerical sorption modeling. Another aspect discussed is the correct treatment of decay within established radioactive decay chains. First, the physical fundamentals are explained of the processes determining the radionuclide transport in the cap rock, and hence are the basis of the program discussed. The numeric algorithms the CHET2 code is based are explained, showing the details of realisation and the function of the various defaults and corrections. The iterative coupling of transport and sorption computation is illustrated by means of a program flowchart. Furthermore, the actvities for verification of the program are explained, as well as qualitative effects of computations assuming concentration-dependent sorption. The computation of the decay within decay chains is verified, and application programming using nonlinear sorption isotherms as well as the entire process of transport calculations with CHET2 are shown. (orig./DG) [de
Nonlinear frequency conversion in fiber lasers
DEFF Research Database (Denmark)
Svane, Ask Sebastian
The concept of nonlinear frequency conversion entails generating light at new frequencies other than those of the source light. The emission wavelength of typical fiber laser systems, relying on rare-earth dopants, are constrained within specific bands of the infrared region. By exploiting...... nonlinear processes, light from these specific wavelength bands can be used to generate light at new frequencies otherwise not obtainable by rare-earth elements. This thesis describes work covering Raman fiber lasers (RFLs) and amplifiers for nonlinear frequency down-conversion, and also the method...... of fiberoptic Cherenkov radiation (FCR) using ultrafast pulses as a means for generating tunable visible (VIS) light at higher frequencies. Two different polarization maintaining (PM) RFL cavities are studied with an emphasis on stability and spectral broadening. The cavities are formed by inscription of fiber...
Terahertz Nonlinear Optics in Semiconductors
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.
2013-01-01
We demonstrate the nonlinear optical effects – selfphase modulation and saturable absorption of a single-cycle THz pulse in a semiconductor. Resulting from THz-induced modulation of Drude plasma, these nonlinear optical effects, in particular, lead to self-shortening and nonlinear spectral...... breathing of a single-cycle THz pulse in a semiconductor....
de Wit, A.J.; Akcay-Perdahcioglu, Didem; van den Brink, W.M.; de Boer, Andries; Rolfes, R.; Jansen, E.L.
2011-01-01
Depending on the type of analysis, Finite Element(FE) models of different fidelity are necessary. Creating these models manually is a labor intensive task. This paper discusses a generic approach for generating FE models of different fidelity from a single reference FE model. These different
Energy Technology Data Exchange (ETDEWEB)
Sarler, B; Alujevic, A [Univerza B. Kardelja, Institut ' Jozef Stefan' , Ljubljana (Yugoslavia)
1988-07-01
The basic principles of self-adaptive algorithm for treatment of transient nonlinear nonhomogeneous radial heat flow, based on direct Boundary Element method formulation, are presented. The indicators of discretization error are developed, together with binary-tree strategy for manipulation with time domain mesh, assuring automatic optimisation of calculation procedure with respect to predetermined error. The developed method is particularly suitable for use in a spectrum of extremely nonlinear cases, occurring in thermal analyses of reactor components.(author)
Varga, Peter; Schwiedrzik, Jakob; Zysset, Philippe K; Fliri-Hofmann, Ladina; Widmer, Daniel; Gueorguiev, Boyko; Blauth, Michael; Windolf, Markus
2016-04-01
Osteoporotic proximal femur fractures are caused by low energy trauma, typically when falling on the hip from standing height. Finite element simulations, widely used to predict the fracture load of femora in fall, usually include neither mass-related inertial effects, nor the viscous part of bone׳s material behavior. The aim of this study was to elucidate if quasi-static non-linear homogenized finite element analyses can predict in vitro mechanical properties of proximal femora assessed in dynamic drop tower experiments. The case-specific numerical models of 13 femora predicted the strength (R(2)=0.84, SEE=540N, 16.2%), stiffness (R(2)=0.82, SEE=233N/mm, 18.0%) and fracture energy (R(2)=0.72, SEE=3.85J, 39.6%); and provided fair qualitative matches with the fracture patterns. The influence of material anisotropy was negligible for all predictions. These results suggest that quasi-static homogenized finite element analysis may be used to predict mechanical properties of proximal femora in the dynamic sideways fall situation. Copyright © 2015 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
M. Bauwens
2010-11-01
Full Text Available A long standing problem in paleoceanography concerns the reconstruction of water temperature from δ^{18}O carbonate. It is problematic in the case of freshwater influenced environments because the δ^{18}O isotopic composition of the ambient water (related to salinity needs to be known. In this paper we argue for the use of a nonlinear multi-proxy method called Weight Determination by Manifold Regularization (WDMR to develop a temperature reconstruction model that is less sensitive to salinity variations. The motivation for using this type of model is twofold: firstly, observed nonlinear relations between specific proxies and water temperature motivate the use of nonlinear models. Secondly, the use of multi-proxy models enables salinity related variations of a given temperature proxy to be explained by salinity-related information carried by a separate proxy. Our findings confirm that Mg/Ca is a powerful paleothermometer and highlight that reconstruction performance based on this proxy is improved significantly by combining its information with the information for other trace elements in multi-proxy models. Although the models presented here are black-box models that do not use any prior knowledge about the proxies, the comparison of model reconstruction performances based on different proxy combinations do yield useful information about proxy characteristics. Using Mg/Ca, Sr/Ca, Ba/Ca and Pb/Ca the WDMR model enables a temperature reconstruction with a root mean squared error of ± 2.19 °C for a salinity range between 15 and 32.
International Nuclear Information System (INIS)
1983-04-01
VISCOT is a non-linear, transient, thermal-stress finite-element code designed to determine the viscoelastic, fiscoplastic, or elastoplastic deformation of a rock mass due to mechanical and thermal loading. The numerical solution of the nonlinear incremental equilibrium equations within VISCOT is performed by using an explicit Euler time-stepping scheme. The rock mass may be modeled as a viscoplastic or viscoelastic material. The viscoplastic material model can be described by a Tresca, von Mises, Drucker-Prager or Mohr-Coulomb yield criteria (with or without strain hardening) with an associated flow rule which can be a power or an exponential law. The viscoelastic material model within VISCOT is a temperature- and stress-dependent law which has been developed specifically for salt rock masses by Pfeifle, Mellegard and Senseny in ONWI-314 topical report (1981). Site specific parameters for this creep law at the Richton, Permian, Paradox and Vacherie salt sites have been calculated and are given in ONWI-314 topical report (1981). A major application of VISCOT (in conjunction with a SCEPTER heat transfer code such as DOT) is the thermomechanical analysis of a rock mass such as salt in which significant time-dependent nonlinear deformations are expected to occur. Such problems include room- and canister-scale studies during the excavation, operation, and long-term post-closure stages in a salt repository. In Section 1.5 of this document the code custodianship and control is described along with the status of verification, validation and peer review of this report
Lundström, T; Jonas, T; Volkwein, A
2008-01-01
Thirteen Norway spruce [Picea abies (L.) Karst.] trees of different size, age, and social status, and grown under varying conditions, were investigated to see how they react to complex natural static loading under summer and winter conditions, and how they have adapted their growth to such combinations of load and tree state. For this purpose a non-linear finite-element model and an extensive experimental data set were used, as well as a new formulation describing the degree to which the exploitation of the bending stress capacity is uniform. The three main findings were: material and geometric non-linearities play important roles when analysing tree deflections and critical loads; the strengths of the stem and the anchorage mutually adapt to the local wind acting on the tree crown in the forest canopy; and the radial stem growth follows a mechanically high-performance path because it adapts to prevailing as well as acute seasonal combinations of the tree state (e.g. frozen or unfrozen stem and anchorage) and load (e.g. wind and vertical and lateral snow pressure). Young trees appeared to adapt to such combinations in a more differentiated way than older trees. In conclusion, the mechanical performance of the Norway spruce studied was mostly very high, indicating that their overall growth had been clearly influenced by the external site- and tree-specific mechanical stress.
Understanding Soliton Spectral Tunneling as a Spectral Coupling Effect
DEFF Research Database (Denmark)
Guo, Hairun; Wang, Shaofei; Zeng, Xianglong
2013-01-01
Soliton eigenstate is found corresponding to a dispersive phase profile under which the soliton phase changes induced by the dispersion and nonlinearity are instantaneously counterbalanced. Much like a waveguide coupler relying on a spatial refractive index profile that supports mode coupling...... between channels, here we suggest that the soliton spectral tunneling effect can be understood supported by a spectral phase coupler. The dispersive wave number in the spectral domain must have a coupler-like symmetric profile for soliton spectral tunneling to occur. We show that such a spectral coupler...
Tesoniero, A.; Leng, K.; Long, M. D.; Nissen-Meyer, T.
