Assessment of Finite Element Approximations for Nonlinear Flexible Multibody Dynamics
1991-05-01
dynamics. Two nonlinear beam finite elements are consistently derived from virtual work principle using Bernoulli Euler and Timoshenko beam...and dynamic buckling. Equations of motion are derived for rigid central body with flexible appendage using virtual work principle. Virtual work principle
Massey, Thomas Christopher
2002-01-01
A Flexible Galerkin Finite Element Method (FGM) is a hybrid class of finite element methods that combine the usual continuous Galerkin method with the now popular discontinuous Galerkin method (DGM). A detailed description of the formulation of the FGM on a hyperbolic partial differential equation, as well as the data structures used in the FGM algorithm is presented. Some hp-convergence results and computational cost are included. Additionally, an a posteriori error estimate f...
ELLIPT2D: A Flexible Finite Element Code Written Python
International Nuclear Information System (INIS)
Pletzer, A.; Mollis, J.C.
2001-01-01
The use of the Python scripting language for scientific applications and in particular to solve partial differential equations is explored. It is shown that Python's rich data structure and object-oriented features can be exploited to write programs that are not only significantly more concise than their counter parts written in Fortran, C or C++, but are also numerically efficient. To illustrate this, a two-dimensional finite element code (ELLIPT2D) has been written. ELLIPT2D provides a flexible and easy-to-use framework for solving a large class of second-order elliptic problems. The program allows for structured or unstructured meshes. All functions defining the elliptic operator are user supplied and so are the boundary conditions, which can be of Dirichlet, Neumann or Robbins type. ELLIPT2D makes extensive use of dictionaries (hash tables) as a way to represent sparse matrices.Other key features of the Python language that have been widely used include: operator over loading, error handling, array slicing, and the Tkinter module for building graphical use interfaces. As an example of the utility of ELLIPT2D, a nonlinear solution of the Grad-Shafranov equation is computed using a Newton iterative scheme. A second application focuses on a solution of the toroidal Laplace equation coupled to a magnetohydrodynamic stability code, a problem arising in the context of magnetic fusion research
Integral finite element analysis of turntable bearing with flexible rings
Deng, Biao; Liu, Yunfei; Guo, Yuan; Tang, Shengjin; Su, Wenbin; Lei, Zhufeng; Wang, Pengcheng
2018-03-01
This paper suggests a method to calculate the internal load distribution and contact stress of the thrust angular contact ball turntable bearing by FEA. The influence of the stiffness of the bearing structure and the plastic deformation of contact area on the internal load distribution and contact stress of the bearing is considered. In this method, the load-deformation relationship of the rolling elements is determined by the finite element contact analysis of a single rolling element and the raceway. Based on this, the nonlinear contact between the rolling elements and the inner and outer ring raceways is same as a nonlinear compression spring and bearing integral finite element analysis model including support structure was established. The effects of structural deformation and plastic deformation on the built-in stress distribution of slewing bearing are investigated on basis of comparing the consequences of load distribution, inner and outer ring stress, contact stress and other finite element analysis results with the traditional bearing theory, which has guiding function for improving the design of slewing bearing.
Finite element method analysis of surface roughness transfer in micro flexible rolling
Qu Feijun; Xie Haibo; Jiang Zhengyi
2016-01-01
Micro flexible rolling aims to fabricate submillimeter thick strips with varying thickness profile, where the surface quality of products is mainly determined by initial workpiece surface roughness and subsequent surface asperity flattening process, which is affected by process parameters during rolling. This paper shows a 3D finite element model for flexible rolling of a 250 μm thick workpiece with reduction of 20 to 50%, and rolling phase with thinner thickness indicates a better ability to...
Generalized finite element dynamic modelling and simulation for flexible robot manipulators
Zhou, Feng
1993-01-01
The finite element approach is used to model multi-link flexible robotic manipulators. The kinematic character of flexible manipulators is analyzed using body-fixed and link element attached coordinates. Dynamic equations for flexible robot manipulators are then derived. The position of each point on the link is expressed using a transformation matrix, and the kinetic and potential energy for each element is computed and summed over all the elements. The Lagrangian formulation is applied to set up the dynamic equations of the system. Computational simulations are performed on single- and two-link manipulators with and without torque to check the validity and correctness of the derived dynamic equations. The Runge-Kutta method is used to solve the dynamic equations for flexible manipulators on which all the joints are revolute.
A finite element model for the stress and flexibility analysis of curved pipes
International Nuclear Information System (INIS)
Guerreiro, J.N.C.
1987-03-01
We present a finite element model for the analysis of pipe bends with flanged ends or flanged tangents. Comments are made on the consideration of the internal pressure load. Flexibility and stress instensification factores obtained with the present model are compared with others available. (Author) [pt
Finite Element Analysis of a Highly Flexible Flapping Wing
2013-03-01
arm and could account for some difference in tip deflection as well as the wing kinematics. The low stiffness of the membrane made the model...S. Zhu, Z. Su and H. Zhang, "Added Mass Effect and an Extended Unsteady Blade Element Mode of Insect Hovering," Journal of Bionic Engineering, vol
Directory of Open Access Journals (Sweden)
Rodolfo André Kuche Sanches
Full Text Available Abstract This paper presents a two-dimensional frame finite element methodology to deal with flexible multi-body dynamic systems and applies it to building progressive collapse analysis. The proposed methodology employs a frame element with Timoshenko kinematics and the dynamic governing equation is solved based on the stationary potential energy theorem written regarding nodal positions and generalized vectors components instead of displacements and rotations. The bodies are discretized by lose finite elements, which are assembled by Lagrange multipliers in order to make possible dynamical detachment. Due to the absence of rotation, the time integration is carried by classical Newmark algorithm, which reveals to be stable to the position based formulation. The accuracy of the proposed formulation is verified by simple examples and its capabilities regarding progressive collapse analysis is demonstrated in a more complete building analysis.
Accounting for straight parts effects on elbow's flexibilities in a beam type finite element program
International Nuclear Information System (INIS)
Millard, A.
1983-01-01
An extension of Von Karman's theory is applied to the calculations of the flexibility factor of a pipe bend terminated by a straight part or a flange. This analysis is restricted to the linear elastic deformation behaviour under in plane bending. Analytical solutions are given for the propagation of ovalization in the elbow and in the straight part. Considering the response of the piping structures, we note that the ovalization of the piping systems are reduced significantly when the straight parts or flanges effects are included. This results are presented in terms of global as well local flexibility factors. They have been compared to numerical results obtained by shell type finite elements method. A complete piping system is analyzed, for economical reasons, with a beam type approach. Also, we show how it is possible to take into account an elbow's flexibilities the straight parts effects by means of flexibilities factors introduced in a beam type elements. We have implemented this method in the computer program TEDEL. In some specific geometrical features, we compare solutions using shell type elements and our formulation. (orig.)
Accounting for straight parts effects on elbow's flexibilities in a beam type finite element program
International Nuclear Information System (INIS)
Millard, A.; Vaghi, H.; Ricard, A.
1983-08-01
An extension of Von Karman's theory is applied to the calculations of the flexibility factor of a pipe bend terminated by a straight part or a flange. This analysis is restricted to the linear elastic deformation behaviour under in plane bending. Analytical solutions are given for the propagation of ovalization in the elbow and in the straight part. Considering the response of the piping structures, we note that the ovalization of the piping systems are reduced significantly when the straight parts or flanges effects are included. The results are presented in terms of global as well local flexibility factors. They have been compared to numerical results obtained by shell type finite element method. A complete piping system is analyzed, for economical reasons, with a beam type approach. Also, we show how it is possible to take into account on elbow's flexibilities the straight parts effects by means of flexibilities factors introduced in a beam type element. We have implemented this method in the computer program TEDEL. In some specific geometrical features, we compare solutions using shell type elements and our formulation
Development of a Dynamic Finite Element Model for Unrestrained Flexible Structures.
1984-10-01
2.5 Conservation of Angular Momentum 8 2.6 Principle of Virtual Work 10 2.6.1 The Elastic Stiffness Matrix 12 2.6.2 Finite Element Approximation 15 III...Matrices and Vectors Resulting 119 From the Inertia Term in the Principle of Virtual Work References 123 v LIST OF TABLES Table Page e 1 Natural...principle of virtual work which describes the deformations. If the structure is very flexible, the deformed configuration may be quite different from the
Finite element method analysis of surface roughness transfer in micro flexible rolling
Directory of Open Access Journals (Sweden)
Qu Feijun
2016-01-01
Full Text Available Micro flexible rolling aims to fabricate submillimeter thick strips with varying thickness profile, where the surface quality of products is mainly determined by initial workpiece surface roughness and subsequent surface asperity flattening process, which is affected by process parameters during rolling. This paper shows a 3D finite element model for flexible rolling of a 250 μm thick workpiece with reduction of 20 to 50%, and rolling phase with thinner thickness indicates a better ability to decrease the surface roughness. Four types of initial workpiece surface roughness are studied in the simulation, and the influences of process parameters, such as friction coefficient, rolling speed and roll gap adjusting speed, on surface asperity flattening of workpieces with different initial surface roughness have been numerically investigated and analysed.
Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick; Ortensi, Javier; Baker, Benjamin; Laboure, Vincent; Wang, Congjian; DeHart, Mark; Martineau, Richard
2017-06-01
This work presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the SN transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form is based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. While NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in
Finite element analysis of a fluid-structure interaction in flexible pipe ...
African Journals Online (AJOL)
The obtained mathematical system is constituted of four non-linear hyperbolic partial differential equations describing the wave propagation in both pipe wall and liquid flow. The fluid-structure interaction is found to be governed by Poisson's ratio. In this steady finite element method based on Galerkin formulation is applied.
Fluid-conveying flexible pipes modeled by large-deflection finite elements in multibody systems
Meijaard, Jacob Philippus
2013-01-01
The modeling and simulation of flexible multibody systems containing fluid-conveying pipes are considered. It is assumed that the mass-flow rate is prescribed and constant and the pipe cross section is piecewise uniform. An existing beam element capable of handling large motions is modified to
Stability analysis of flexible wind turbine blades using finite element method
Kamoulakos, A.
1982-08-01
Static vibration and flutter analysis of a straight elastic axis blade was performed based on a finite element method solution. The total potential energy functional was formulated according to linear beam theory. The inertia and aerodynamic loads were formulated according to the blade absolute acceleration and absolute velocity vectors. In vibration analysis, the direction of motion of the blade during the first out-of-lane and first in-plane modes was examined; numerical results involve NASA/DOE Mod-0, McCauley propeller, north wind turbine and flat plate behavior. In flutter analysis, comparison cases were examined involving several references. Vibration analysis of a nonstraight elastic axis blade based on a finite element method solution was performed in a similar manner with the straight elastic axis blade, since it was recognized that a curved blade can be approximated by an assembly of a sufficient number of straight blade elements at different inclinations with respect to common system of axes. Numerical results involve comparison between the behavior of a straight and a curved cantilever beam during the lowest two in-plane and out-of-plane modes.
Ting, Eric; Nguyen, Nhan; Trinh, Khanh
2014-01-01
This paper presents a static aeroelastic model and longitudinal trim model for the analysis of a flexible wing transport aircraft. The static aeroelastic model is built using a structural model based on finite-element modeling and coupled to an aerodynamic model that uses vortex-lattice solution. An automatic geometry generation tool is used to close the loop between the structural and aerodynamic models. The aeroelastic model is extended for the development of a three degree-of-freedom longitudinal trim model for an aircraft with flexible wings. The resulting flexible aircraft longitudinal trim model is used to simultaneously compute the static aeroelastic shape for the aircraft model and the longitudinal state inputs to maintain an aircraft trim state. The framework is applied to an aircraft model based on the NASA Generic Transport Model (GTM) with wing structures allowed to flexibly deformed referred to as the Elastically Shaped Aircraft Concept (ESAC). The ESAC wing mass and stiffness properties are based on a baseline "stiff" values representative of current generation transport aircraft.
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)
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.
International Nuclear Information System (INIS)
Lee, Byeong Hae
1992-02-01
This book gives descriptions of basic finite element method, which includes basic finite element method and data, black box, writing of data, definition of VECTOR, definition of matrix, matrix and multiplication of matrix, addition of matrix, and unit matrix, conception of hardness matrix like spring power and displacement, governed equation of an elastic body, finite element method, Fortran method and programming such as composition of computer, order of programming and data card and Fortran card, finite element program and application of nonelastic problem.