2017-12-01
Constraining the nature of the anisotropy in the core-mantle boundary region is a key factor for properly predicting the flow of the lowermost mantle. The lack of seismic waves sampling this region and their uneven azimuthal distribution hamper a correct representation of mantle dynamics. We present preliminary results for a series of SKS-SKKS splitting analysis based on numerical forward synthetic tests in a realistic 3-D Earth model using the software AXISEM3D, a newly developed efficient hybrid spectral element method solver for 3-D structures. The anisotropic property of the computational domain in the bottom 300km of the Earth's mantle is fully described with a fourth-order elastic tensor with 21 independent coefficients. We tested a single crystal mineralogy of postperovskite with different orientations that are consistent with realistic mantle flow models and accounted for a wide coverage of azimuthal seismic raypaths. We take advantage of the computational efficiency of the method to achieve resolutions for seismic periods as low as 8s. Our preliminary results, based on forward full waveform modeling, represent a step forward for validating hypotheses for the anisotropy in the D'' layer derived by direct splitting measurements and ray-theoretical mineral physics based modeling tests. Our study also highlights the capability of AXISEM3D to handle high degrees of model complexity in full anisotropy and its potentials for future endeavours.
Żak, A.; Krawczuk, M.; Palacz, M.; Doliński, Ł.; Waszkowiak, W.
2017-11-01
In this work results of numerical simulations and experimental measurements related to the high frequency dynamics of an aluminium Timoshenko periodic beam are presented. It was assumed by the authors that the source of beam structural periodicity comes from periodical alterations to its geometry due to the presence of appropriately arranged drill-holes. As a consequence of these alterations dynamic characteristics of the beam are changed revealing a set of frequency band gaps. The presence of the frequency band gaps can help in the design process of effective sound filters or sound barriers that can selectively attenuate propagating wave signals of certain frequency contents. In order to achieve this a combination of three numerical techniques were employed by the authors. They comprise the application of the Time-domain Spectral Finite Element Method in the case of analysis of finite and semi-infinite computational domains, damage modelling in the case of analysis of drill-hole influence, as well as the Bloch reduction in the case of analysis of periodic computational domains. As an experimental technique the Scanning Laser Doppler Vibrometry was chosen. A combined application of all these numerical and experimental techniques appears as new for this purpose and not reported in the literature available.
He, Yue-Jing; Hung, Wei-Chih; Syu, Cheng-Jyun
2017-12-01
The finite-element method (FEM) and eigenmode expansion method (EEM) were adopted to analyze the guided modes and spectrum of phase-shift fiber Bragg grating at five phase-shift degrees (including zero, 1/4π, 1/2π, 3/4π, and π). In previous studies on optical fiber grating, conventional coupled-mode theory was crucial. This theory contains abstruse knowledge about physics and complex computational processes, and thus is challenging for users. Therefore, a numerical simulation method was coupled with a simple and rigorous design procedure to help beginners and users to overcome difficulty in entering the field; in addition, graphical simulation results were presented. To reduce the difference between the simulated context and the actual context, a perfectly matched layer and perfectly reflecting boundary were added to the FEM and the EEM. When the FEM was used for grid cutting, the object meshing method and the boundary meshing method proposed in this study were used to effectively enhance computational accuracy and substantially reduce the time required for simulation. In summary, users can use the simulation results in this study to easily and rapidly design an optical fiber communication system and optical sensors with spectral characteristics.
Garai, Anirban; Diosady, Laslo T.; Murman, Scott M.; Madavan, Nateri K.
2016-01-01
Recent progress towards developing a new computational capability for accurate and efficient high-fidelity direct numerical simulation (DNS) and large-eddy simulation (LES) of turbomachinery is described. This capability is based on an entropy- stable Discontinuous-Galerkin spectral-element approach that extends to arbitrarily high orders of spatial and temporal accuracy, and is implemented in a computationally efficient manner on a modern high performance computer architecture. An inflow turbulence generation procedure based on a linear forcing approach has been incorporated in this framework and DNS conducted to study the effect of inflow turbulence on the suction- side separation bubble in low-pressure turbine (LPT) cascades. The T106 series of airfoil cascades in both lightly (T106A) and highly loaded (T106C) configurations at exit isentropic Reynolds numbers of 60,000 and 80,000, respectively, are considered. The numerical simulations are performed using 8th-order accurate spatial and 4th-order accurate temporal discretization. The changes in separation bubble topology due to elevated inflow turbulence is captured by the present method and the physical mechanisms leading to the changes are explained. The present results are in good agreement with prior numerical simulations but some expected discrepancies with the experimental data for the T106C case are noted and discussed.
Spectral element simulation of ultrafiltration
DEFF Research Database (Denmark)
Hansen, M.; Barker, Vincent A.; Hassager, Ole
1998-01-01
for the unknowns at the mesh nodes. This system is solved via a technique combining the penalty method, Newton-Raphson iterations, static condensation, and a solver for banded linear systems. In addition, a smoothing technique is used to handle a singularity in the boundary condition at the membrane...
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.
International Nuclear Information System (INIS)
Sun Feng; Pan Rong
2014-01-01
According to a large-span half-steel-concrete (HSC) composited beam in the composited roof in the HTR-PM, a 1:3 scale specimen is investigated by the static load test. By analyzing the loading, deflection, strain and fracture development of the specimen in the process, studying the mechanical characteristics and failure pattern of such components. The ANSYS finite element software is utilized in this paper to analyze the nonlinearity behavior of the HSC beam specimen, and through comparing the experimental results and the numerical simulation, it can be illustrated that the finite element model can simulate the HSC beam accurately. From the test results, it can be concluded that by means of appropriate shear connection and anchorage length, steel plate and concrete can work together very well and the HSC beam has good load carrying capacity and ductility. These conclusions can serve as a preliminary design reference for the large span half-steel-concrete composite beam in NPP. (author)
Directory of Open Access Journals (Sweden)
V. L. Levshin
2015-01-01
Full Text Available The previous authors’ works have shown that the system of quasi-optimal linear spatial filtering, due to the restriction of this class of filters, related to the superposition principle, has very limited capacity to suppress the most critical interference spatially inhomogeneous background. Such partial suppression does not meet extreme approach requirements for providing high probability characteristics to detect small targets in the most difficult background conditions.In this regard, there is a conclusion that it is necessary to find a different approach, in which the result of the system operation in complex background does not depend on the level of the background noise at the input. This article performs an engineering synthesis of the system with the artificial visual intelligence elements, which recognizes a class of the small-sized radiating objects with the suppression of the most critical interference through nonlinear topological selection.Consideration of this problem begins with the formation of the filter-discriminator aperture, which is a basis for this theory, «echoing» with the theory of optimal nonlinear filtering spatial Poisson processes. Thus, formation of the optimized nonlinear filter structure is based on the optimal linear filter (Wiener filter structure. As a result, there are three versions of filter apertures (4-, 8- and 16-connected ones, with one of which later providing operations of the object shape discrimination. The focus of the article is, mainly, on the 8-connected aperture, as the average in balance of efficiency and complexity option.The article pays considerable attention to development of signs and algorithms to select the objects by size and shape. It shows that selection on a uniform background is possible by the maximum value of the first derivative and to separate the most critical form of Markov’s field inhomogeneities and background brightness, as the fragments of component boundaries of
Energy Technology Data Exchange (ETDEWEB)
Biffle, J.H.
1993-02-01
JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.
Energy Technology Data Exchange (ETDEWEB)
Biffle, J.H.; Blanford, M.L.
1994-05-01
JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.
International Nuclear Information System (INIS)
Kasahara, Naoto
1997-01-01
Supposing that the nuclear reactor stops on any reason, the temperature of flown out coolant from the reactor core will decrease and the temperature of elements touched with the coolant in the nuclear plant equipments also decreases on response to this. On the other hand, temperature pursuit at non-touched portions is delayed to form a thermal stress due to their temperature difference. In particular, a stress over its yield value at discontinuous portion of structure due to stress concentration generates, which could be thought of possibility to form a creep fatigue crack if repeating such thermal stress under high temperature. The Power Reactor and Nuclear Fuel Development Corporation has developed the transient thermal stress real time simulation code for calculating thermal stress formed within a construction in accompany with temperature changes of the coolant once and at high speed since 1994 FY, and after 1995 FY the development of FEM simulation technique from macroscopic region to microscopic region which set an objective regions from construction level to material texture has been promoted. In future, development of total simulation technique connected both and optimum design technique due to its results will be planned. (G.K.)
Directory of Open Access Journals (Sweden)
Bég Anwar O.
2014-01-01
Full Text Available A mathematical model is presented for viscous hydromagnetic flow through a hybrid non-Darcy porous media rotating generator. The system is simulated as steady, incompressible flow through a nonlinear porous regime intercalated between parallel plates of the generator in a rotating frame of reference in the presence of a strong, inclined magnetic field A pressure gradient term is included which is a function of the longitudinal coordinate. The general equations for rotating viscous magnetohydrodynamic flow are presented and neglecting convective acceleration effects, the two-dimensional viscous flow equations are derived incorporating current density components, porous media drag effects, Lorentz drag force components and Hall current effects. Using an appropriate group of dimensionless variables, the momentum equations for primary and secondary flow are rendered nondimensional and shown to be controlled by six physical parameters-Hartmann number (Ha, Hall current parameter (Nh, Darcy number (Da, Forchheimer number (Fs, Ekman number (Ek and dimensionless pressure gradient parameter (Np, in addition to one geometric parameter-the orientation of the applied magnetic field (θ . Several special cases are extracted from the general model, including the non-porous case studied earlier by Ghosh and Pop (2006. A numerical solution is presented to the nonlinear coupled ordinary differential equations using both the Network Simulation Method and Finite Element Method, achieving excellent agreement. Additionally very good agreement is also obtained with the earlier analytical solutions of Ghosh and Pop (2006. for selected Ha, Ek and Nh values. We examine in detail the effects of magnetic field, rotation, Hall current, bulk porous matrix drag, second order porous impedance, pressure gradient and magnetic field inclination on primary and secondary velocity distributions and also frictional shear stresses at the plates. Primary velocity is seen to decrease
Cunha, Katia; Smith, Verne V.; Hasselquist, Sten; Souto, Diogo; Shetrone, Matthew D.; Allende Prieto, Carlos; Bizyaev, Dmitry; Frinchaboy, Peter; García-Hernández, D. Anibal; Holtzman, Jon; Johnson, Jennifer A.; Jőnsson, Henrik; Majewski, Steven R.; Mészáros, Szabolcs; Nidever, David; Pinsonneault, Mark; Schiavon, Ricardo P.; Sobeck, Jennifer; Skrutskie, Michael F.; Zamora, Olga; Zasowski, Gail; Fernández-Trincado, J. G.
2017-08-01
Nine Ce II lines have been identified and characterized within the spectral window observed by the Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey (between λ1.51 and 1.69 μm). At solar metallicities, cerium is an element that is produced predominantly as a result of the slow capture of neutrons (the s-process) during asymptotic giant branch stellar evolution. The Ce II lines were identified using a combination of a high-resolution (R=λ /δ λ ={{100,000}}) Fourier Transform Spectrometer (FTS) spectrum of α Boo and an APOGEE spectrum (R = 22,400) of a metal-poor, but s-process enriched, red giant (2M16011638-1201525). Laboratory oscillator strengths are not available for these lines. Astrophysical gf-values were derived using α Boo as a standard star, with the absolute cerium abundance in α Boo set by using optical Ce II lines that have precise published laboratory gf-values. The near-infrared Ce II lines identified here are also analyzed, as consistency checks, in a small number of bright red giants using archival FTS spectra, as well as a small sample of APOGEE red giants, including two members of the open cluster NGC 6819, two field stars, and seven metal-poor N- and Al-rich stars. The conclusion is that this set of Ce II lines can be detected and analyzed in a large fraction of the APOGEE red giant sample and will be useful for probing chemical evolution of the s-process products in various populations of the Milky Way.
Nagaso, Masaru; Komatitsch, Dimitri; Moysan, Joseph; Lhuillier, Christian
2018-01-01
ASTRID project, French sodium cooled nuclear reactor of 4th generation, is under development at the moment by Alternative Energies and Atomic Energy Commission (CEA). In this project, development of monitoring techniques for a nuclear reactor during operation are identified as a measure issue for enlarging the plant safety. Use of ultrasonic measurement techniques (e.g. thermometry, visualization of internal objects) are regarded as powerful inspection tools of sodium cooled fast reactors (SFR) including ASTRID due to opacity of liquid sodium. In side of a sodium cooling circuit, heterogeneity of medium occurs because of complex flow state especially in its operation and then the effects of this heterogeneity on an acoustic propagation is not negligible. Thus, it is necessary to carry out verification experiments for developments of component technologies, while such kind of experiments using liquid sodium may be relatively large-scale experiments. This is why numerical simulation methods are essential for preceding real experiments or filling up the limited number of experimental results. Though various numerical methods have been applied for a wave propagation in liquid sodium, we still do not have a method for verifying on three-dimensional heterogeneity. Moreover, in side of a reactor core being a complex acousto-elastic coupled region, it has also been difficult to simulate such problems with conventional methods. The objective of this study is to solve these 2 points by applying three-dimensional spectral element method. In this paper, our initial results on three-dimensional simulation study on heterogeneous medium (the first point) are shown. For heterogeneity of liquid sodium to be considered, four-dimensional temperature field (three spatial and one temporal dimension) calculated by computational fluid dynamics (CFD) with Large-Eddy Simulation was applied instead of using conventional method (i.e. Gaussian Random field). This three-dimensional numerical
Nieto, Alejandra; Roehl, Holger
2018-03-15
There has been a growing interest in recent years in the assessment of suitable vial/stopper combinations for storage and shipment of frozen drug products. Considering that the glass transition temperature (Tg) of butyl rubber stoppers used in Container Closure Systems (CCS) is between -55°C to -65°C, a storage or shipment temperature of a frozen product below the Tg of the rubber stopper, may require special attention, since below the Tg the rubber becomes more plastic-like and loses its elastic (sealing) characteristics. Thus they risk maintaining Container Closure Integrity (CCI). Given that the rubber regains its elastic properties and reseals after rewarming to ambient temperature, leaks during frozen temperature storage and transportation are transient and the CCI methods used at room temperature conditions are unable to confirm CCI in the frozen state. Hence, several experimental methods have been developed in recent years in order to evaluate CCI at low temperatures. Finite Element (FE) simulations were applied in order to investigate the sealing behaviour of rubber stoppers for the drug product CCS under frozen storage conditions. FE analysis can help reducing the experimental design space and thus number of measurements needed, as they can be used as an ad-on to experimental testing. Several scenarios have been simulated including the effect of thermal history, rubber type, storage time, worst case CCS geometric tolerances and capping pressure. The results of these calculations have been validated with experimental data derived from laboratory experiments (CCI at low temperatures), and a concept for tightness has been developed. It has been concluded that FE simulations have the potential to become a powerful predictive tool towards a better understanding of the influence of cold storage on the rubber sealing properties (and hence on CCI) when dealing with frozen drug products. Copyright © 2018, Parenteral Drug Association.
Mechanical spectral shift reactor
International Nuclear Information System (INIS)
Sherwood, D.G.; Wilson, J.F.; Salton, R.B.; Fensterer, H.F.
1981-01-01
A mechanical spectral shift reactor comprises apparatus for inserting and withdrawing water displacer elements from the reactor core for selectively changing the water-moderator volume in the core thereby changing the reactivity of the core. The apparatus includes drivemechanisms for moving the displacer elements relative to the core and guide mechanisms for guiding the displayer rods through the reactor vessel
Mechanical spectral shift reactor
International Nuclear Information System (INIS)
Sherwood, D.G.; Wilson, J.F.; Salton, R.B.; Fensterer, H.F.
1982-01-01
A mechanical spectral shift reactor comprises apparatus for inserting and withdrawing water displacer elements from the reactor core for selectively changing the water-moderator volume in the core thereby changing the reactivity of the core. The apparatus includes drive mechanisms for moving the displacer elements relative to the core and guide mechanisms for guiding the displacer rods through the reactor vessel. (author)
Dhavamurthy, M.; Peramaiyan, G.; Babu, K. Syed Suresh; Mohan, R.
2015-04-01
Organosulfur nonlinear optical single crystals of orthorhombic bis(guanidinium) 5-sulfosalicylate (2CH6N3 +·C7H4O6S2-·H2O) with dimension 14 mm × 4 mm × 5 mm have been grown from methanol and water solvents in 1:1 ratio by the slow evaporation growth technique. The crystal structure and morphology of the crystals have been studied by single-crystal X-ray diffraction. FTIR spectroscopic studies were carried out to identify the functional groups and vibrational modes present in the grown crystals. The UV-Vis spectrum was studied to analyze the linear optical properties of the grown crystals. The thermal gravimetric analysis was conducted on the grown crystals, and the result revealed that the grown crystal is thermally stable up to 65 °C. The dielectric tensor components ɛ 11, ɛ 22 and ɛ 33 of BG5SS crystal were evaluated as a function of frequency at 40 °C. The surface laser damage threshold for the grown crystal was measured using Nd:YAG laser. Further, Vickers micro-hardness study was carried out to analyze the mechanical strength of the grown crystals for various loads.
Directory of Open Access Journals (Sweden)
K. A. Eftaxias
2006-01-01
Full Text Available An important question in geophysics is whether earthquakes (EQs can be anticipated prior to their occurrence. Pre-seismic electromagnetic (EM emissions provide a promising window through which the dynamics of EQ preparation can be investigated. However, the existence of precursory features in pre-seismic EM emissions is still debatable: in principle, it is difficult to prove associations between events separated in time, such as EQs and their EM precursors. The scope of this paper is the investigation of the pre-seismic EM activity in terms of complexity. A basic reason for our interest in complexity is the striking similarity in behavior close to irreversible phase transitions among systems that are otherwise quite different in nature. Interestingly, theoretical studies (Hopfield, 1994; Herz and Hopfield 1995; Rundle et al., 1995; Corral et al., 1997 suggest that the EQ dynamics at the final stage and neural seizure dynamics should have many similar features and can be analyzed within similar mathematical frameworks. Motivated by this hypothesis, we evaluate the capability of linear and non-linear techniques to extract common features from brain electrical activities and pre-seismic EM emissions predictive of epileptic seizures and EQs respectively. The results suggest that a unified theory may exist for the ways in which firing neurons and opening cracks organize themselves to produce a large crisis, while the preparation of an epileptic shock or a large EQ can be studied in terms of ''Intermittent Criticality''.