Finite element method solution of simplified P3 equation for flexible geometry handling
International Nuclear Information System (INIS)
Ryu, Eun Hyun; Joo, Han Gyu
2011-01-01
In order to obtain efficiently core flux solutions which would be much closer to the transport solution than the diffusion solution is, not being limited by the geometry of the core, the simplified P 3 (SP 3 ) equation is solved with the finite element method (FEM). A generic mesh generator, GMSH, is used to generate linear and quadratic mesh data. The linear system resulting from the SP 3 FEM discretization is solved by Krylov subspace methods (KSM). A symmetric form of the SP 3 equation is derived to apply the conjugate gradient method rather than the KSMs for nonsymmetric linear systems. An optional iso-parametric quadratic mapping scheme, which is to selectively model nonlinear shapes with a quadratic mapping to prevent significant mismatch in local domain volume, is also implemented for efficient application of arbitrary geometry handling. The gain in the accuracy attainable by the SP 3 solution over the diffusion solution is assessed by solving numerous benchmark problems having various core geometries including the IAEA PWR problems involving rectangular fuels and the Takeda fast reactor problems involving hexagonal fuels. The reference transport solution is produced by the McCARD Monte Carlo code and the multiplication factor and power distribution errors are assessed. In addition, the effect of quadratic mapping is examined for circular cell problems. It is shown that significant accuracy gain is possible with the SP 3 solution for the fast reactor problems whereas only marginal improvement is noted for thermal reactor problems. The quadratic mapping is also quite effective handling geometries with curvature. (author)
Non-linear finite element analysis of flexible pipes for deep-water applications
Edmans, Ben
2013-01-01
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University London Flexible pipes are essential components in the subsea oil and gas industry, where they are used to convey fluids under conditions of extreme external pressure and (often) axial load, while retaining low bending stiffness. This is made possible by their complex internal structure, consisting of unbonded components that are, to a certain extent, free to move internally relative to eac...
Luo, Min
2018-02-01
On the basis of consulting data, the bearing mechanism of gravel pile composite foundation is analyzed in this paper. The use of ANSYS software under flexible foundation according to the plum blossoms gravel pile additional stress between pile and soil additional stress distribution, load on pile top stress and pile bearing rate of modulus ratio between pile and soil on the pile top stress and rate of pile bearing capacity, pile-soil effect the stress ratio was calculated and analyzed, providing reasonable design reference for the design of gravel pile composite foundation.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Nguyen, Nhan; Ting, Eric; Nguyen, Daniel; Dao, Tung; Trinh, Khanh
2013-01-01
This paper presents a coupled vortex-lattice flight dynamic model with an aeroelastic finite-element model to predict dynamic characteristics of a flexible wing transport aircraft. The aircraft model is based on NASA Generic Transport Model (GTM) with representative mass and stiffness properties to achieve a wing tip deflection about twice that of a conventional transport aircraft (10% versus 5%). This flexible wing transport aircraft is referred to as an Elastically Shaped Aircraft Concept (ESAC) which is equipped with a Variable Camber Continuous Trailing Edge Flap (VCCTEF) system for active wing shaping control for drag reduction. A vortex-lattice aerodynamic model of the ESAC is developed and is coupled with an aeroelastic finite-element model via an automated geometry modeler. This coupled model is used to compute static and dynamic aeroelastic solutions. The deflection information from the finite-element model and the vortex-lattice model is used to compute unsteady contributions to the aerodynamic force and moment coefficients. A coupled aeroelastic-longitudinal flight dynamic model is developed by coupling the finite-element model with the rigid-body flight dynamic model of the GTM.
Weiser, Martin
2016-01-01
All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms. Throughout the exercises a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave.
Directory of Open Access Journals (Sweden)
M.H.R. Ghoreishy
2008-02-01
Full Text Available This research work is devoted to the footprint analysis of a steel-belted radial tyre (185/65R14 under vertical static load using finite element method. Two models have been developed in which in the first model the tread patterns were replaced by simple ribs while the second model was consisted of details of the tread blocks. Linear elastic and hyper elastic (Arruda-Boyce material models were selected to describe the mechanical behavior of the reinforcing and rubbery parts, respectively. The above two finite element models of the tyre were analyzed under inflation pressure and vertical static loads. The second model (with detailed tread patterns was analyzed with and without friction effect between tread and contact surfaces. In every stage of the analysis, the results were compared with the experimental data to confirm the accuracy and applicability of the model. Results showed that neglecting the tread pattern design not only reduces the computational cost and effort but also the differences between computed deformations do not show significant changes. However, more complicated variables such as shape and area of the footprint zone and contact pressure are affected considerably by the finite element model selected for the tread blocks. In addition, inclusion of friction even in static state changes these variables significantly.
DeBenedictis, Andrew; Atherton, Timothy J.; Rodarte, Andrea L.; Hirst, Linda S.
2018-03-01
A micrometer-scale elastic shell immersed in a nematic liquid crystal may be deformed by the host if the cost of deformation is comparable to the cost of elastic deformation of the nematic. Moreover, such inclusions interact and form chains due to quadrupolar distortions induced in the host. A continuum theory model using finite elements is developed for this system, using mesh regularization and dynamic refinement to ensure quality of the numerical representation even for large deformations. From this model, we determine the influence of the shell elasticity, nematic elasticity, and anchoring condition on the shape of the shell and hence extract parameter values from an experimental realization. Extending the model to multibody interactions, we predict the alignment angle of the chain with respect to the host nematic as a function of aspect ratio, which is found to be in excellent agreement with experiments.
Optical Finite Element Processor
Casasent, David; Taylor, Bradley K.
1986-01-01
A new high-accuracy optical linear algebra processor (OLAP) with many advantageous features is described. It achieves floating point accuracy, handles bipolar data by sign-magnitude representation, performs LU decomposition using only one channel, easily partitions and considers data flow. A new application (finite element (FE) structural analysis) for OLAPs is introduced and the results of a case study presented. Error sources in encoded OLAPs are addressed for the first time. Their modeling and simulation are discussed and quantitative data are presented. Dominant error sources and the effects of composite error sources are analyzed.
Directory of Open Access Journals (Sweden)
Bulent Yardimoglu
2004-01-01
Full Text Available The purpose of this paper is to extend a previously published beam model of a turbine blade including the centrifugal force field and root flexibility effects on a finite element model and to demonstrate the performance, accuracy and efficiency of the extended model for computing the natural frequencies. Therefore, only the modifications due to rotation and elastic root are presented in great detail. Considering the shear center effect on the transverse displacements, the geometric stiffness matrix due to the centrifugal force is developed from the geometric strain energy expression based on the large deflections and the increase of torsional stiffness because of the axial stress. In this work, the root flexibility of the blade is idealized by a continuum model unlike the discrete model approach of a combination of translational and rotational elastic springs, as used by other researchers. The cross-section properties of the fir-tree root of the blade considered as an example are expressed by assigning proper order polynomial functions similar to cross-sectional properties of a tapered blade. The correctness of the present extended finite element model is confirmed by the experimental and calculated results available in the literature. Comparisons of the present model results with those in the literature indicate excellent agreement.
Energy Technology Data Exchange (ETDEWEB)
Zhou, Shui-Ting; Huang, Hong-Wu [Hunan University, Changsha (China); Chiu, Yi-Jui; Yu, Guo-Fei [Xiamen University of Technology, Xiamen (China); Yang, Chia-Hao [Taipei Chengshih University of Science and Technology, Taipei (China); Jian, Sheng-Rui [I-Shou University, Kaohsiung (China)
2017-02-15
The Assumed mode method (AMM) and Finite element method (FEM) were used. Their results were compared to investigate the coupled shaft-torsion, disk-transverse, and blade-bending vibrations in a flexible-disk rotor system. The blades were grouped with a spring. The flexible-disk rotor system was divided into three modes of coupled vibrations: Shaft-disk-blade, disk-blade, and blade-blade. Two new modes of coupled vibrations were introduced, namely, lacing wires-blade and lacing wires-disk-blade. The patterns of change of the natural frequencies and mode shapes of the system were discussed. The results showed the following: first, mode shapes and natural frequencies varied, and the results of the AMM and FEM differed; second, numerical calculation results showed three influencing factors on natural frequencies, namely, the lacing wire constant, the lacing wire location, and the flexible disk; lastly, the flexible disk could affect the stability of the system as reflected in the effect of the rotational speed.
Statistical finite element analysis.
Khalaji, Iman; Rahemifar, Kaamran; Samani, Abbas
2008-01-01
A novel technique is introduced for tissue deformation and stress analysis. Compared to the conventional Finite Element method, this technique is orders of magnitude faster and yet still very accurate. The proposed technique uses preprocessed data obtained from FE analyses of a number of similar objects in a Statistical Shape Model framework as described below. This technique takes advantage of the fact that the body organs have limited variability, especially in terms of their geometry. As such, it is well suited for calculating tissue displacements of body organs. The proposed technique can be applied in many biomedical applications such as image guided surgery, or virtual reality environment development where tissue behavior is simulated for training purposes.
Peridynamic Multiscale Finite Element Methods
Energy Technology Data Exchange (ETDEWEB)
Costa, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-12-01
art of local models with the flexibility and accuracy of the nonlocal peridynamic model. In the mixed locality method this coupling occurs across scales, so that the nonlocal model can be used to communicate material heterogeneity at scales inappropriate to local partial differential equation models. Additionally, the computational burden of the weak form of the peridynamic model is reduced dramatically by only requiring that the model be solved on local patches of the simulation domain which may be computed in parallel, taking advantage of the heterogeneous nature of next generation computing platforms. Addition- ally, we present a novel Galerkin framework, the 'Ambulant Galerkin Method', which represents a first step towards a unified mathematical analysis of local and nonlocal multiscale finite element methods, and whose future extension will allow the analysis of multiscale finite element methods that mix models across scales under certain assumptions of the consistency of those models.
Solution of Finite Element Equations
DEFF Research Database (Denmark)
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...... features that justify the development of specialized solution algorithms....
Massively Parallel Finite Element Programming
Heister, Timo
2010-01-01
Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.
quadratic spline finite element method
Directory of Open Access Journals (Sweden)
A. R. Bahadir
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
Programming the finite element method
Smith, I M; Margetts, L
2013-01-01
Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c
FEBio: finite elements for biomechanics.
Maas, Steve A; Ellis, Benjamin J; Ateshian, Gerard A; Weiss, Jeffrey A
2012-01-01
In the field of computational biomechanics, investigators have primarily used commercial software that is neither geared toward biological applications nor sufficiently flexible to follow the latest developments in the field. This lack of a tailored software environment has hampered research progress, as well as dissemination of models and results. To address these issues, we developed the FEBio software suite (http://mrl.sci.utah.edu/software/febio), a nonlinear implicit finite element (FE) framework, designed specifically for analysis in computational solid biomechanics. This paper provides an overview of the theoretical basis of FEBio and its main features. FEBio offers modeling scenarios, constitutive models, and boundary conditions, which are relevant to numerous applications in biomechanics. The open-source FEBio software is written in C++, with particular attention to scalar and parallel performance on modern computer architectures. Software verification is a large part of the development and maintenance of FEBio, and to demonstrate the general approach, the description and results of several problems from the FEBio Verification Suite are presented and compared to analytical solutions or results from other established and verified FE codes. An additional simulation is described that illustrates the application of FEBio to a research problem in biomechanics. Together with the pre- and postprocessing software PREVIEW and POSTVIEW, FEBio provides a tailored solution for research and development in computational biomechanics.
Directory of Open Access Journals (Sweden)
CHUN-SEAN LAU
2014-02-01
Full Text Available In the present study, three-dimensional (3D finite element simulation on 132 PIN fleXBGATM package was performed to predict the effect of solder joint geometry on the reliability of Ball Grid Array (BGA solder joints on flexible and rigid PCBs subjected to thermo-cyclic loading. The commercial FEA tool ABAQUS Version 6.9 was used for the simulations of various shapes of solder joints such as barrel, column and hourglass. Apart from a global modeling, the submodeling analysis technique (local modeling was also used on the critically affected solder joints, in order to enhance the computation efficiency. The accumulated creep strain and strain energy density were observed for each case, and optimum geometries were obtained. The model was validated with the published experimental data with the minimum percentage error of 3%. It was observed that the hourglass solder joint geometry was very crucial on the reliability of BGA solder joints, and for a given PCB, the optimal choice of hourglass solder joint geometry depended on its rigidity.
On symmetric pyramidal finite elements
Czech Academy of Sciences Publication Activity Database
Liu, L.; Davies, K. B.; Yuan, K.; Křížek, Michal
2004-01-01
Roč. 11, 1-2 (2004), s. 213-227 ISSN 1492-8760 R&D Projects: GA AV ČR IAA1019201 Institutional research plan: CEZ:AV0Z1019905 Keywords : mesh generation * finite element method * composite elements Subject RIV: BA - General Mathematics Impact factor: 0.108, year: 2004
Finite element methods for engineers
Fenner, Roger T
2013-01-01
This book is intended as a textbook providing a deliberately simple introduction to finite element methods in a way that should be readily understandable to engineers, both students and practising professionals. Only the very simplest elements are considered, mainly two dimensional three-noded “constant strain triangles”, with simple linear variation of the relevant variables. Chapters of the book deal with structural problems (beams), classification of a broad range of engineering into harmonic and biharmonic types, finite element analysis of harmonic problems, and finite element analysis of biharmonic problems (plane stress and plane strain). Full Fortran programs are listed and explained in detail, and a range of practical problems solved in the text. Despite being somewhat unfashionable for general programming purposes, the Fortran language remains very widely used in engineering. The programs listed, which were originally developed for use on mainframe computers, have been thoroughly updated for use ...