Fabrication of the polarization independent spectral beam combining grating
Liu, Quan; Jin, Yunxia; Wu, Jianhong; Guo, Peiliang
2016-03-01
Owing to damage, thermal issues, and nonlinear optical effects, the output power of fiber laser has been proven to be limited. Beam combining techniques are the attractive solutions to achieve high-power high-brightness fiber laser output. The spectral beam combining (SBC) is a promising method to achieve high average power output without influencing the beam quality. A polarization independent spectral beam combining grating is one of the key elements in the SBC. In this paper the diffraction efficiency of the grating is investigated by rigorous coupled-wave analysis (RCWA). The theoretical -1st order diffraction efficiency of the grating is more than 95% from 1010nm to 1080nm for both TE and TM polarizations. The fabrication tolerance is analyzed. The polarization independent spectral beam combining grating with the period of 1.04μm has been fabricated by holographic lithography - ion beam etching, which are within the fabrication tolerance.
Mechanical spectral shift reactor
International Nuclear Information System (INIS)
Wilson, J.F.; Sherwood, D.G.
1982-01-01
A mechanical spectral shift reactor comprises a reactive core having fuel assemblies accommodating both water displacer elements and neutron absorbing control rods for selectively changing the volume of water-moderator in the core. The fuel assemblies with displacer and control rods are arranged in alternating fashion so that one displacer element drive mechanism may move displacer elements in more than one fuel assembly without interfering with the movement of control rods of a corresponding control rod drive mechanisms. (author)
Directory of Open Access Journals (Sweden)
Chouaib Labiod
2017-01-01
Full Text Available This paper presents torque ripple reduction with speed control of 8/6 Switched Reluctance Motor (SRM by the determination of the optimal parameters of the turn on, turn off angles Theta_(on, Theta_(off, and the supply voltage using Particle Swarm Optimization (PSO algorithm and steady state Genetic Algorithm (ssGA. With SRM model, there is difficulty in the control relapsed into highly non-linear static characteristics. For this, the Finite Elements Method (FEM has been used because it is a powerful tool to get a model closer to reality. The mechanism used in this kind of machine control consists of a speed controller in order to determine current reference which must be produced to get the desired speed, hence, hysteresis controller is used to compare current reference with current measured up to achieve switching signals needed in the inverter. Depending on this control, the intelligent routing algorithms get the fitness equation from torque ripple and speed response so as to give the optimal parameters for better results. Obtained results from the proposed strategy based on metaheuristic methods are compared with the basic case without considering the adjustment of specific parameters. Optimized results found clearly confirmed the ability and the efficiency of the proposed strategy based on metaheuristic methods in improving the performances of the SRM control considering different torque loads.
Krishnakumar, M.; Karthick, S.; Thirupugalmani, K.; Babu, B.; Vinitha, G.
2018-05-01
In present investigation, single crystals of organic charge transfer complex, 2-amino-4-methyl pyridinium-4-methoxy benzoate (2A4MP4MB) was grown by controlled slow evaporation solution growth technique using methanol as a solvent at room temperature. Single crystal XRD analysis confirmed the crystal system and lattice parameters of 2A4MP4MB. The crystalline nature, presence of various vibrational modes and other chemical bonds in the compound have been recognized and confirmed by powder X-ray diffraction, FT-IR and FT-Raman spectroscopic techniques respectively. The presence of various proton and carbon positions in title compound was confirmed using 1H NMR and 13C NMR spectral studies. The wide optical operating window and cut-off wavelength were identified and band gap value of the title compound was calculated using UV-vis-NIR study. The specific heat capacity (cp) values of the title compound, 1.712 J g-1·K-1 at 300 K and 13.6 J g-1 K-1 at 433 K (melting point) were measured using Modulated Differential Scanning Calorimetric studies (MDSC). From Z-scan study, nonlinear refractive index (n2), nonlinear absorption (β) and third order nonlinear susceptibility (χ(3)) values were determined. The self-defocusing effect and saturable absorption behavior of the material were utilized to exhibit the optical limiting action at λ = 532 nm by employing the same continuous wave (cw) Nd: YAG laser source. The laser damage threshold (LDT) study of title compound was carried out using Nd: YAG laser of 532 nm wavelength. The Vickers' micro hardness test was carried out at room temperature and obtained results were investigated using classical Meyer's law. In addition, DFT calculations were carried out for the first time for this compound. These characterization studies performed on the title compound planned to probe the valuable and safe region of optical, thermal and mechanical properties to improve efficacy of 2A4MP4MB single crystals in optoelectronic device
FRF decoupling of nonlinear systems
Kalaycıoğlu, Taner; Özgüven, H. Nevzat
2018-03-01
Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.
Periaux, J.
1979-01-01
The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.
Nieto, Alejandra; Roehl, Holger; Brown, Helen; Adler, Michael; Chalus, Pascal; Mahler, Hanns-Christian
2016-01-01
Container closure integrity (CCI) testing is required by different regulatory authorities in order to provide assurance of tightness of the container closure system against possible contamination, for example, by microorganisms. Microbial ingress CCI testing is performed by incubation of the container closure system with microorganisms under specified testing conditions. Physical CCI uses surrogate endpoints, such as coloration by dye solution ingress or gas flow (helium leakage testing). In order to correlate microbial CCI and physical CCI test methods and to evaluate the methods' capability to detect a given leak, artificial leaks are being introduced into the container closure system in a variety of different ways. In our study, artificial leaks were generated using inserted copper wires between the glass vial opening and rubber stopper. However, the insertion of copper wires introduces leaks of unknown size and shape. With nonlinear finite element simulations, the aperture size between the rubber stopper and the glass vial was calculated, depending on wire diameter and capping force. The dependency of the aperture size on the copper wire diameter was quadratic. With the data obtained, we were able to calculate the leak size and model leak shape. Our results suggest that the size as well as the shape of the artificial leaks should be taken into account when evaluating critical leak sizes, as flow rate does not, independently, correlate to hole size. Capping force also affected leak size. An increase in the capping force from 30 to 70 N resulted in a reduction of the aperture (leak size) by approximately 50% for all wire diameters. From 30 to 50 N, the reduction was approximately 33%. Container closure integrity (CCI) testing is required by different regulatory authorities in order to provide assurance of tightness of the container closure system against contamination, for example, by microorganisms. Microbial ingress CCI testing is performed by incubation of the
Jörn, Daniela; Kohorst, Philipp; Besdo, Silke; Borchers, Lothar; Stiesch, Meike
2016-01-01
Since bacterial leakage along the implant-abutment interface may be responsible for peri-implant infections, a realistic estimation of the interface gap width during function is important for risk assessment. The purpose of this study was to compare two methods for investigating microgap formation in a loaded dental implant, namely, microcomputed tomography (micro-CT) and three-dimensional (3D) nonlinear finite element analysis (FEA); additionally, stresses to be expected during loading were also evaluated by FEA. An implant-abutment complex was inspected for microgaps between the abutment and implant in a micro-CT scanner under an oblique load of 200 N. A numerical model of the situation was constructed; boundary conditions and external load were defined according to the experiment. The model was refined stepwise until its load-displacement behavior corresponded sufficiently to data from previous load experiments. FEA of the final, validated model was used to determine microgap widths. These were compared with the widths as measured in micro-CT inspection. Finally, stress distributions were evaluated in selected regions. No microgaps wider than 13 μm could be detected by micro-CT for the loaded implant. FEA revealed gap widths up to 10 μm between the implant and abutment at the side of load application. Furthermore, FEA predicted plastic deformation in a limited area at the implant collar. FEA proved to be an adequate method for studying microgap formation in dental implant-abutment complexes. FEA is not limited in gap width resolution as are radiologic techniques and can also provide insight into stress distributions within the loaded complex.
Festa, G.; Vilotte, J.; Scala, A.