FINITE ELEMENT ANALYSIS OF STRUCTURES
Directory of Open Access Journals (Sweden)
PECINGINA OLIMPIA-MIOARA
2015-05-01
Full Text Available The application of finite element method is analytical when solutions can not be applied for deeper study analyzes static, dynamic or other types of requirements in different points of the structures .In practice it is necessary to know the behavior of the structure or certain parts components of the machine under the influence of certain factors static and dynamic . The application of finite element in the optimization of components leads to economic growth , to increase reliability and durability organs studied, thus the machine itself.
Solid finite elements through three decades
Venkatesh, DN; Shrinivasa, U
1994-01-01
conventionally, solid finite elements have been looked upon as just generalizations of two-dimensional finite elements. In this article we trace their development starting from the days of their inception. Keeping in tune with our perceptions on developing finite elements, without taking recourse to any extra variational techniques, we discuss a few of the techniques which have been applied to solid finite elements. Finally we critically examine our own work on formulating solid finite elemen...
Finite elements methods in mechanics
Eslami, M Reza
2014-01-01
This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams, and elasticity with detailed derivations for the mass, stiffness, and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams, and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems, and the third one presents the three dimensional transient heat conducti...
Automation of finite element methods
Korelc, Jože
2016-01-01
New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.
Nonlinear, finite deformation, finite element analysis
Nguyen, Nhung; Waas, Anthony M.
2016-06-01
The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli ( C e ) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated
ANSYS duplicate finite-element checker routine
Ortega, R.
1995-01-01
An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.
An efficient finite element solution for gear dynamics
Cooley, C. G.; Parker, R. G.; Vijayakar, S. M.
2010-06-01
A finite element formulation for the dynamic response of gear pairs is proposed. Following an established approach in lumped parameter gear dynamic models, the static solution is used as the excitation in a frequency domain solution of the finite element vibration model. The nonlinear finite element/contact mechanics formulation provides accurate calculation of the static solution and average mesh stiffness that are used in the dynamic simulation. The frequency domain finite element calculation of dynamic response compares well with numerically integrated (time domain) finite element dynamic results and previously published experimental results. Simulation time with the proposed formulation is two orders of magnitude lower than numerically integrated dynamic results. This formulation admits system level dynamic gearbox response, which may include multiple gear meshes, flexible shafts, rolling element bearings, housing structures, and other deformable components.
Entropy conservative finite element schemes
Tadmor, E.
1986-01-01
The question of entropy stability for discrete approximations to hyperbolic systems of conservation laws is studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end, two main ingredients are used: entropy variables and the construction of certain entropy conservative schemes in terms of piecewise-linear finite element approximations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only if, they contain more numerical viscosity than the abovementioned entropy conservation ones.
Domain decomposition methods for mortar finite elements
Energy Technology Data Exchange (ETDEWEB)
Widlund, O.
1996-12-31
In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.
A first course in finite elements
Fish, Jacob
2007-01-01
Developed from the authors, combined total of 50 years undergraduate and graduate teaching experience, this book presents the finite element method formulated as a general-purpose numerical procedure for solving engineering problems governed by partial differential equations. Focusing on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application, the book is both introductory and self-contained, as well as being a hands-on experience for any student. This authoritative text on Finite Elements:Adopts
Generalized multiscale finite element methods: Oversampling strategies
Efendiev, Yalchin R.
2014-01-01
In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local
Finite element coiled cochlea model
Isailovic, Velibor; Nikolic, Milica; Milosevic, Zarko; Saveljic, Igor; Nikolic, Dalibor; Radovic, Milos; Filipović, Nenad
2015-12-01
Cochlea is important part of the hearing system, and thanks to special structure converts external sound waves into neural impulses which go to the brain. Shape of the cochlea is like snail, so geometry of the cochlea model is complex. The simplified cochlea coiled model was developed using finite element method inside SIFEM FP7 project. Software application is created on the way that user can prescribe set of the parameters for spiral cochlea, as well as material properties and boundary conditions to the model. Several mathematical models were tested. The acoustic wave equation for describing fluid in the cochlea chambers - scala vestibuli and scala timpani, and Newtonian dynamics for describing vibrations of the basilar membrane are used. The mechanical behavior of the coiled cochlea was analyzed and the third chamber, scala media, was not modeled because it does not have a significant impact on the mechanical vibrations of the basilar membrane. The obtained results are in good agreement with experimental measurements. Future work is needed for more realistic geometry model. Coiled model of the cochlea was created and results are compared with initial simplified coiled model of the cochlea.
(ajst) finite element analysis of a fluid-structure
African Journals Online (AJOL)
liquid flow. The fluid-structure interaction is found to be governed by Poisson's ratio. In this steady finite element method based on Galerkin formulation is applied. Numerical results show a good similarity with those of the literature obtained by the characteristics method. Key words : Fluid-structure interaction, flexible pipe, ...
Finite-Element Software for Conceptual Design
DEFF Research Database (Denmark)
Lindemann, J.; Sandberg, G.; Damkilde, Lars
2010-01-01
and research. Forcepad is an effort to provide a conceptual design and teaching tool in a finite-element software package. Forcepad is a two-dimensional finite-element application based on the same conceptual model as image editing applications such as Adobe Photoshop or Microsoft Paint. Instead of using...
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...
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...
Least-squares finite element methods
Bochev, Pavel
2009-01-01
Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. This book presents the theory and practice of least-square finite element methods, their strengths and weaknesses, successes, and open problems
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca
Books and monographs on finite element technology
Noor, A. K.
1985-01-01
The present paper proviees a listing of all of the English books and some of the foreign books on finite element technology, taking into account also a list of the conference proceedings devoted solely to finite elements. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary element methods, proceedings of symmposia and conferences on finite element technology, bibliographies, handbooks, and historical accounts.
Finite element analysis of piezoelectric materials
International Nuclear Information System (INIS)
Lowrie, F.; Stewart, M.; Cain, M.; Gee, M.
1999-01-01
This guide is intended to help people wanting to do finite element analysis of piezoelectric materials by answering some of the questions that are peculiar to piezoelectric materials. The document is not intended as a complete beginners guide for finite element analysis in general as this is better dealt with by the individual software producers. The guide is based around the commercial package ANSYS as this is a popular package amongst piezoelectric material users, however much of the information will still be useful to users of other finite element codes. (author)
Electrical machine analysis using finite elements
Bianchi, Nicola
2005-01-01
OUTLINE OF ELECTROMAGNETIC FIELDSVector AnalysisElectromagnetic FieldsFundamental Equations SummaryReferencesBASIC PRINCIPLES OF FINITE ELEMENT METHODSIntroductionField Problems with Boundary ConditionsClassical Method for the Field Problem SolutionThe Classical Residual Method (Galerkin's Method)The Classical Variational Method (Rayleigh-Ritz's Method)The Finite Element MethodReferencesAPPLICATIONS OF THE FINITE ELEMENT METHOD TO TWO-DIMENSIONAL FIELDSIntroductionLinear Interpolation of the Function fApplication of the Variational MethodSimple Descriptions of Electromagnetic FieldsAppendix: I
On higher order pyramidal finite elements
Czech Academy of Sciences Publication Activity Database
Liu, L.; Davies, K.B.; Křížek, Michal; Guan, L.
2011-01-01
Roč. 3, č. 2 (2011), s. 131-140 ISSN 2070-0733 R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional research plan: CEZ:AV0Z10190503 Keywords : pyramidal polynomial basis functions * finite element method * composite elements * three-dimensional mortar elements Subject RIV: BA - General Mathematics Impact factor: 0.750, year: 2011
Finite element methods a practical guide
Whiteley, Jonathan
2017-01-01
This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
Advanced finite element method in structural engineering
Long, Yu-Qiu; Long, Zhi-Fei
2009-01-01
This book systematically introduces the research work on the Finite Element Method completed over the past 25 years. Original theoretical achievements and their applications in the fields of structural engineering and computational mechanics are discussed.
Multigrid methods for mortar finite elements
Wohlmuth, Barbara
2000-01-01
Multigrid methods for mortar finite elements / R. Krause ; B. Wohlmuth. - In: Multigrid methods VI / Erik Dick ... (ed.). - Berlin u.a. : Springer, 2000. - S. 136-142 (Lecture notes in computational science and engineering ; 14)
FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL ...
African Journals Online (AJOL)
direction (σx) had a maximum value of 375MPa (tensile) and minimum value of ... These results shows that the residual stresses obtained by prediction from the finite element method are in fair agreement with the experimental results.
Discrete mechanics Based on Finite Element Methods
Chen, Jing-bo; Guo, Han-Ying; Wu, Ke
2002-01-01
Discrete Mechanics based on finite element methods is presented in this paper. We also explore the relationship between this discrete mechanics and Veselov discrete mechanics. High order discretizations are constructed in terms of high order interpolations.
ANSYS mechanical APDL for finite element analysis
Thompson, Mary Kathryn
2017-01-01
ANSYS Mechanical APDL for Finite Element Analysis provides a hands-on introduction to engineering analysis using one of the most powerful commercial general purposes finite element programs on the market. Students will find a practical and integrated approach that combines finite element theory with best practices for developing, verifying, validating and interpreting the results of finite element models, while engineering professionals will appreciate the deep insight presented on the program's structure and behavior. Additional topics covered include an introduction to commands, input files, batch processing, and other advanced features in ANSYS. The book is written in a lecture/lab style, and each topic is supported by examples, exercises and suggestions for additional readings in the program documentation. Exercises gradually increase in difficulty and complexity, helping readers quickly gain confidence to independently use the program. This provides a solid foundation on which to build, preparing readers...
Finite elements in CAD and ADINA
International Nuclear Information System (INIS)
Bathe, K.J.
1986-01-01
The use of finite element methods in computer-aided-design - CAD - is discussed. Some current capabilities are presented and important future developments are outlined. The discussion focusses on the use of the ADINA program in CAD applications. (orig.)
Finite element approximation of the Isaacs equation
Salgado, Abner J.; Zhang, Wujun
2015-01-01
We propose and analyze a two-scale finite element method for the Isaacs equation. The fine scale is given by the mesh size $h$ whereas the coarse scale $\\varepsilon$ is dictated by an integro-differential approximation of the partial differential equation. We show that the method satisfies the discrete maximum principle provided that the mesh is weakly acute. This, in conjunction with weak operator consistency of the finite element method, allows us to establish convergence of the numerical s...
Finite Element Model of Gear Induction Hardening
Hodek, J; Zemko, M; Shykula, P
2015-01-01
International audience; This paper presents a finite element model of a gear induction hardening process. The gear was surface-heated by an induction coil and quickly cooled by spraying water. The finite element model was developed as a three-dimensional model. The electromagnetic field, temperature field, stress distribution and microstructure distribution were examined. Temperature and microstructural characteristics were measured and used. The gear material data was obtained in part by mea...
The finite element method in electromagnetics
Jin, Jianming
2014-01-01
A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The
Surgery simulation using fast finite elements
DEFF Research Database (Denmark)
Bro-Nielsen, Morten
1996-01-01
This paper describes our recent work on real-time surgery simulation using fast finite element models of linear elasticity. In addition, we discuss various improvements in terms of speed and realism......This paper describes our recent work on real-time surgery simulation using fast finite element models of linear elasticity. In addition, we discuss various improvements in terms of speed and realism...
Finite element method for eigenvalue problems in electromagnetics
Reddy, C. J.; Deshpande, Manohar D.; Cockrell, C. R.; Beck, Fred B.
1994-01-01
Finite element method (FEM) has been a very powerful tool to solve many complex problems in electromagnetics. The goal of the current research at the Langley Research Center is to develop a combined FEM/method of moments approach to three-dimensional scattering/radiation problem for objects with arbitrary shape and filled with complex materials. As a first step toward that goal, an exercise is taken to establish the power of FEM, through closed boundary problems. This paper demonstrates the developed of FEM tools for two- and three-dimensional eigenvalue problems in electromagnetics. In section 2, both the scalar and vector finite elements have been used for various waveguide problems to demonstrate the flexibility of FEM. In section 3, vector finite element method has been extended to three-dimensional eigenvalue problems.
Quadrature representation of finite element variational forms
DEFF Research Database (Denmark)
Ølgaard, Kristian Breum; Wells, Garth N.
2012-01-01
This chapter addresses the conventional run-time quadrature approach for the numerical integration of local element tensors associated with finite element variational forms, and in particular automated optimizations that can be performed to reduce the number of floating point operations. An alter......This chapter addresses the conventional run-time quadrature approach for the numerical integration of local element tensors associated with finite element variational forms, and in particular automated optimizations that can be performed to reduce the number of floating point operations...
Stabilized Finite Elements in FUN3D
Anderson, W. Kyle; Newman, James C.; Karman, Steve L.
2017-01-01
A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.
Choice of input fields in stochastic finite elements
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1999-01-01
, the flexibility field, as the input to the stochastic finite element model. To answer this question the focus should be on the error of the output of the mechanical model rather than on the input field itself when discretizing the held through replacing it by a field defined in terms of a finite number of random...... variables. Several reported discretization methods define these random variables as integrals of the product of the held and some suitable weight functions. In particular, the weight functions can be Dirac delta functions whereby the random variables become the field values at a finite set of given points...... the differential equation of the column displacement and the relevant boundary conditions, it can be expected that the discretization of the flexibility field is preferable over the discretization of the stiffness field. Direct mechanical considerations support this expectation. (C) 1998 Published by Elsevier...
Choice of input fields in stochastic finite elements
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1996-01-01
, the flexibility field, as the input to the stochastic finite element model. To answer this question the focus should be on the error of the output of the mechanical model rather than on the input field itself when discretizing the field through replacing it by a field defined in terms of a finite number of random...... variables. Several reported discretization methods define these random variables as integrals of the product of the field and some suitable weight functions. In particular, the weight functions can be Dirac delta functions whereby the random variables become the field values at a finite set of given points...... the differential equation of the column displacement and the relevant boundarv conditions, it can be expected that the discretization of the flexibility field is preferable over the discretization of the stiffness field. Direct mechanical considerations support this expectation.Keywords: Random stiffness...
Finite element analysis of tibial fractures
DEFF Research Database (Denmark)
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner
2010-01-01
INTRODUCTION: Fractures of the tibial shaft are relatively common injuries. There are indications that tibial shaft fractures share characteristics in terms of site, type and local fracture mechanisms. In this study, we aimed to set up a mathematical, computer-based model using finite element...... of bony healing. The biomechanical results are the basis for fracture healing, biomechanical fall analysis and stability analysis of osteosynthesis. MATERIAL AND METHODS: A finite element model of the bony part of the lower leg was generated on the basis of computed tomography data from the Visible Human...... Project. The data consisted of 21,219 3D elements with a cortical shell and a trabecular core. Three types of load of torsion, a direct lateral load and axial compression were applied. RESULTS: The finite element linear static analysis resulted in relevant fracture localizations and indicated relevant...
The Development of Piezoelectric Accelerometers Using Finite Element Analysis
DEFF Research Database (Denmark)
Liu, Bin
1999-01-01
This paper describes the application of Finite Element (FE) approach for the development of piezoelectric accelerometers. An accelerometer is simulated using the FE approach as an example. Good agreement is achieved between simulated results and calibrated results. It is proved that the FE modeling...... can be effectively used to predict the specifications of the accelerometer, especially when modification of the accelerometer is required. The FE developing technology forms the bases of fast responsiveness and flexible customized design of piezoelectric accelerometers....
Quadrilateral finite element mesh coarsening
Staten, Matthew L; Dewey, Mark W; Benzley, Steven E
2012-10-16
Techniques for coarsening a quadrilateral mesh are described. These techniques include identifying a coarsening region within the quadrilateral mesh to be coarsened. Quadrilateral elements along a path through the coarsening region are removed. Node pairs along opposite sides of the path are identified. The node pairs along the path are then merged to collapse the path.
Choice of input fields in stochastic finite elements
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1996-01-01
variables. Several reported discretization methods define these random variables as integrals of the product of the field and some suitable weight functions. In particular, the weight functions can be Dirac delta functions whereby the random variables become the field values at a finite set of given points......The problem of the arbitrary choice of variables for random field modelling in structural mechanics or in soil mechanics is treated. For example, it is relevant to ask the question of whether it is best to choose a stiffness field along a beam element or to choose its reciprocal field......, the flexibility field, as the input to the stochastic finite element model. To answer this question the focus should be on the error of the output of the mechanical model rather than on the input field itself when discretizing the field through replacing it by a field defined in terms of a finite number of random...
A finite element solution of transonic flow
Tatum, K. E.
1978-01-01
The use of finite elements is explored in a field in which its use has previously not been deemed very feasible, that of transonic flow. The specific problem chosen is that of steady small-disturbance transonic flow. The nonlinear equations are formulated with an artificial viscosity term added to yield the proper domain of dependence and directional bias in supersonic regions and across imbedded shock waves. Justification is given for the problem and means of solution chosen, and the potential advantages of the finite element procedure over standard finite difference procedures are discussed. Several possible improvements on the method as presently derived are stated. Computational mesh requirements and certain mesh variations are described. Some results equivalent to finite difference calculations are given as a sample solution.
Geometrically unfitted finite element methods and applications
Burman, Erik; Larson, Mats; Olshanskii, Maxim
2017-01-01
This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and aug...
Verification of Orthogrid Finite Element Modeling Techniques
Steeve, B. E.
1996-01-01
The stress analysis of orthogrid structures, specifically with I-beam sections, is regularly performed using finite elements. Various modeling techniques are often used to simplify the modeling process but still adequately capture the actual hardware behavior. The accuracy of such 'Oshort cutso' is sometimes in question. This report compares three modeling techniques to actual test results from a loaded orthogrid panel. The finite element models include a beam, shell, and mixed beam and shell element model. Results show that the shell element model performs the best, but that the simpler beam and beam and shell element models provide reasonable to conservative results for a stress analysis. When deflection and stiffness is critical, it is important to capture the effect of the orthogrid nodes in the model.
Finite Element Modeling of Cracks and Joints
Directory of Open Access Journals (Sweden)
Jozef Čížik
2006-12-01
Full Text Available The application of finite element method to the analysis of discontinuous structural systems has received a considerable interest in recent years. Examples of problems in which discontinuities play a prominent role in the physical behaviour of a system are numerous and include various types of contact problems and layered or jointed systems. This paper gives a state-of-the-art report on the different methods developed to date for the finite element modelling of cracks and joints in discontinuous systems. Particular attention, however, has been given to the use of joint/interface elements, since their application is considered to be most appropriate for modelling of all kinds of discontinuities that may present in a structural system. A chronology of development of the main types of joint elements, including their pertinent characteristics, is also given. Advantages and disadvantages of the individual methods and types of joint elements presented are briefly discussed, together with various applications of interest.
On the reliability of finite element solutions
International Nuclear Information System (INIS)
Prasad, K.S.R.K.
1975-01-01
The extent of reliability of the finite element method for analysis of nuclear reactor structures, and that of reactor vessels in particular and the need for the engineer to guard against the pitfalls that may arise out of both physical and mathematical models have been high-lighted. A systematic way of checking the model to obtain reasonably accurate solutions is presented. Quite often sophisticated elements are suggested for specific design and stress concentration problems. The desirability or otherwise of these elements, their scope and utility vis-a-vis the use of large stack of conventional elements are discussed from the view point of stress analysts. The methods of obtaining a check on the reliability of the finite element solutions either through modelling changes or an extrapolation technique are discussed. (author)
Visualizing higher order finite elements. Final report
Energy Technology Data Exchange (ETDEWEB)
Thompson, David C; Pebay, Philippe Pierre
2005-11-01
This report contains an algorithm for decomposing higher-order finite elements into regions appropriate for isosurfacing and proves the conditions under which the algorithm will terminate. Finite elements are used to create piecewise polynomial approximants to the solution of partial differential equations for which no analytical solution exists. These polynomials represent fields such as pressure, stress, and momentum. In the past, these polynomials have been linear in each parametric coordinate. Each polynomial coefficient must be uniquely determined by a simulation, and these coefficients are called degrees of freedom. When there are not enough degrees of freedom, simulations will typically fail to produce a valid approximation to the solution. Recent work has shown that increasing the number of degrees of freedom by increasing the order of the polynomial approximation (instead of increasing the number of finite elements, each of which has its own set of coefficients) can allow some types of simulations to produce a valid approximation with many fewer degrees of freedom than increasing the number of finite elements alone. However, once the simulation has determined the values of all the coefficients in a higher-order approximant, tools do not exist for visual inspection of the solution. This report focuses on a technique for the visual inspection of higher-order finite element simulation results based on decomposing each finite element into simplicial regions where existing visualization algorithms such as isosurfacing will work. The requirements of the isosurfacing algorithm are enumerated and related to the places where the partial derivatives of the polynomial become zero. The original isosurfacing algorithm is then applied to each of these regions in turn.
Fatigue analysis of flexible pipes using alternative element types and bend stiffener data
Chen, Minghao
2011-01-01
The flexible pipe is a vital part of a floating production system. The lifetime of a flexible riser system is crucial for the Health Safety and Environment (HSE) management. As a result of this, it is very necessary to carry out research on the lifetime of flexible pipe. In this thesis we formalized analysis on flexible pipes, utilizing the finite element analysis software BFLEX 2010, developed by MARINTEK. Chapter 1 describes basic knowledge about flexible pipe and relevant facilities. C...
A multiscale mortar multipoint flux mixed finite element method
Wheeler, Mary Fanett
2012-02-03
In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.
Finite elements for analysis and design
Akin, J E; Davenport, J H
1994-01-01
The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material.Key Features* Akin clearly explains the FEM, a numerical analysis tool for problem-solving throughout applied mathematics, engineering and scientific computing* Basic theory has bee
Finite element and boundary element applications in quantum mechanics
International Nuclear Information System (INIS)
Ueta, Tsuyoshi
2003-01-01
Although this book is one of the Oxford Texts in Applied and Engineering Mathematics, we may think of it as a physics book. It explains how to solve the problem of quantum mechanics using the finite element method (FEM) and the boundary element method (BEM). Many examples analysing actual problems are also shown. As for the ratio of the number of pages of FEM and BEM, the former occupies about 80%. This is, however, reasonable reflecting the flexibility of FEM. Although many explanations of FEM and BEM exist, most are written using special mathematical expressions and numerical computation fields. However, this book is written in the 'language of physicists' throughout. I think that it is very readable and easy to understand for physicists. In the derivation of FEM and the argument on calculation accuracy, the action integral and a variation principle are used consistently. In the numerical computation of matrices, such as simultaneous equations and eigen value problems, a description of important points is also fully given. Moreover, the practical problems which become important in the electron device design field and the condensed matter physics field are dealt with as example computations, so that this book is very practical and applicable. It is characteristic and interesting that FEM is applied to solve the Schroedinger and Poisson equations consistently, and to the solution of the Ginzburg--Landau equation in superconductivity. BEM is applied to treat electric field enhancements due to surface plasmon excitations at metallic surfaces. A number of references are cited at the end of all the chapters, and this is very helpful. The description of quantum mechanics is also made appropriately and the actual application of quantum mechanics in condensed matter physics can also be surveyed. In the appendices, the mathematical foundation, such as numerical quadrature formulae and Green's functions, is conveniently described. I recommend this book to those who need to
Quadrilateral/hexahedral finite element mesh coarsening
Staten, Matthew L; Dewey, Mark W; Scott, Michael A; Benzley, Steven E
2012-10-16
A technique for coarsening a finite element mesh ("FEM") is described. This technique includes identifying a coarsening region within the FEM to be coarsened. Perimeter chords running along perimeter boundaries of the coarsening region are identified. The perimeter chords are redirected to create an adaptive chord separating the coarsening region from a remainder of the FEM. The adaptive chord runs through mesh elements residing along the perimeter boundaries of the coarsening region. The adaptive chord is then extracted to coarsen the FEM.
Slave finite elements: The temporal element approach to nonlinear analysis
Gellin, S.
1984-01-01
A formulation method for finite elements in space and time incorporating nonlinear geometric and material behavior is presented. The method uses interpolation polynomials for approximating the behavior of various quantities over the element domain, and only explicit integration over space and time. While applications are general, the plate and shell elements that are currently being programmed are appropriate to model turbine blades, vanes, and combustor liners.
Finite element analysis of photonic crystal fibers
Uranus, H.P.; Hoekstra, Hugo; van Groesen, Embrecht W.C.
2005-01-01
A finite-element-based vectorial optical mode solver, furnished with Bayliss-Gunzburger-Turkel-like transparent boundary conditions, is used to rigorously analyze photonic crystal fibers (PCFs). Both the real and imaginary part of the modal indices can be computed in a relatively small computational
Finite element simulation of asphalt fatigue testing
DEFF Research Database (Denmark)
Ullidtz, Per; Kieler, Thomas Lau; Kargo, Anders
1997-01-01
damage mechanics.The paper describes how continuum damage mechanics may be used with a finite element program to explain the progressive deterioration of asphalt mixes under laboratory fatigue testing. Both constant stress and constant strain testing are simulated, and compared to the actual results from...