2012-12-01
The M 9.0, 2011 Tohoku earthquake, along the North American-Pacific plate boundary, East of the Honshu Island, yielded a complex broadband rupture extending southwards over 600 km along strike and triggering a large tsunami that ravaged the East coast of North Japan. Strong motion and high-rate continuous GPS data, recorded all along the Japanese archipelago by the national seismic networks K-Net and Kik-net and geodetic network Geonet, together with teleseismic data, indicated a complex frequency dependent rupture. Low frequency signals (fmeters), extending along-dip over about 100 km, between the hypocenter and the trench, and 150 to 200 km along strike. This slip asperity was likely the cause of the localized tsunami source and of the large amplitude tsunami waves. High-frequency signals (f>0.5 Hz) were instead generated close to the coast in the deeper part of the subduction zone, by at least four smaller size asperities, with possible repeated slip, and were mostly the cause for the ground shaking felt in the Eastern part of Japan. The deep origin of the high-frequency radiation was also confirmed by teleseismic high frequency back projection analysis. Intermediate frequency analysis showed a transition between the shallow and deeper part of the fault, with the rupture almost confined in a small stripe containing the hypocenter before propagating southward along the strike, indicating a predominant in-plane rupture mechanism in the initial stage of the rupture itself. We numerically investigate the role of the geometry of the subduction interface and of the structural properties of the subduction zone on the broadband dynamic rupture and radiation of the Tohoku earthquake. Based upon the almost in-plane behavior of the rupture in its initial stage, 2D non-smooth spectral element dynamic simulations of the earthquake rupture propagation are performed including the non planar and kink geometry of the subduction interface, together with bi-material interfaces
Estimation of spectral kurtosis
Sutawanir
2017-03-01
Rolling bearings are the most important elements in rotating machinery. Bearing frequently fall out of service for various reasons: heavy loads, unsuitable lubrications, ineffective sealing. Bearing faults may cause a decrease in performance. Analysis of bearing vibration signals has attracted attention in the field of monitoring and fault diagnosis. Bearing vibration signals give rich information for early detection of bearing failures. Spectral kurtosis, SK, is a parameter in frequency domain indicating how the impulsiveness of a signal varies with frequency. Faults in rolling bearings give rise to a series of short impulse responses as the rolling elements strike faults, SK potentially useful for determining frequency bands dominated by bearing fault signals. SK can provide a measure of the distance of the analyzed bearings from a healthy one. SK provides additional information given by the power spectral density (psd). This paper aims to explore the estimation of spectral kurtosis using short time Fourier transform known as spectrogram. The estimation of SK is similar to the estimation of psd. The estimation falls in model-free estimation and plug-in estimator. Some numerical studies using simulations are discussed to support the methodology. Spectral kurtosis of some stationary signals are analytically obtained and used in simulation study. Kurtosis of time domain has been a popular tool for detecting non-normality. Spectral kurtosis is an extension of kurtosis in frequency domain. The relationship between time domain and frequency domain analysis is establish through power spectrum-autocovariance Fourier transform. Fourier transform is the main tool for estimation in frequency domain. The power spectral density is estimated through periodogram. In this paper, the short time Fourier transform of the spectral kurtosis is reviewed, a bearing fault (inner ring and outer ring) is simulated. The bearing response, power spectrum, and spectral kurtosis are plotted to
A Fiber-Optic System Generating Pulses of High Spectral Density
Abramov, A. S.; Zolotovskii, I. O.; Korobko, D. A.; Fotiadi, A. A.
2018-03-01
A cascade fiber-optic system that generates pulses of high spectral density by using the effect of nonlinear spectral compression is proposed. It is demonstrated that the shape of the pulse envelope substantially influences the degree of compression of its spectrum. In so doing, maximum compression is achieved for parabolic pulses. The cascade system includes an optical fiber exhibiting normal dispersion that decreases along the fiber length, thereby ensuring that the pulse envelope evolves toward a parabolic shape, along with diffraction gratings and a fiber spectral compressor. Based on computer simulation, we determined parameters of cascade elements leading to maximum spectral density of radiation originating from a subpicosecond laser pulse of medium energy.
Spectral Purity Enhancement via Polyphase Multipath Circuits
Mensink, E.; Klumperink, Eric A.M.; Nauta, Bram
2004-01-01
The central question of this paper is: can we enhance the spectral purity of nonlinear circuits by using polyphase multipath circuits? The basic idea behind polyphase multipath circuits is to split the nonlinear circuits into two or more paths and exploit phase differences between these paths to
Nonlinear single-spin spectrum analyzer.
Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee
2013-03-15
Qubits have been used as linear spectrum analyzers of their environments. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis.
Lang, Harold R.
1991-01-01
A new approach to stratigraphic analysis is described which uses photogeologic and spectral interpretation of multispectral remote sensing data combined with topographic information to determine the attitude, thickness, and lithology of strata exposed at the surface. The new stratigraphic procedure is illustrated by examples in the literature. The published results demonstrate the potential of spectral stratigraphy for mapping strata, determining dip and strike, measuring and correlating stratigraphic sequences, defining lithofacies, mapping biofacies, and interpreting geological structures.
International Nuclear Information System (INIS)
Buravlev, Yu.M.; Zamarajev, V.P.; Chernyavskaya, N.V.
1989-01-01
The experimental technique consists in estimation of mutual arrangement of the calibration curves obtained using standard reference materials of low-alloyed and high-alloyed (high-chrome, stainless, high-speed) steels as well as of the curves for carbon steels and cast iron differing in their structure. ARL-31000 and Polyvac E-1000 quantometers with U=1300 V, I=0.12 A and argon pressure ∼1 kPa are used. The influence of third elements is shown in shift and slope changes of the curves for abovementioned high-alloyed steels in comparison to ones for low-alloyed steels accepted as basic. The influence magnitude runs up to 10-30 relative percents and more in the case of analysis of carbon, phosphorus, sulfur, silicon and other elements and depends on the type of the element and on the alloy composition. It is shown that the contribution of structure factor caused by different alloy thermal treatment makes up 10 to 20 relative percents. The experiments showed that the increase of influence of these factors caused by their imposing as well as the weakening of this influence caused by their counteraction is possible. When analyzed alloys differ in their composition and manufacturing technology it is necessary to take into consideration the influence of these effects. (author)
Photovoltaic spectral responsivity measurements
Energy Technology Data Exchange (ETDEWEB)
Emery, K.; Dunlavy, D.; Field, H.; Moriarty, T. [National Renewable Energy Lab., Golden, CO (United States)
1998-09-01
This paper discusses the various elemental random and nonrandom error sources in typical spectral responsivity measurement systems. The authors focus specifically on the filter and grating monochrometer-based spectral responsivity measurement systems used by the Photovoltaic (PV) performance characterization team at NREL. A variety of subtle measurement errors can occur that arise from a finite photo-current response time, bandwidth of the monochromatic light, waveform of the monochromatic light, and spatial uniformity of the monochromatic and bias lights; the errors depend on the light source, PV technology, and measurement system. The quantum efficiency can be a function of he voltage bias, light bias level, and, for some structures, the spectral content of the bias light or location on the PV device. This paper compares the advantages and problems associated with semiconductor-detector-based calibrations and pyroelectric-detector-based calibrations. Different current-to-voltage conversion and ac photo-current detection strategies employed at NREL are compared and contrasted.
International Nuclear Information System (INIS)
Boyd, R.W.
1992-01-01
Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics
Characterization of Passive Spectral Regrowth in Radio Frequency Systems
2013-01-01
as using RF absorber and Faraday cages around sensi- tive spots. To ensure maximum radiated isolation, each cable or component should be shielded...nonlinear effects of spectral-regrowth-generating phenomena on an RF signal. Detection of low-level passive spectral regrowth close in frequency to a...experimentally and analytically characterize the nonlinear effects of spectral- regrowth-generating phenomena on an RF signal. Detection of low-level passive
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
International Nuclear Information System (INIS)
Llobet, X.; Appert, K.; Bondeson, A.; Vaclavik, J.
1990-01-01
Finite difference and finite element approximations of eigenvalue problems, under certain circumstances exhibit spectral pollution, i.e. the appearance of eigenvalues that do not converge to the correct value when the mesh density is increased. In the present paper this phenomenon is investigated in a homogeneous case by means of discrete dispersion relations: the polluting modes belong to a branch of the dispersion relation that is strongly distorted by the discretization method employed, or to a new, spurious branch. The analysis is applied to finite difference methods and to finite element methods, and some indications about how to avoiding polluting schemes are given. (author) 5 figs., 10 refs
International Nuclear Information System (INIS)
Carlson, W.R.; Piplica, E.J.
1982-01-01
A spectral shift pressurized water reactor comprising apparatus for inserting and withdrawing water displacer elements having differing neutron absorbing capabilities for selectively changing the water-moderator volume in the core thereby changing the reactivity of the core. The displacer elements comprise substantially hollow cylindrical low neutron absorbing rods and substantially hollow cylindrical thick walled stainless rods. Since the stainless steel displacer rods have greater neutron absorbing capability, they can effect greater reactivity change per rod. However, by arranging fewer stainless steel displacer rods in a cluster, the reactivity worth of the stainless steel displacer rod cluster can be less than a low neutron absorbing displacer rod cluster. (author)
Nonlinear photonic metasurfaces
Li, Guixin; Zhang, Shuang; Zentgraf, Thomas
2017-03-01
Compared with conventional optical elements, 2D photonic metasurfaces, consisting of arrays of antennas with subwavelength thickness (the 'meta-atoms'), enable the manipulation of light-matter interactions on more compact platforms. The use of metasurfaces with spatially varying arrangements of meta-atoms that have subwavelength lateral resolution allows control of the polarization, phase and amplitude of light. Many exotic phenomena have been successfully demonstrated in linear optics; however, to meet the growing demand for the integration of more functionalities into a single optoelectronic circuit, the tailorable nonlinear optical properties of metasurfaces will also need to be exploited. In this Review, we discuss the design of nonlinear photonic metasurfaces — in particular, the criteria for choosing the materials and symmetries of the meta-atoms — for the realization of nonlinear optical chirality, nonlinear geometric Berry phase and nonlinear wavefront engineering. Finally, we survey the application of nonlinear photonic metasurfaces in optical switching and modulation, and we conclude with an outlook on their use for terahertz nonlinear optics and quantum information processing.