Finite element modelling of solidification phenomena
Indian Academy of Sciences (India)
The process of solidification process is complex in nature and the simulation of such process is required in industry before it is actually undertaken. Finite element method is used to simulate the heat transfer process accompanying the solidification process. The metal and the mould along with the air gap formation is ...
Fast finite elements for surgery simulation
DEFF Research Database (Denmark)
Bro-Nielsen, Morten
1997-01-01
This paper discusses volumetric deformable models for modeling human body parts and organs in surgery simulation systems. These models are built using finite element models for linear elastic materials. To achieve real-time response condensation has been applied to the system stiffness matrix...
Galerkin finite element methods for wave problems
Indian Academy of Sciences (India)
these methods. Keywords. hp-Finite element method; continuous Galerkin methods; wave solutions; Gibbs' phenomenon. 1. Introduction. Galerkin methods belong to the class of solution methods for PDEs where the solution residue is minimized giving rise to the well-known weak formulation of problems. In this approach,.
Equivalent drawbead model in finite element simulations
Carleer, Bart D.; Carleer, B.D.; Meinders, Vincent T.; Huetink, Han; Lee, J.K.; Kinzel, G.L.; Wagoner, R.
1996-01-01
In 3D simulations of the deep drawing process the drawbead geometries are seldom included. Therefore equivalent drawbeads are used. In order to investigate the drawbead behaviour a 2D plane strain finite element model was used. For verification of this model experiments were performed. The analyses
Simplicial Finite Elements in Higher Dimensions
Czech Academy of Sciences Publication Activity Database
Brandts, J.; Korotov, S.; Křížek, Michal
2007-01-01
Roč. 52, č. 3 (2007), s. 251-265 ISSN 0862-7940 R&D Projects: GA ČR GA201/04/1503 Institutional research plan: CEZ:AV0Z10190503 Keywords : n-simplex * finite element method * superconvergence Subject RIV: BA - General Mathematics
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.
Finite element modeling of trolling-mode AFM.
Sajjadi, Mohammadreza; Pishkenari, Hossein Nejat; Vossoughi, Gholamreza
2018-03-14
Trolling mode atomic force microscopy (TR-AFM) has overcome many imaging problems in liquid environments by considerably reducing the liquid-resonator interaction forces. The finite element model of the TR-AFM resonator considering the effects of fluid and nanoneedle flexibility is presented in this research, for the first time. The model is verified by ABAQUS software. The effect of installation angle of the microbeam relative to the horizon and the effect of fluid on the system behavior are investigated. Using the finite element model, frequency response curve of the system is obtained and validated around the frequency of the operating mode by the available experimental results, in air and liquid. The changes in the natural frequencies in the presence of liquid are studied. The effects of tip-sample interaction on the excitation of higher order modes of the system are also investigated in air and liquid environments. Copyright © 2018 Elsevier B.V. All rights reserved.
Rigid body formulation in a finite element context with contact interaction
Refachinho de Campos, Paulo R.; Gay Neto, Alfredo
2018-03-01
The present work proposes a formulation to employ rigid bodies together with flexible bodies in the context of a nonlinear finite element solver, with contact interactions. Inertial contributions due to distribution of mass of a rigid body are fully developed, considering a general pole position associated with a single node, representing a rigid body element. Additionally, a mechanical constraint is proposed to connect a rigid region composed by several nodes, which is useful for linking rigid/flexible bodies in a finite element environment. Rodrigues rotation parameters are used to describe finite rotations, by an updated Lagrangian description. In addition, the contact formulation entitled master-surface to master-surface is employed in conjunction with the rigid body element and flexible bodies, aiming to consider their interaction in a rigid-flexible multibody environment. New surface parameterizations are presented to establish contact pairs, permitting pointwise interaction in a frictional scenario. Numerical examples are provided to show robustness and applicability of the methods.
FINITE ELEMENT ANALYSIS OF ELEMENT ANALYSIS OF A FREE ...
African Journals Online (AJOL)
eobe
formulated as functional minimization. Finite Element Method (FEM) is regarde accurate and versatile numerical too differential equations that model phys. The methodology is used in vari engineering in which the problems ar partial differential equations. The met considerable application in structural e related disciplines.
Finite element simulations with ANSYS workbench 16
Lee , Huei-Huang
2015-01-01
Finite Element Simulations with ANSYS Workbench 16 is a comprehensive and easy to understand workbook. It utilizes step-by-step instructions to help guide readers to learn finite element simulations. Twenty seven real world case studies are used throughout the book. Many of these cases are industrial or research projects the reader builds from scratch. All the files readers may need if they have trouble are available for download on the publishers website. Companion videos that demonstrate exactly how to preform each tutorial are available to readers by redeeming the access code that comes in the book. Relevant background knowledge is reviewed whenever necessary. To be efficient, the review is conceptual rather than mathematical. Key concepts are inserted whenever appropriate and summarized at the end of each chapter. Additional exercises or extension research problems are provided as homework at the end of each chapter. A learning approach emphasizing hands-on experiences spreads through this entire book. A...
A finite element method for neutron transport
International Nuclear Information System (INIS)
Ackroyd, R.T.
1983-01-01
A completely boundary-free maximum principle for the first-order Boltzmann equation is derived from the completely boundary-free maximum principle for the mixed-parity Boltzmann equation. When continuity is imposed on the trial function for directions crossing interfaces the completely boundary-free principle for the first-order Boltzmann equation reduces to a maximum principle previously established directly from first principles and indirectly by the Euler-Lagrange method. Present finite element methods for the first-order Boltzmann equation are based on a weighted-residual method which permits the use of discontinuous trial functions. The new principle for the first-order equation can be used as a basis for finite-element methods with the same freedom from boundary conditions as those based on the weighted-residual method. The extremum principle as the parent of the variationally-derived weighted-residual equations ensures their good behaviour. (author)
Finite element reliability analysis of fatigue life
International Nuclear Information System (INIS)
Harkness, H.H.; Belytschko, T.; Liu, W.K.
1992-01-01
Fatigue reliability is addressed by the first-order reliability method combined with a finite element method. Two-dimensional finite element models of components with cracks in mode I are considered with crack growth treated by the Paris law. Probability density functions of the variables affecting fatigue are proposed to reflect a setting where nondestructive evaluation is used, and the Rosenblatt transformation is employed to treat non-Gaussian random variables. Comparisons of the first-order reliability results and Monte Carlo simulations suggest that the accuracy of the first-order reliability method is quite good in this setting. Results show that the upper portion of the initial crack length probability density function is crucial to reliability, which suggests that if nondestructive evaluation is used, the probability of detection curve plays a key role in reliability. (orig.)
Finite element analysis of human joints
International Nuclear Information System (INIS)
Bossart, P.L.; Hollerbach, K.
1996-09-01
Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described
Finite element analysis of tibial fractures
DEFF Research Database (Denmark)
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner
2010-01-01
INTRODUCTION: Fractures of the tibial shaft are relatively common injuries. There are indications that tibial shaft fractures share characteristics in terms of site, type and local fracture mechanisms. In this study, we aimed to set up a mathematical, computer-based model using finite element...... analysis of the bones of the lower leg to examine if such a model is adequate for prediction of fracture locations and patterns. In future studies, we aim to use these biomechanical results to examine fracture prevention, among others, and to simulate different types of osteosynthesis and the process...... of bony healing. The biomechanical results are the basis for fracture healing, biomechanical fall analysis and stability analysis of osteosynthesis. MATERIAL AND METHODS: A finite element model of the bony part of the lower leg was generated on the basis of computed tomography data from the Visible Human...
Finite element analysis of human joints
Energy Technology Data Exchange (ETDEWEB)
Bossart, P.L.; Hollerbach, K.
1996-09-01
Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.
Finite element modelling of TRIP steels
Energy Technology Data Exchange (ETDEWEB)
Papatriantafillou, I.; Aravas, N.; Haidemenopoulos, G.N. [Dept. of Mechanical and Industrial Engineering, Univ. of Thessaly, Volos (Greece)
2004-11-01
A constitutive model that describes the mechanical behaviour of steels exhibiting ''Transformation Induced Plasticity'' (TRIP) during martensitic transformation is presented. Multiphase TRIP steels are considered as composite materials with a ferritic matrix containing bainite and retained austenite, which gradually transforms into martensite. The effective properties and overall behaviour of TRIP steels are determined by using homogenization techniques for non-linear composites. The developed constitutive model considers the different hardening behaviour of the individual phases and estimates the apportionment of plastic strain and stress between the individual phases of the composite. A methodology for the numerical integration of the resulting elastoplastic constitutive equations in the context of the finite element method is developed and the constitutive model is implemented in a general-purpose finite element program. The prediction of the model in uniaxial tension agrees well with the experimental data. The problem of necking of a bar in uniaxial tension is studied in detail. (orig.)
Finite Element Analysis of Honeycomb Impact Attenuator
Yang, Seung-Yong; Choi, Seung-Kyu; Kim, Nohyu
To participate in Student Formula Society of Automotive Engineers (SAE) competitions, it is necessary to build an impact attenuator that would give an average deceleration not to exceed 20g when it runs into a rigid wall. Students can use numerical simulations or experimental test data to show that their car satisfies this safety requirement. A student group to study formula cars at the Korea University of Technology and Education has designed a vehicle to take part in a SAE competition, and a honeycomb structure was adopted as the impact attenuator. In this paper, finite element calculations were carried out to investigate the dynamic behavior of the honeycomb attenuator. Deceleration and deformation behaviors were studied. Effect of the yield strength was checked by comparing the numerical results. ABAQUS/Explicit finite element code was used.
FINITE ELEMENT ANALYSIS FOR PERIFLEX COUPLINGS
Directory of Open Access Journals (Sweden)
URDEA Mihaela
2015-06-01
Full Text Available The Periflex shaft couplings with rubber sleeve have a hig elasticity and link two shafts in diesel-engine and electric drives. They are simple from the point of view of construction, easily mounted and dismounted. The main goal of this paper is to present a finite element analysis for the Periflex coupling using the Generative Structural Analysis from CATIA software package. This paper presents important information about how to prepare an assembly for creating a static analysis case and also the important steps for developing a finite element analysis. It is very important that the analysis model should have the same behavior as the real, also the loading model. The results are images corresponding to Von Mises Stresses and Translational Displacement magnitude.
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 · ...
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
Finite element simulation of heat transfer
Bergheau, Jean-Michel
2010-01-01
This book introduces the finite element method applied to the resolution of industrial heat transfer problems. Starting from steady conduction, the method is gradually extended to transient regimes, to traditional non-linearities, and to convective phenomena. Coupled problems involving heat transfer are then presented. Three types of couplings are discussed: coupling through boundary conditions (such as radiative heat transfer in cavities), addition of state variables (such as metallurgical phase change), and coupling through partial differential equations (such as electrical phenomena).? A re
Finite element methods for incompressible flow problems
John, Volker
2016-01-01
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations, and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
Coupled finite element modeling of piezothermoelastic materials
Senousy, M. S.; Rajapakse, R. K. N. D.; Gadala, M.
2007-04-01
The governing equations of piezo-thermoelastic materials show full coupling between mechanical, electric, and temperature fields. It is often assumed in the literature that in high-frequency oscillations, the coupling between the temperature and mechanical displacement and electric field is small and, therefore, can be neglected. A solution for the temperature field is then determined from an uncoupled equation. A finite element (FE) model that accounts for full coupling between the mechanical, electric, and thermal fields, nonlinear constitutive behavior and heat generation resulting from dielectric losses under alternating driving fields is under development. This paper presents a linear fully coupled model as an early development of the fully coupled nonlinear FE model. In the linear model, a solution for all field variables is obtained simultaneously and compared with the uncoupled solution. The finite element model is based on the weighted-residual principle and uses 2-D four-node isoparametric finite elements with four degrees of freedom per node. A thin piezoelectric square disk is modeled to obtain some preliminary understanding of the coupled fields in a piezoelectric stack actuator.
Finite element modeling of lipid bilayer membranes
Feng, Feng; Klug, William S.
2006-12-01
A numerical simulation framework is presented for the study of biological membranes composed of lipid bilayers based on the finite element method. The classic model for these membranes employs a two-dimensional-fluid-like elastic constitutive law which is sensitive to curvature, and subjects vesicles to physically imposed constraints on surface area and volume. This model is implemented numerically via the use of C1-conforming triangular Loop subdivision finite elements. The validity of the framework is tested by computing equilibrium shapes from previously-determined axisymmetric shape-phase diagram of lipid bilayer vesicles with homogeneous material properties. Some of the benefits and challenges of finite element modeling of lipid bilayer systems are discussed, and it is indicated how this framework is natural for future investigation of biologically realistic bilayer structures involving nonaxisymmetric geometries, binding and adhesive interactions, heterogeneous mechanical properties, cytoskeletal interactions, and complex loading arrangements. These biologically relevant features have important consequences for the shape mechanics of nonidealized vesicles and cells, and their study requires not simply advances in theory, but also advances in numerical simulation techniques, such as those presented here.
Finite element modelling of contracting skeletal muscle.
Oomens, C W J; Maenhout, M; van Oijen, C H; Drost, M R; Baaijens, F P
2003-09-29
To describe the mechanical behaviour of biological tissues and transport processes in biological tissues, conservation laws such as conservation of mass, momentum and energy play a central role. Mathematically these are cast into the form of partial differential equations. Because of nonlinear material behaviour, inhomogeneous properties and usually a complex geometry, it is impossible to find closed-form analytical solutions for these sets of equations. The objective of the finite element method is to find approximate solutions for these problems. The concepts of the finite element method are explained on a finite element continuum model of skeletal muscle. In this case, the momentum equations have to be solved with an extra constraint, because the material behaves as nearly incompressible. The material behaviour consists of a highly nonlinear passive part and an active part. The latter is described with a two-state Huxley model. This means that an extra nonlinear partial differential equation has to be solved. The problems and solutions involved with this procedure are explained. The model is used to describe the mechanical behaviour of a tibialis anterior of a rat. The results have been compared with experimentally determined strains at the surface of the muscle. Qualitatively there is good agreement between measured and calculated strains, but the measured strains were higher.
BERSAFE: (BERkeley Structural Analysis by Finite Elements)
International Nuclear Information System (INIS)
Anon.
1991-01-01
BERSAFE is a well-known finite element system which has been under continuous use and development for over 20 years. The BERSAFE system comprises an inter-compatible set of program modules covering static stress analysis, linear dynamics and thermal analysis. Data generation and results presentation modules are also available, along with special supporting functions including automatic crack growth through a model with adaptive meshing. The functionality of BERSAFE, is nowadays very advanced, both in engineering scope and finite element technology. It has seen many firsts, including the front solution and Virtual Crack Extension methods (VCE). More recent additions which have developed out of the Power Industry's requirements are a finite element computational fluid dynamics code, FEAT, and engineering design assessment procedures. These procedures include R6 and R5 for the assessment of the integrity of structures containing defects below and within the creep regime. To use all this software in a user-friendly manner, a new computational environment has been developed, called 'The Harness' which takes advantage of modern hardware and software philosophies. This provides the tool-kit to undertake complete problems, covering determination of fluid loads, structural analysis and failure assessment. In the following sections we describe briefly various components of the BERSAFE suite. (author)
Finite element analysis of coupled electromechanical problems
International Nuclear Information System (INIS)
Melgoza-Vazquez, E.
2001-01-01
The modeling of electromechanical problems is discussed. The simultaneous consideration of two distinct phenomena is required, as the evolution of the electromagnetic and the mechanical parts are influenced by each other. In this work the equations of the coupled problem are described and possible methods of solution are considered. Three general approaches with varying degrees of detail are considered. In the first, a lumped parameter model of the device is constructed from the finite element solution of the electromagnetic problem. A second approach links the electromagnetic field directly with the lumped mechanical part. Lastly, both the electromagnetic and the mechanical systems are considered to be distributed, with the individual domains solved by using the finite element method. In the process of solution of transient problems the need to solve differential-algebraic systems of equations arises and some approaches are presented. It is shown that traditional finite difference formulas may be applied as long as the discretization is made at the element level. Higher order methods and step adaptation are discussed. (author)
Sparse adaptive finite elements for radiative transfer
International Nuclear Information System (INIS)
Widmer, G.; Hiptmair, R.; Schwab, Ch.
2008-01-01
The linear radiative transfer equation, a partial differential equation for the radiation intensity u(x,s), with independent variables x element of D is contained in R n in the physical domain D of dimension n=2,3, and angular variable s element of S 2 :={y element of R 3 :|y|=1}, is solved in the n+2-dimensional computational domain DxS 2 . We propose an adaptive multilevel Galerkin finite element method (FEM) for its numerical solution. Our approach is based on (a) a stabilized variational formulation of the transport operator, (b) on so-called sparse tensor products of two hierarchic families of finite element spaces in H 1 (D) and in L 2 (S 2 ), respectively, and (c) on wavelet thresholding techniques to adapt the discretization to the underlying problem. An a priori error analysis shows, under strong regularity assumptions on the solution, that the sparse tensor product method is clearly superior to a discrete ordinates method, as it converges with essentially optimal asymptotic rates while its complexity grows essentially only as that for a linear transport problem in R n . Numerical experiments for n=2 on a set of example problems agree with the convergence and complexity analysis of the method and show that introducing adaptivity can improve performance in terms of accuracy vs. number of degrees even further
Finite element modeling for materials engineers using Matlab
Oluwole, Oluleke
2014-01-01
Finite Element Modeling for Materials Engineers Using MATLAB® combines the finite element method with MATLAB to offer materials engineers a fast and code-free way of modeling for many materials processes.
Finite Element Based Design and Optimization for Piezoelectric Accelerometers
DEFF Research Database (Denmark)
Liu, Bin; Kriegbaum, B.; Yao, Q.
1998-01-01
A systematic Finite Element design and optimisation procedure is implemented for the development of piezoelectric accelerometers. Most of the specifications of accelerometers can be obtained using the Finite Element simulations. The deviations between the simulated and calibrated sensitivities...
Error-controlled adaptive finite elements in solid mechanics
National Research Council Canada - National Science Library
Stein, Erwin; Ramm, E
2003-01-01
... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Error-controlled Adaptive Finite-element-methods . . . . . . . . . . . . Missing Features and Properties of Today's General Purpose FE Programs for Structural...
Cojocaru, E.
2009-01-01
The finite element method has become a preeminent simulation technique in electromagnetics. For problems involving anisotropic media and metamaterials, proper algorithms should be developed. It has been proved that discretizing in quadratic triangular elements may lead to an improved accuracy. Here we present a collection of elemental matrices evaluated analytically for quadratic triangular elements. They could be useful for the finite element method in advanced electromagnetics.
The Total Number of Parameters in the Finite Element ...
African Journals Online (AJOL)
Rectangular finite elements are important in Finite Element Method. This paper establishes a general formula for obtaining the total number of parameters associated with any finite element rectangulation of a domain. This number is also the dimension of the trail space as well as the size of the associated linear system.
Parallel direct solver for finite element modeling of manufacturing processes
DEFF Research Database (Denmark)
Nielsen, Chris Valentin; Martins, P.A.F.
2017-01-01
The central processing unit (CPU) time is of paramount importance in finite element modeling of manufacturing processes. Because the most significant part of the CPU time is consumed in solving the main system of equations resulting from finite element assemblies, different approaches have been...... developed to optimize solutions and reduce the overall computational costs of large finite element models....
Finite element modelling of helmeted head impact under frontal ...
Indian Academy of Sciences (India)
Abstract. Finite element models of the head and helmet were used to study contact forces during frontal impact of the head with a rigid surface. The finite element model of the head consists of skin, skull, cerebro-spinal fluid (CSF), brain, tentorium and falx. The finite element model of the helmet consists of shell and foam.
Adaptive Smoothed Finite Elements (ASFEM) for history dependent material models
Quak, W.; van den Boogaard, Antonius H.; Menary, Gary
2011-01-01
A successful simulation of a bulk forming process with finite elements can be difficult due to distortion of the finite elements. Nodal smoothed Finite Elements (NSFEM) are an interesting option for such a process since they show good distortion insensitivity and moreover have locking-free behavior
The finite element method in engineering, 2nd edition
International Nuclear Information System (INIS)
Rao, S.S.
1986-01-01
This work provides a systematic introduction to the various aspects of the finite element method as applied to engineering problems. Contents include: introduction to finite element method; solution of finite element equations; solid and structural mechanics; static analysis; dynamic analysis; heat transfer; fluid mechanics and additional applications
Finite element simulation and testing of ISW CFRP anchorage
DEFF Research Database (Denmark)
Schmidt, Jacob Wittrup; Goltermann, Per; Hertz, Kristian Dahl
2013-01-01
is modelled in the 3D finite Element program ABAQUS, just as digital image correlation (DIC) testing was performed to verify the finite element simulation. Also a new optimized design was produced to ensure that the finite element simulation and anchorage behaviour correlated well. It is seen...
Modelling bucket excavation by finite element
Pecingina, O. M.
2015-11-01
Changes in geological components of the layers from lignite pits have an impact on the sustainability of the cup path elements and under the action of excavation force appear efforts leading to deformation of the entire assembly. Application of finite element method in the optimization of components leads to economic growth, to increase the reliability and durability of the studied machine parts thus the machine. It is obvious usefulness of knowledge the state of mechanical tensions that the designed piece or the assembly not to break under the action of tensions that must cope during operation. In the course of excavation work on all bucket cutting force components, the first coming into contact with the material being excavated cutting edge. Therefore in the study with finite element analysis is retained only cutting edge. To study the field of stress and strain on the cutting edge will be created geometric patterns for each type of cup this will be subject to static analysis. The geometric design retains the cutting edge shape and on this on the tooth cassette location will apply an areal force on the abutment tooth. The cutting edge real pattern is subjected to finite element study for the worst case of rock cutting by symmetrical and asymmetrical cups whose profile is different. The purpose of this paper is to determine the displacement and tensions field for both profiles considering the maximum force applied on the cutting edge and the depth of the cutting is equal with the width of the cutting edge of the tooth. It will consider the worst case when on the structure will act both the tangential force and radial force on the bucket profile. For determination of stress and strain field on the form design of cutting edge profile will apply maximum force assuming uniform distribution and on the edge surface force will apply a radial force. After geometric patterns discretization on the cutting knives and determining stress field, can be seen that at the
Finite rotation shells basic equations and finite elements for Reissner kinematics
Wisniewski, K
2010-01-01
This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements - not included in standard textbooks on finite elements - are addressed, and the book includes an extensive bibliography.
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.
Finite element simulation of piezoelectric transformers.
Tsuchiya, T; Kagawa, Y; Wakatsuki, N; Okamura, H
2001-07-01
Piezoelectric transformers are nothing but ultrasonic resonators with two pairs of electrodes provided on the surface of a piezoelectric substrate in which electrical energy is carried in the mechanical form. The input and output electrodes are arranged to provide the impedance transformation, which results in the voltage transformation. As they are operated at a resonance, the electrical equivalent circuit approach has traditionally been developed in a rather empirical way and has been used for analysis and design. The present paper deals with the analysis of the piezoelectric transformers based on the three-dimensional finite element modelling. The PIEZO3D code that we have developed is modified to include the external loading conditions. The finite element approach is now available for a wide variety of the electrical boundary conditions. The equivalent circuit of lumped parameters can also be derived from the finite element method (FEM) solution if required. The simulation of the present transformers is made for the low intensity operation and compared with the experimental results. Demonstration is made for basic Rosen-type transformers in which the longitudinal mode of a plate plays an important role; in which the equivalent circuit of lumped constants has been used. However, there are many modes of vibration associated with the plate, the effect of which cannot always be ignored. In the experiment, the double resonances are sometimes observed in the vicinity of the operating frequency. The simulation demonstrates that this is due to the coupling of the longitudinal mode with the flexural mode. Thus, the simulation provides an invaluable guideline to the transformer design.
A finite element method for neutron transport
International Nuclear Information System (INIS)
Ackroyd, R.T.
1978-01-01
A variational treatment of the finite element method for neutron transport is given based on a version of the even-parity Boltzmann equation which does not assume that the differential scattering cross-section has a spherical harmonic expansion. The theory of minimum and maximum principles is based on the Cauchy-Schwartz equality and the properties of a leakage operator G and a removal operator C. For systems with extraneous sources, two maximum and one minimum principles are given in boundary free form, to ease finite element computations. The global error of an approximate variational solution is given, the relationship of one the maximum principles to the method of least squares is shown, and the way in which approximate solutions converge locally to the exact solution is established. A method for constructing local error bounds is given, based on the connection between the variational method and the method of the hypercircle. The source iteration technique and a maximum principle for a system with extraneous sources suggests a functional for a variational principle for a self-sustaining system. The principle gives, as a consequence of the properties of G and C, an upper bound to the lowest eigenvalue. A related functional can be used to determine both upper and lower bounds for the lowest eigenvalue from an inspection of any approximate solution for the lowest eigenfunction. The basis for the finite element is presented in a general form so that two modes of exploitation can be undertaken readily. The model can be in phase space, with positional and directional co-ordinates defining points of the model, or it can be restricted to the positional co-ordinates and an expansion in orthogonal functions used for the directional co-ordinates. Suitable sets of functions are spherical harmonics and Walsh functions. The latter set is appropriate if a discrete direction representation of the angular flux is required. (author)
Gelinas, R. J.; Doss, S. K.; Vajk, J. P.; Djomehri, J.; Miller, K.