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Advances in nonlinear vibration analysis of structures. Part-I. Beams
Indian Academy of Sciences (India)
Unknown
element analysis of nonlinear beams under static and dynamic loads. ... linearization, substitution of inplane boundary conditions at element level rather .... Modelling the nonlinear vibration problems using finite elements, albeit with a couple.
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
Nonlinear Whistler Wave Physics in the Radiation Belts
Crabtree, Chris
2016-10-01
Wave particle interactions between electrons and whistler waves are a dominant mechanism for controlling the dynamics of energetic electrons in the radiation belts. They are responsible for loss, via pitch-angle scattering of electrons into the loss cone, and energization to millions of electron volts. It has previously been theorized that large amplitude waves on the whistler branch may scatter their wave-vector nonlinearly via nonlinear Landau damping leading to important consequences for the global distribution of whistler wave energy density and hence the energetic electrons. It can dramatically reduce the lifetime of energetic electrons in the radiation belts by increasing the pitch angle scattering rate. The fundamental building block of this theory has now been confirmed through laboratory experiments. Here we report on in situ observations of wave electro-magnetic fields from the EMFISIS instrument on board NASA's Van Allen Probes that show the signatures of nonlinear scattering of whistler waves in the inner radiation belts. In the outer radiation belts, whistler mode chorus is believed to be responsible for the energization of electrons from 10s of Kev to MeV energies. Chorus is characterized by bursty large amplitude whistler mode waves with frequencies that change as a function of time on timescales corresponding to their growth. Theories explaining the chirping have been developed for decades based on electron trapping dynamics in a coherent wave. New high time resolution wave data from the Van Allen probes and advanced spectral techniques are revealing that the wave dynamics is highly structured, with sub-elements consisting of multiple chirping waves with discrete frequency hops between sub-elements. Laboratory experiments with energetic electron beams are currently reproducing the complex frequency vs time dynamics of whistler waves and in addition revealing signatures of wave-wave and beat-wave nonlinear wave-particle interactions. These new data
International Nuclear Information System (INIS)
Wysocka-Lisek, J.; Paszkowska, B.; Mularczyk, K.
1976-01-01
In the beginning the influence of Sn, Pb, Sb, Bi, Cu, Ag, Zn and Cd on the light rare earth spectral lines using Ni as the internal standard, during the intermittent current arc excitation between C-electrodes was studied. On the basis of the spectral lines intensity measurements, it was stated that one may apply the addition of Ni as the internal standard by the quantitative determination of Sn, Pb, Sb, Bi, Zn and Cd in the light rare earth mixtures with one of the above. Also a great influence of the presence of the individually studied metal was observed on the spectral line intensity of rare earth elements and nickel. The differences of the thermo-chemical reactions nature between excited elements and the carbon of the electrodes may cause that influence. (author)
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
National Research Council Canada - National Science Library
Drazin, P. G
1992-01-01
This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...
Gasinski, Leszek
2005-01-01
Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.
International Nuclear Information System (INIS)
Luyt, P.C.B.; Theron, N.J.; Pietra, F.
2017-01-01
It is well known that gasket creep-relaxation results in a reduction of contact pressure between the surface of a gasket and the face of a flange over an extended period of time. This reduction may result in the subsequent failure of the circular bolted flange connection due to leakage. In this paper a pair of flat and raised face integral flanges, PN 10 DN 50 (in accordance with the European EN 1092-1 standard), with non-asbestos compressed fibre ring gaskets with aramid and a nitrile rubber binder were considered. Finite element modelling and analyses were done, for both the circular bolted flange configurations, during the seating condition. The results of the finite element analyses were experimentally validated. It was found that the number of bolt tightening increments as well as the time between the bolt tightening increments had a significant impact on the effect which gasket creep-relaxation had after the seating condition. An increase in either the number of bolting increments or the time between the bolting increments will reduce the effect which gasket creep-relaxation has once the bolts had been fastened. Based on these results it is possible to develop an optimisation scheme to minimize the effect which gasket creep-relaxation has on the contact pressure between the face of the flange and the gasket, after seating, by either increasing or decreasing the number of bolt tightening increments or the time between the bolt tightening increments. - Highlights: • Number of bolt tightening increments and time between bolt tightening increments had significant impact on effect of gasket creep-relaxation after the seating condition. • Impact of gasket creep-relaxation during seating and operating phases investigated by means of finite element analysis and experimentally verified. • Possible to develop optimisation scheme to minimize effect ofh gasket creep-relaxation on contact pressure between flange face and gasket. • Knowing the contact pressure is
Nonlinear dynamics of quadratically cubic systems
International Nuclear Information System (INIS)
Rudenko, O V
2013-01-01
We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)
AUTHOR|(CDS)2067087
In one of its acceptation, the word quench is synonym of destruction. And this is even more consistent with reality in the case of the Large Hadron Collider dipole magnets, whose magnetic field and stored energy are unprecedented: the uncontrolled transition from the superconducting to the resistive state can be the origin of dramatic events. This is why the protection of magnets is so important, and why so many studies and investigations have been carried out on quench origin. The production, cold testing and installation of the 1232 arc dipole magnets is completed. They have fulfilled all the requirements and the operation reliability of these magnets has already been partially confirmed. From an academic standpoint, nevertheless, the anomalous mechanical behaviour, which was sometimes observed during power tests, has not yet been given a clear explanation. The work presented in this thesis aims at providing an instrument to better understand the reasons for such anomalies, by means of finite element modell...
Spectral tunneling of lattice nonlocal solitons
International Nuclear Information System (INIS)
Kartashov, Yaroslav V.; Torner, Lluis; Vysloukh, Victor A.
2010-01-01
We address spectral tunneling of walking spatial solitons in photorefractive media with nonlocal diffusion component of the nonlinear response and an imprinted shallow optical lattice. In contrast to materials with local nonlinearities, where solitons traveling across the lattice close to the Bragg angle suffer large radiative losses, in photorefractive media with diffusion nonlinearity resulting in self-bending, solitons survive when their propagation angle approaches and even exceeds the Bragg angle. In the spatial frequency domain this effect can be considered as tunneling through the band of spatial frequencies centered around the Bragg frequency where the spatial group velocity dispersion is positive.
Single-shot measurement of nonlinear absorption and nonlinear refraction.
Jayabalan, J; Singh, Asha; Oak, Shrikant M
2006-06-01
A single-shot method for measurement of nonlinear optical absorption and refraction is described and analyzed. A spatial intensity variation of an elliptical Gaussian beam in conjugation with an array detector is the key element of this method. The advantages of this single-shot technique were demonstrated by measuring the two-photon absorption and free-carrier absorption in GaAs as well as the nonlinear refractive index of CS2 using a modified optical Kerr setup.
Topology optimization of nonlinear optical devices
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2011-01-01
This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation and an incremen......This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation...... limiter. Here, air, a linear and a nonlinear material are distributed so that the wave transmission displays a strong sensitivity to the amplitude of the incoming wave....
Model of anisotropic nonlinearity in self-defocusing photorefractive media.
Barsi, C; Fleischer, J W
2015-09-21
We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.
Carvalho, Marco Aurélio; Sotto-Maior, Bruno Salles; Del Bel Cury, Altair Antoninha; Pessanha Henriques, Guilherme Elias
2014-11-01
Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections
Yang, Y.; Solis Escalante, T.; van der Helm, F.C.T.; Schouten, A.C.
2016-01-01
Objective: This paper introduces a generalized coherence framework for detecting and characterizing nonlinear interactions in the nervous system, namely cross-spectral coherence (CSC). CSC can detect different types of nonlinear interactions including harmonic and intermodulation coupling as present
Saravanan, R
2018-01-01
Non-linear optical materials have widespread and promising applications, but the efforts to understand the local structure, electron density distribution and bonding is still lacking. The present work explores the structural details, the electron density distribution and the local bond length distribution of some non-linear optical materials. It also gives estimation of the optical band gap, the particle size, crystallite size, and the elemental composition from UV-Visible analysis, SEM, XRD and EDS of some non-linear optical materials respectively.
Matsuura, Yusuke; Rokkaku, Tomoyuki; Suzuki, Takane; Thoreson, Andrew Ryan; An, Kai-Nan; Kuniyoshi, Kazuki
2017-08-01
Forearm diaphysis fractures are usually managed by open reduction internal fixation. Recently, locking plates have been used for treatment. In the long-term period after surgery, some patients present with bone atrophy adjacent to the plate. However, a comparison of locking and conventional plates as a cause of atrophy has not been reported. The aim of this study was to investigate long-term bone atrophy associated with use of locking and conventional plates for forearm fracture treatment. In this study we included 15 patients with forearm fracture managed by either locking or conventional plates and with more than 5 years of follow-up. Computed tomographic imaging of both forearms was performed to assess bone thickness and local bone mineral density and to predict bone strength without plate reinforcement based on finite element analysis. Mean patient age at surgery was 48.0 years. Eight patients underwent reduction with fixed locking plates and were followed up for a mean of 79.5 months; the remaining 7 patients were treated with conventional plates and were followed up for a mean of 105.0 months. Compared with the conventional plate group, the locking plate group had the same fractured limb-contralateral limb ratio of cortex bone thickness, but had significantly lower ratios of mineral density adjacent to the plate and adjusted bone strength. This study demonstrated bone atrophy after locking plate fixation for forearm fractures. Treatment plans for forearm fracture should take into consideration the impact of bone atrophy long after plate fixation. Therapeutic IV. Copyright © 2017 American Society for Surgery of the Hand. Published by Elsevier Inc. All rights reserved.
Ikman Ishak, Muhammad; Shafi, Aisyah Ahmad; Mohamad, Su Natasha; Jizat, Noorlindawaty Md
2018-03-01
The design of dental implant body has a major influence on the stress dissipation over adjacent bone as numbers of implant failure cases reported in past clinical studies. Besides, the inappropriate implant features may cause excessive high or low stresses which could possibly contribute to pathologic bone resorption or atrophy. The aim of this study is to evaluate the effect of different configurations of implant neck on stress dispersion within the adjacent bone via three-dimensional (3-D) finite element analysis (FEA). A set of computed tomography (CT) images of craniofacial was used to reconstruct a 3-D model of mandible using an image-processing software. The selected region of interest was the left side covering the second premolar, first molar and second molar regions. The bone model consisted of both compact (cortical) and porous (cancellous) structures. Three dental implant sets (crown, implant body, and abutment) with different designs of implant neck – straight, tapered with 15°, and tapered with 30° were modelled using a computer-aided design (CAD) software and all models were then analysed via 3-D FEA software. Top surface of first molar crown was subjected to occlusal forces of 114.6 N, 17.2 N, and 23.4 N in the axial, lingual, and mesio-distal directions, respectively. All planes of the mandible model were rigidly constrained in all directions. The result has demonstrated that the straight implant body neck is superior in attributing to high stress generation over adjacent bone as compared to others. This may associate with lower frictional resistance produced than those of tapered designs to withstand the applied loads.
International Nuclear Information System (INIS)
Abbott, T.I.; Jones, C.G.
1984-01-01
Radiographic elements are disclosed comprised of first and second silver halide emulsion layers separated by an interposed support capable of transmitting radiation to which the second image portion is responsive. At least the first imaging portion contains a silver halide emulsion in which thin tubular silver halide grains of intermediate aspect ratios (from 5:1 to 8:1) are present. Spectral sensitizing dye is adsorbed to the surface of the tubular grains. Increased photographic speeds can be realized at comparable levels of crossover. (author)
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...
Nonlinear optical crystals a complete survey
Nikogosyan, David N
2005-01-01
Nonlinear optical crystals are widely used in modern optical science and technology for frequency conversion of laser light, i.e. to generate laser radiation at any specific wavelength in visible, UV or IR spectral regions. This unrivalled reference book contains the most complete and up-to-date information on properties of nonlinear optical crystals. It includes: * Database of 63 common and novel nonlinear optical crystals * Periodically-poled and self-frequency-doubling materials * Full description of linear and nonlinear optical properties * Significant amount of crystallophysical, thermophysical, spectroscopic, electro-optic and magneto-optic information * 7 mini-reviews on novel applications, such as deep-UV light generation, terahertz-wave generation, ultrashort laser pulse compression, photonic band-gap crystals, x3 nonlinearity, etc. * More than 1500 different references with full titles It is a vital source of information for scientists and engineers dealing with modern applications of nonlinear opti...
Nonlinear problems in theoretical physics
International Nuclear Information System (INIS)
Ranada, A.F.
1979-01-01
This volume contains the lecture notes and review talks delivered at the 9th GIFT international seminar on theoretical physics on the general subject 'Nonlinear Problems in Theoretical Physics'. Mist contributions deal with recent developments in the theory of the spectral transformation and solitons, but there are also articles from the field of transport theory and plasma physics and an unconventional view of classical and quantum electrodynamics. All contributions to this volume will appear under their corresponding subject categories. (HJ)
Nonlinear generalization of the Kallen-Welton formula
International Nuclear Information System (INIS)
Kargin, A.Yu.
1982-01-01
Nonlinear dissipative-fluctuation relations permitting to find spectral correlation functions of (n+1) order for fluctuations of different electrodynamic values in plasma using the given value of tensor of nonlinear response of n order have been obtained for equilibrium plasma. At n=1 the relations obtained transform to the Kallen-Welton dissipative-fluctuation relation. Transformation of the nonlinear dissipative-fluctuation relation for cubical nonlinearity permitting to find nonlinear electric plasma susceptibility from the Known spectral correlation function of fourth order for charge density fluctUations in the absence of particle interaction is considered as an example. A compact expression for tensor of nonlinear plasma response has been obtained for an arbitrary order of nonlinearity
Nonlinear Single Spin Spectrum Analayzer
Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee
2014-05-01
Qubits are excellent probes of their environment. When operating in the linear regime, they can be used as linear spectrum analyzers of the noise processes surrounding them. These methods fail for strong non-Gaussian noise where the qubit response is no longer linear. Here we solve the problem of nonlinear spectral analysis, required for strongly coupled environments. Our non-perturbative analytic model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We developed a noise characterization scheme adapted to this non-linearity. We then applied it using a single trapped 88Sr+ ion as the a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. With this method, we attained a ten fold improvement over the standard Fourier limit. Finally, we experimentally compared the performance of equidistant vs. Uhrig modulation schemes for spectral analysis. Phys. Rev. Lett. 110, 110503 (2013), Synopsis at http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.110503 Current position: National Institute of Standards and Tehcnology, Boulder, CO.
Spacetime Discontinuous Galerkin FEM: Spectral Response
International Nuclear Information System (INIS)
Abedi, R; Omidi, O; Clarke, P L
2014-01-01
Materials in nature demonstrate certain spectral shapes in terms of their material properties. Since successful experimental demonstrations in 2000, metamaterials have provided a means to engineer materials with desired spectral shapes for their material properties. Computational tools are employed in two different aspects for metamaterial modeling: 1. Mircoscale unit cell analysis to derive and possibly optimize material's spectral response; 2. macroscale to analyze their interaction with conventional material. We compare two different approaches of Time-Domain (TD) and Frequency Domain (FD) methods for metamaterial applications. Finally, we discuss advantages of the TD method of Spacetime Discontinuous Galerkin finite element method (FEM) for spectral analysis of metamaterials
Spectral Cauchy Characteristic Extraction: Gravitational Waves and Gauge Free News
Handmer, Casey; Szilagyi, Bela; Winicour, Jeff
2015-04-01
We present a fast, accurate spectral algorithm for the characteristic evolution of the full non-linear vacuum Einstein field equations in the Bondi framework. Developed within the Spectral Einstein Code (SpEC), we demonstrate how spectral Cauchy characteristic extraction produces gravitational News without confounding gauge effects. We explain several numerical innovations and demonstrate speed, stability, accuracy, exponential convergence, and consistency with existing methods. We highlight its capability to deliver physical insights in the study of black hole binaries.
Spectral Imaging by Upconversion
DEFF Research Database (Denmark)
Dam, Jeppe Seidelin; Pedersen, Christian; Tidemand-Lichtenberg, Peter
2011-01-01
We present a method to obtain spectrally resolved images using upconversion. By this method an image is spectrally shifted from one spectral region to another wavelength. Since the process is spectrally sensitive it allows for a tailored spectral response. We believe this will allow standard...... silicon based cameras designed for visible/near infrared radiation to be used for spectral images in the mid infrared. This can lead to much lower costs for such imaging devices, and a better performance....
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...
Spectral Decomposition Algorithm (SDA)
National Aeronautics and Space Administration — Spectral Decomposition Algorithm (SDA) is an unsupervised feature extraction technique similar to PCA that was developed to better distinguish spectral features in...