1983-01-01
The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.
Finite Element analysis of jar connections
DEFF Research Database (Denmark)
Kristensen, A.; Toor, Kashif; Solem, Sigurd
2005-01-01
A new tool joint system is considered. Traditionally these rotary connections have been designed with only one shoulder geometry. However, in order to increase the torque rating of the tool joint, a new design is introduced using two shoulders. This design allow reduced tool joint dimensions wher...... whereby down-hole equipment more easily can be fitted. In order to evaluate the validity of the design, finite element analysis have been performed in ANSYS. The results obtained indicate that the new design is valid and further tests can be performed....
Finite element modeling methods for photonics
Rahman, B M Azizur
2013-01-01
The term photonics can be used loosely to refer to a vast array of components, devices, and technologies that in some way involve manipulation of light. One of the most powerful numerical approaches available to engineers developing photonic components and devices is the Finite Element Method (FEM), which can be used to model and simulate such components/devices and analyze how they will behave in response to various outside influences. This resource provides a comprehensive description of the formulation and applications of FEM in photonics applications ranging from telecommunications, astron
Mixed finite elements for global tide models.
Cotter, Colin J; Kirby, Robert C
2016-01-01
We study mixed finite element methods for the linearized rotating shallow water equations with linear drag and forcing terms. By means of a strong energy estimate for an equivalent second-order formulation for the linearized momentum, we prove long-time stability of the system without energy accumulation-the geotryptic state. A priori error estimates for the linearized momentum and free surface elevation are given in [Formula: see text] as well as for the time derivative and divergence of the linearized momentum. Numerical results confirm the theoretical results regarding both energy damping and convergence rates.
Numerical simulation of fluid-structure interactions with stabilized finite element method
Sváček, Petr
2016-03-01
This paper is interested to the interactions of the incompressible flow with a flexibly supported airfoil. The bending and the torsion modes are considered. The problem is mathematically described. The numerical method is based on the finite element method. A combination of the streamline-upwind/Petrov-Galerkin and pressure stabilizing/Petrov-Galerkin method is used for the stabilization of the finite element method. The numerical results for a three-dimensional problem of flow over an airfoil are shown.
A multigrid solution method for mixed hybrid finite elements
Energy Technology Data Exchange (ETDEWEB)
Schmid, W. [Universitaet Augsburg (Germany)
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
The finite element response Matrix method
International Nuclear Information System (INIS)
Nakata, H.; Martin, W.R.
1983-01-01
A new method for global reactor core calculations is described. This method is based on a unique formulation of the response matrix method, implemented with a higher order finite element method. The unique aspects of this approach are twofold. First, there are two levels to the overall calculational scheme: the local or assembly level and the global or core level. Second, the response matrix scheme, which is formulated at both levels, consists of two separate response matrices rather than one response matrix as is generally the case. These separate response matrices are seen to be quite beneficial for the criticality eigenvalue calculation, because they are independent of k /SUB eff/. The response matrices are generated from a Galerkin finite element solution to the weak form of the diffusion equation, subject to an arbitrary incoming current and an arbitrary distributed source. Calculational results are reported for two test problems, the two-dimensional International Atomic Energy Agency benchmark problem and a two-dimensional pressurized water reactor test problem (Biblis reactor), and they compare well with standard coarse mesh methods with respect to accuracy and efficiency. Moreover, the accuracy (and capability) is comparable to fine mesh for a fraction of the computational cost. Extension of the method to treat heterogeneous assemblies and spatial depletion effects is discussed
Finite element modeling of piezoelectric elements with complex electrode configuration
International Nuclear Information System (INIS)
Paradies, R; Schläpfer, B
2009-01-01
It is well known that the material properties of piezoelectric materials strongly depend on the state of polarization of the individual element. While an unpolarized material exhibits mechanically isotropic material properties in the absence of global piezoelectric capabilities, the piezoelectric material properties become transversally isotropic with respect to the polarization direction after polarization. Therefore, for evaluating piezoelectric elements the material properties, including the coupling between the mechanical and the electromechanical behavior, should be addressed correctly. This is of special importance for the micromechanical description of piezoelectric elements with interdigitated electrodes (IDEs). The best known representatives of this group are active fiber composites (AFCs), macro fiber composites (MFCs) and the radial field diaphragm (RFD), respectively. While the material properties are available for a piezoelectric wafer with a homogeneous polarization perpendicular to its plane as postulated in the so-called uniform field model (UFM), the same information is missing for piezoelectric elements with more complex electrode configurations like the above-mentioned ones with IDEs. This is due to the inhomogeneous field distribution which does not automatically allow for the correct assignment of the material, i.e. orientation and property. A variation of the material orientation as well as the material properties can be accomplished by including the polarization process of the piezoelectric transducer in the finite element (FE) simulation prior to the actual load case to be investigated. A corresponding procedure is presented which automatically assigns the piezoelectric material properties, e.g. elasticity matrix, permittivity, and charge vector, for finite element models (FEMs) describing piezoelectric transducers according to the electric field distribution (field orientation and strength) in the structure. A corresponding code has been
Finite element form of FDV for widely varying flowfields
Richardson, G. A.; Cassibry, J. T.; Chung, T. J.; Wu, S. T.
2010-01-01
We present the Flowfield Dependent Variation (FDV) method for physical applications that have widely varying spatial and temporal scales. Our motivation is to develop a versatile numerical method that is accurate and stable in simulations with complex geometries and with wide variations in space and time scales. The use of a finite element formulation adds capabilities such as flexible grid geometries and exact enforcement of Neumann boundary conditions. While finite element schemes are used extensively by researchers solving computational fluid dynamics in many engineering fields, their use in space physics, astrophysical fluids and laboratory magnetohydrodynamic simulations with shocks has been predominantly overlooked. The FDV method is unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in these regimes. The first part of this paper concentrates on the presentation of our numerical method formulation for Newtonian and relativistic hydrodynamics. In the second part we present several standard simulation examples that test the method's limitations and verify the FDV method. We show that our finite element formulation is stable and accurate for a range of both Mach numbers and Lorentz factors in one-dimensional test problems. We also present the converging/diverging nozzle which contains both incompressible and compressible flow in the flowfield over a range of subsonic and supersonic regions. We demonstrate the stability of our method and the accuracy by comparison with the results of other methods including the finite difference Total Variation Diminishing method. We explore the use of FDV for both non-relativistic and relativistic fluids (hydrodynamics) with strong shocks in order to establish the effectiveness in future applications of this method in astrophysical and laboratory plasma environments.
Nodally Integrated Finite Element Formulation for Mindlin-Reissner Plates
Simoes, D. A.; Jadhav, T. A.
2014-01-01
This work describes a nodally integrated finite element formulation for plates under the Mindlin-Reissner theory. The formulation makes use of the weighted residual method and nodal integration to derive the assumed strain relations. An element formulation for four-node quadrilateral elements is implemented in the nonlinear finite element solver Abaqus using the UEL user element subroutine. Numerical tests are carried out on the new element and the results are presented.
Finite element or Galerkin type semidiscrete schemes
Durgun, K.
1983-01-01
A finite element of Galerkin type semidiscrete method is proposed for numerical solution of a linear hyperbolic partial differential equation. The question of stability is reduced to the stability of a system of ordinary differential equations for which Dahlquist theory applied. Results of separating the part of numerical solution which causes the spurious oscillation near shock-like response of semidiscrete scheme to a step function initial condition are presented. In general all methods produce such oscillatory overshoots on either side of shocks. This overshoot pathology, which displays a behavior similar to Gibb's phenomena of Fourier series, is explained on the basis of dispersion of separated Fourier components which relies on linearized theory to be satisfactory. Expository results represented.
Computational structural analysis and finite element methods
Kaveh, A
2014-01-01
Graph theory gained initial prominence in science and engineering through its strong links with matrix algebra and computer science. Moreover, the structure of the mathematics is well suited to that of engineering problems in analysis and design. The methods of analysis in this book employ matrix algebra, graph theory and meta-heuristic algorithms, which are ideally suited for modern computational mechanics. Efficient methods are presented that lead to highly sparse and banded structural matrices. The main features of the book include: application of graph theory for efficient analysis; extension of the force method to finite element analysis; application of meta-heuristic algorithms to ordering and decomposition (sparse matrix technology); efficient use of symmetry and regularity in the force method; and simultaneous analysis and design of structures.
Quality management of finite element analysis
Barlow, John
1991-09-01
A quality management system covering the use of finite element analysis is described. The main topics are as follows: acquisition, development and verification of software (including the software suppliers software quality control system), support, documentation, error control, internal software, software acceptance and release; development and qualification of analysis methods, including software evaluation, analysis procedure qualification and documentation, procedure quality checks, control of analysis procedure errors; product design and integrity analysis, including project quality assurance and analysis planning, task specification and allocation, analysis, execution, results checking and analysis records. Other issues include the commercial and business advantages of quality systems, project and technical management and the training and experience of personnel. The items are correlated with the requirements of International Standard Organization 9001.
Adaptive finite element method for shape optimization
Morin, Pedro
2012-01-16
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Adaptive finite element methods for differential equations
Bangerth, Wolfgang
2003-01-01
These Lecture Notes discuss concepts of `self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order ...
Finite-Element Modelling of Biotransistors
Directory of Open Access Journals (Sweden)
Selvaganapathy PR
2010-01-01
Full Text Available Abstract Current research efforts in biosensor design attempt to integrate biochemical assays with semiconductor substrates and microfluidic assemblies to realize fully integrated lab-on-chip devices. The DNA biotransistor (BioFET is an example of such a device. The process of chemical modification of the FET and attachment of linker and probe molecules is a statistical process that can result in variations in the sensed signal between different BioFET cells in an array. In order to quantify these and other variations and assess their importance in the design, complete physical simulation of the device is necessary. Here, we perform a mean-field finite-element modelling of a short channel, two-dimensional BioFET device. We compare the results of this model with one-dimensional calculation results to show important differences, illustrating the importance of the molecular structure, placement and conformation of DNA in determining the output signal.
The computation of linear triangular matrices in the finite element ...
African Journals Online (AJOL)
An algorithm is developed for generating the system matrices for the Finite Element Method of solving some classes of second order partial differential equations problems using the linear triangular elements. This algorithm reduces the complexity normally associated with the finite element approximation and makes the ...
Review on finite element method | Erhunmwun | Journal of Applied ...
African Journals Online (AJOL)
... finite elements, so that it is possible to systematically construct the approximation functions needed in a variational or weighted-residual approximation of the solution of a problem over each element. Keywords: Weak Formulation, Discretisation, Numerical methods, Finite element method, Global equations, Nodal solution ...
Finite element analysis theory and application with ANSYS
Moaveni, Saeed
2015-01-01
For courses in Finite Element Analysis, offered in departments of Mechanical or Civil and Environmental Engineering. While many good textbooks cover the theory of finite element modeling, Finite Element Analysis: Theory and Application with ANSYS is the only text available that incorporates ANSYS as an integral part of its content. Moaveni presents the theory of finite element analysis, explores its application as a design/modeling tool, and explains in detail how to use ANSYS intelligently and effectively. Teaching and Learning Experience This program will provide a better teaching and learning experience-for you and your students. It will help: *Present the Theory of Finite Element Analysis: The presentation of theoretical aspects of finite element analysis is carefully designed not to overwhelm students. *Explain How to Use ANSYS Effectively: ANSYS is incorporated as an integral part of the content throughout the book. *Explore How to Use FEA as a Design/Modeling Tool: Open-ended design problems help stude...
Symplectic and multisymplectic schemes with the simple finite element method
International Nuclear Information System (INIS)
Zhen Liu; Bai Yongqiang; Li Qisheng; Wu Ke
2003-01-01
We study the numerical scheme of elliptic equations by the finite element method. With the special finite element domain, we can find that the scheme can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimensional case. Then we consider the discrete variational principle with the finite element method in the corresponding Lagrangian formalism for classical mechanics and field theory and get the symplectic or multisymplectic scheme of the Euler-Lagrangian equation
The finite element method its basis and fundamentals
Zienkiewicz, Olek C; Zhu, JZ
2013-01-01
The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book's content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field prob
Finite Element Modeling of Burr Formation in Metal Cutting
Min, Sangkee; Dornfeld, David; Kim, J.; Shyu, B.