Qiao, Shan; Jackson, Edward; Coussios, Constantin C; Cleveland, Robin O
2016-09-01
Nonlinear acoustics plays an important role in both diagnostic and therapeutic applications of biomedical ultrasound and a number of research and commercial software packages are available. In this manuscript, predictions of two solvers available in a commercial software package, pzflex, one using the finite-element-method (FEM) and the other a pseudo-spectral method, spectralflex, are compared with measurements and the Khokhlov-Zabolotskaya-Kuznetsov (KZK) Texas code (a finite-difference time-domain algorithm). The pzflex methods solve the continuity equation, momentum equation and equation of state where they account for nonlinearity to second order whereas the KZK code solves a nonlinear wave equation with a paraxial approximation for diffraction. Measurements of the field from a single element 3.3 MHz focused transducer were compared with the simulations and there was good agreement for the fundamental frequency and the harmonics; however the FEM pzflex solver incurred a high computational cost to achieve equivalent accuracy. In addition, pzflex results exhibited non-physical oscillations in the spatial distribution of harmonics when the amplitudes were relatively low. It was found that spectralflex was able to accurately capture the nonlinear fields at reasonable computational cost. These results emphasize the need to benchmark nonlinear simulations before using codes as predictive tools.
Analysis of wheezes using wavelet higher order spectral features.
Taplidou, Styliani A; Hadjileontiadis, Leontios J
2010-07-01
Wheezes are musical breath sounds, which usually imply an existing pulmonary obstruction, such as asthma and chronic obstructive pulmonary disease (COPD). Although many studies have addressed the problem of wheeze detection, a limited number of scientific works has focused in the analysis of wheeze characteristics, and in particular, their time-varying nonlinear characteristics. In this study, an effort is made to reveal and statistically analyze the nonlinear characteristics of wheezes and their evolution over time, as they are reflected in the quadratic phase coupling of their harmonics. To this end, the continuous wavelet transform (CWT) is used in combination with third-order spectra to define the analysis domain, where the nonlinear interactions of the harmonics of wheezes and their time variations are revealed by incorporating instantaneous wavelet bispectrum and bicoherence, which provide with the instantaneous biamplitude and biphase curves. Based on this nonlinear information pool, a set of 23 features is proposed for the nonlinear analysis of wheezes. Two complementary perspectives, i.e., general and detailed, related to average performance and to localities, respectively, were used in the construction of the feature set, in order to embed trends and local behaviors, respectively, seen in the nonlinear interaction of the harmonic elements of wheezes over time. The proposed feature set was evaluated on a dataset of wheezes, acquired from adult patients with diagnosed asthma and COPD from a lung sound database. The statistical evaluation of the feature set revealed discrimination ability between the two pathologies for all data subgroupings. In particular, when the total breathing cycle was examined, all 23 features, but one, showed statistically significant difference between the COPD and asthma pathologies, whereas for the subgroupings of inspiratory and expiratory phases, 18 out of 23 and 22 out of 23 features exhibited discrimination power, respectively
Model reduction tools for nonlinear structural dynamics
Slaats, P.M.A.; Jongh, de J.; Sauren, A.A.H.J.
1995-01-01
Three mode types are proposed for reducing nonlinear dynamical system equations, resulting from finite element discretizations: tangent modes, modal derivatives, and newly added static modes. Tangent modes are obtained from an eigenvalue problem with a momentary tangent stiffness matrix. Their
Spectral analysis of turbulence propagation mechanisms in solar wind and tokamaks plasmas
International Nuclear Information System (INIS)
Dong, Yue
2014-01-01
This thesis takes part in the study of spectral transfers in the turbulence of magnetized plasmas. We will be interested in turbulence in solar wind and tokamaks. Spacecraft measures, first principle simulations and simple dynamical systems will be used to understand the mechanisms behind spectral anisotropy and spectral transfers in these plasmas. The first part of this manuscript will introduce the common context of solar wind and tokamaks, what is specific to each of them and present some notions needed to understand the work presented here. The second part deals with turbulence in the solar wind. We will present first an observational study on the spectral variability of solar wind turbulence. Starting from the study of Grappin et al. (1990, 1991) on Helios mission data, we bring a new analysis taking into account a correct evaluation of large scale spectral break, provided by the higher frequency data of the Wind mission. This considerably modifies the result on the spectral index distribution of the magnetic and kinetic energy. A second observational study is presented on solar wind turbulence anisotropy using autocorrelation functions. Following the work of Matthaeus et al. (1990); Dasso et al. (2005), we bring a new insight on this statistical, in particular the question of normalisation choices used to build the autocorrelation function, and its consequence on the measured anisotropy. This allows us to bring a new element in the debate on the measured anisotropy depending on the choice of the referential either based on local or global mean magnetic field. Finally, we study for the first time in 3D the effects of the transverse expansion of solar wind on its turbulence. This work is based on a theoretical and numerical scheme developed by Grappin et al. (1993); Grappin and Velli (1996), but never used in 3D. Our main results deal with the evolution of spectral and polarization anisotropy due to the competition between non-linear and linear (Alfven coupling
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...
Nonlinear optics quantum computing with circuit QED.
Adhikari, Prabin; Hafezi, Mohammad; Taylor, J M
2013-02-08
One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation.
Information-efficient spectral imaging sensor
Sweatt, William C.; Gentry, Stephen M.; Boye, Clinton A.; Grotbeck, Carter L.; Stallard, Brian R.; Descour, Michael R.
2003-01-01
A programmable optical filter for use in multispectral and hyperspectral imaging. The filter splits the light collected by an optical telescope into two channels for each of the pixels in a row in a scanned image, one channel to handle the positive elements of a spectral basis filter and one for the negative elements of the spectral basis filter. Each channel for each pixel disperses its light into n spectral bins, with the light in each bin being attenuated in accordance with the value of the associated positive or negative element of the spectral basis vector. The spectral basis vector is constructed so that its positive elements emphasize the presence of a target and its negative elements emphasize the presence of the constituents of the background of the imaged scene. The attenuated light in the channels is re-imaged onto separate detectors for each pixel and then the signals from the detectors are combined to give an indication of the presence or not of the target in each pixel of the scanned scene. This system provides for a very efficient optical determination of the presence of the target, as opposed to the very data intensive data manipulations that are required in conventional hyperspectral imaging systems.
Nonlinear GARCH model and 1 / f noise
Kononovicius, A.; Ruseckas, J.
2015-06-01
Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.
Fu, Y. B.; Ogden, R. W.
2001-05-01
This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
Spectral gamuts and spectral gamut mapping
Rosen, Mitchell R.; Derhak, Maxim W.
2006-01-01
All imaging devices have two gamuts: the stimulus gamut and the response gamut. The response gamut of a print engine is typically described in CIE colorimetry units, a system derived to quantify human color response. More fundamental than colorimetric gamuts are spectral gamuts, based on radiance, reflectance or transmittance units. Spectral gamuts depend on the physics of light or on how materials interact with light and do not involve the human's photoreceptor integration or brain processing. Methods for visualizing a spectral gamut raise challenges as do considerations of how to utilize such a data-set for producing superior color reproductions. Recent work has described a transformation of spectra reduced to 6-dimensions called LabPQR. LabPQR was designed as a hybrid space with three explicit colorimetric axes and three additional spectral reconstruction axes. In this paper spectral gamuts are discussed making use of LabPQR. Also, spectral gamut mapping is considered in light of the colorimetric-spectral duality of the LabPQR space.
A spatial discretization of the MHD equations based on the finite volume - spectral method
International Nuclear Information System (INIS)
Miyoshi, Takahiro
2000-05-01
Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA φ , is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)
Spectral properties of electromagnetic turbulence in plasmas
Directory of Open Access Journals (Sweden)
D. Shaikh
2009-03-01
Full Text Available We report on the nonlinear turbulent processes associated with electromagnetic waves in plasmas. We focus on low-frequency (in comparison with the electron gyrofrequency nonlinearly interacting electron whistlers and nonlinearly interacting Hall-magnetohydrodynamic (H-MHD fluctuations in a magnetized plasma. Nonlinear whistler mode turbulence study in a magnetized plasma involves incompressible electrons and immobile ions. Two-dimensional turbulent interactions and subsequent energy cascades are critically influenced by the electron whisters that behave distinctly for scales smaller and larger than the electron skin depth. It is found that in whistler mode turbulence there results a dual cascade primarily due to the forward spectral migration of energy that coexists with a backward spectral transfer of mean squared magnetic potential. Finally, inclusion of the ion dynamics, resulting from a two fluid description of the H-MHD plasma, leads to several interesting results that are typically observed in the solar wind plasma. Particularly in the solar wind, the high-time-resolution databases identify a spectral break at the end of the MHD inertial range spectrum that corresponds to a high-frequency regime. In the latter, turbulent cascades cannot be explained by the usual MHD model and a finite frequency effect (in comparison with the ion gyrofrequency arising from the ion inertia is essentially included to discern the dynamics of the smaller length scales (in comparison with the ion skin depth. This leads to a nonlinear H-MHD model, which is presented in this paper. With the help of our 3-D H-MHD code, we find that the characteristic turbulent interactions in the high-frequency regime evolve typically on kinetic-Alfvén time-scales. The turbulent fluctuation associated with kinetic-Alfvén interactions are compressive and anisotropic and possess equipartition of the kinetic and magnetic energies.