2007-01-01
In order to advance understanding of the burr formation process, a series of finite element models are introduced. First a finite element model of the burr formation of two-dimensional orthogonal cutting is introduced and validated with experimental observations. A detailed and thorough examination of the drilling burr forming process is undertaken. This information is then used in the construction of an analytical model and, leads to development of a three-dimensional finite element mode...
Impact of new computing systems on finite element computations
International Nuclear Information System (INIS)
Noor, A.K.; Fulton, R.E.; Storaasi, O.O.
1983-01-01
Recent advances in computer technology that are likely to impact finite element computations are reviewed. The characteristics of supersystems, highly parallel systems, and small systems (mini and microcomputers) are summarized. The interrelations of numerical algorithms and software with parallel architectures are discussed. A scenario is presented for future hardware/software environment and finite element systems. A number of research areas which have high potential for improving the effectiveness of finite element analysis in the new environment are identified
Energy Technology Data Exchange (ETDEWEB)
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Ablative Thermal Response Analysis Using the Finite Element Method
Dec John A.; Braun, Robert D.
2009-01-01
A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.
Adaptive Smoothed Finite Elements (ASFEM) for history dependent material models
International Nuclear Information System (INIS)
Quak, W.; Boogaard, A. H. van den
2011-01-01
A successful simulation of a bulk forming process with finite elements can be difficult due to distortion of the finite elements. Nodal smoothed Finite Elements (NSFEM) are an interesting option for such a process since they show good distortion insensitivity and moreover have locking-free behavior and good computational efficiency. In this paper a method is proposed which takes advantage of the nodally smoothed field. This method, named adaptive smoothed finite elements (ASFEM), revises the mesh for every step of a simulation without mapping the history dependent material parameters. In this paper an updated-Lagrangian implementation is presented. Several examples are given to illustrate the method and to show its properties.
Finite element analysis in a minicomputer/mainframe environment
Storaasli, O. O.; Murphy, R. C.
1978-01-01
Design considerations were evaluated for general purpose finite element systems to maximize performance when installed on distributed computer hardware/software systems. It is shown how the features of current minicomputers complement those of a modular implementation of the finite element method for increasing the control, speed, and visibility (interactive graphics) in solving structural problems at reduced cost. The approach used is to implement a finite element system in a distributed computer environment to solve structural problems and to explore alternatives in distributing finite element computations.
Introduction to finite element analysis using MATLAB and Abaqus
Khennane, Amar
2013-01-01
There are some books that target the theory of the finite element, while others focus on the programming side of things. Introduction to Finite Element Analysis Using MATLAB(R) and Abaqus accomplishes both. This book teaches the first principles of the finite element method. It presents the theory of the finite element method while maintaining a balance between its mathematical formulation, programming implementation, and application using commercial software. The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. MA
International Nuclear Information System (INIS)
Lee, H. C.; Jo, C. K.; Noh, J. M.
2008-01-01
In this study, we developed a neutron diffusion equation solver based on the finite element method for CAPP code. Three types of triangular finite elements and five types of rectangular depending on the order of the shape functions were implemented for 2-D application. Ten types of triangular prismatic finite elements and seventeen types of rectangular prismatic finite elements were also implemented for 3-D application. Two types of polynomial mapping from the master finite element to a real finite element were adopted for flexibility in dealing with complex geometry. They are linear mapping and iso-parametric mapping. In linear mapping, only the vertex nodes are used as the mapping points. In iso-parametric mapping, all the nodal points in the finite element are used as the mapping points, which enables the real finite elements to have curved surfaces. For the treatment of spatial dependency of cross-sections in the finite elements, three types of polynomial expansion of the cross-sections in the finite elements were implemented. They are constant, linear, and iso-parametric cross-section expansions. The power method with the Wielandt acceleration technique was adopted as the outer iteration algorithm. The BiCGSTAB algorithm with the ILU (Incomplete LU) decomposition pre-conditioner was used as the linear equation solver in the inner iteration. The neutron diffusion equation solver developed in this study was verified against two well known benchmark problems, IAEA PWR benchmark problem and OECD/NEA PBMR400 benchmark problem. Results of numerical tests showed that the solution converged to the reference solution as the finite elements are refined and as the order of the finite elements increases. Numerical tests also showed that the higher order finite element method is much efficient than lower order finite element method or finite difference method. (authors)
Directory of Open Access Journals (Sweden)
Marek Krynke
2013-02-01
Full Text Available In slewing bearings, a great number of contact pairs are present on the contact surfaces between the rolling elements and raceways of the bearing. Computations to determine the load of the individual rolling elements, taking into account the flexibility of the bearing ring, are most often carried out using the finite element method. Construction of a FEM full model of the bearing, taking into account the shape of the rolling elements and the determination of the contact problem for every rolling element, leads to a singularity of stiffness matrix, which in turn makes the problem impossible to solve. In FEM models the rolling elements are replaced by one-dimensional finite elements (linear elements to simplify the computation procedure and to obtain an optimal time for computations. replaced by truss elements with a material non-linear characteristic located between the raceway centres of the curvatures in their axial section, are presented in the paper
Curvilinear interface methodology for finite-element applications
Rose, Ollie James
2000-10-01
Recent trends in design and manufacturing suggest a tendency toward multiple centers of specialty which results in a need for improved integration methodology for dissimilar finite element or CFD meshes. Since a typical finite element or CFD analysis requires about 50% of an engineers effort to be devoted to modeling and input, there is a need to advance the state-of-the-art in modeling, methodology. These two trends indicate a need to for the capability to combine independently-modeled configurations in an automated and robust way without the need for global remodeling. One approach to addressing this need is the development of interfacing methodology which will automatically integrate independently modeled subdomains. The present research included the following objectives: (i) to develop and implement computational methods for automatically remodeling non-coincident finite element models having a pre-defined interface, (ii) to formulate and implement a parametric representation of general space curves and surfaces with a well-defined orientation, and (iii) to demonstrate the computational methodology with representative two- and three-dimensional finite element models. Methodology for automatically remodeling non-coincident subdomains was developed and tested for two- and three-dimensional, independently modeled subdomains. Representative classes of applications have been solved which gave good agreement with reference solutions obtained with conventional methods. The two-dimensional classes of problems solved included flat and curved membranes multiple subdomains having large gaps between the subdomains and general space curves representing an interface for re-modeling the portions of subdomains adjacent to the interface. The three-dimensional classes of problems solved includes multiple three-dimensional subdomains having large three-dimensional gap between previously modeled subdomains. The interface was represented by general surfaces with a well
A Finite Element Analysis of Optimal Variable Thickness Sheets
DEFF Research Database (Denmark)
Petersson, Joakim S
1996-01-01
A quasimixed Finite Element (FE) method for maximum stiffness of variablethickness sheets is analysed. The displacement is approximated with ninenode Lagrange quadrilateral elements and the thickness is approximated aselementwise constant. One is guaranteed that the FE displacement solutionswill ...
Control volume finite element method for radiation
International Nuclear Information System (INIS)
Ben Salah, M.; Askri, F.; Rousse, D.; Ben Nasrallah, S.
2005-01-01
In this paper a new methodology is presented by the authors for the numerical treatment of radiative heat transfer in emitting, absorbing and scattering media. This methodology is based on the utilisation of Control Volume Finite Element Method (CVFEM) and the use, for the first time, of matrix formulation of the discretized Radiative Transfer Equation (RTE). The advantages of the proposed methodology is to avoid problems that confronted when previous techniques are used to predict radiative heat transfer, essentially, in complex geometries and when there is scattering and/or non-black boundaries surfaces. Besides, the new formulation of the discretized RTE presented in this paper makes it possible to solve the algebraic system by direct or iterative numerical methods. The theoretical background of CVFEM and matrix formulation is presented in the text. The proposed technique is applied to different test problems, and the results compared favourably against other published works. Moreover this paper discusses in detail the effects of some radiative parameters, such as optical thickness and walls emissivities on the spatial evolution of the radiant heat flux. The numerical simulation of radiative heat transfer for different cases using the algorithm proposed in this work has shown that the developed computer procedure needs an accurate CPU time and is exempt of any numerical oscillations
Finite element modelling of composite castellated beam
Directory of Open Access Journals (Sweden)
Frans Richard
2017-01-01
Full Text Available Nowadays, castellated beam becomes popular in building structural as beam members. This is due to several advantages of castellated beam such as increased depth without any additional mass, passing the underfloor service ducts without changing of story elevation. However, the presence of holes can develop various local effects such as local buckling, lateral torsional buckling caused by compression force at the flange section of the steel beam. Many studies have investigated the failure mechanism of castellated beam and one technique which can prevent the beam fall into local failure is the use of reinforced concrete slab as lateral support on castellated beam, so called composite castellated beam. Besides of preventing the local failure of castellated beam, the concrete slab can increase the plasticity moment of the composite castellated beam section which can deliver into increasing the ultimate load of the beam. The aim of this numerical studies of composite castellated beam on certain loading condition (monotonic quasi-static loading. ABAQUS was used for finite element modelling purpose and compared with the experimental test for checking the reliability of the model. The result shows that the ultimate load of the composite castellated beam reached 6.24 times than the ultimate load of the solid I beam and 1.2 times compared the composite beam.
Finite element modeling of retinal prosthesis mechanics
Basinger, B. C.; Rowley, A. P.; Chen, K.; Humayun, M. S.; Weiland, J. D.
2009-10-01
Epiretinal prostheses used to treat degenerative retina diseases apply stimulus via an electrode array fixed to the ganglion cell side of the retina. Mechanical pressure applied by these arrays to the retina, both during initial insertion and throughout chronic use, could cause sufficient retinal damage to reduce the device's effectiveness. In order to understand and minimize potential mechanical damage, we have used finite element analysis to model mechanical interactions between an electrode array and the retina in both acute and chronic loading configurations. Modeling indicates that an acute tacking force distributes stress primarily underneath the tack site and heel edge of the array, while more moderate chronic stresses are distributed more evenly underneath the array. Retinal damage in a canine model chronically implanted with a similar array occurred in correlating locations, and model predictions correlate well with benchtop eyewall compression tests. This model provides retinal prosthesis researchers with a tool to optimize the mechanical electrode array design, but the techniques used here represent a unique effort to combine a modifiable device and soft biological tissues in the same model and those techniques could be extended to other devices that come into mechanical contact with soft neural tissues.
Probabilistic finite element modeling of waste rollover
International Nuclear Information System (INIS)
Khaleel, M.A.; Cofer, W.F.; Al-fouqaha, A.A.
1995-09-01
Stratification of the wastes in many Hanford storage tanks has resulted in sludge layers which are capable of retaining gases formed by chemical and/or radiolytic reactions. As the gas is produced, the mechanisms of gas storage evolve until the resulting buoyancy in the sludge leads to instability, at which point the sludge ''rolls over'' and a significant volume of gas is suddenly released. Because the releases may contain flammable gases, these episodes of release are potentially hazardous. Mitigation techniques are desirable for more controlled releases at more frequent intervals. To aid the mitigation efforts, a methodology for predicting of sludge rollover at specific times is desired. This methodology would then provide a rational basis for the development of a schedule for the mitigation procedures. In addition, a knowledge of the sensitivity of the sludge rollovers to various physical and chemical properties within the tanks would provide direction for efforts to reduce the frequency and severity of these events. In this report, the use of probabilistic finite element analyses for computing the probability of rollover and the sensitivity of rollover probability to various parameters is described
An Abaqus UEL implementation of the smoothed finite element method
Kumbhar, Pramod Y; Francis, Amrita; Swaminathan, Narasimhan; Annabattula, Ratna Kumar; Natarajan, Sundararajan
2017-01-01
In this paper, we discuss the implementation of a cell based smoothed finite element method (CSFEM) within the commercial finite element software Abaqus. The salient feature of the CSFEM is that it does not require an explicit form of the derivative of the shape functions and there is no isoparametric mapping. This implementation is accomplished by employing the user element subroutine (UEL) feature of the software. The details on the input data format together with the proposed user element ...
Hydrothermal analysis in engineering using control volume finite element method
Sheikholeslami, Mohsen
2015-01-01
Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems),
Geotechnical Ultimate Limit State Design Using Finite Elements
Brinkgreve, R.B.J.; Post, M.
2015-01-01
Displacement-based finite element calculations are primarily used for serviceability limit state (SLS) analysis, but the finite element method also offers possibilities for ultimate limit state (ULS) design in geotechnical engineering. The combined use of SLS and ULS calculations with partial safety
Parallel direct solver for finite element modeling of manufacturing processes
DEFF Research Database (Denmark)
Nielsen, Chris Valentin; Martins, P.A.F.
2017-01-01
The central processing unit (CPU) time is of paramount importance in finite element modeling of manufacturing processes. Because the most significant part of the CPU time is consumed in solving the main system of equations resulting from finite element assemblies, different approaches have been d...
A geometric toolbox for tetrahedral finite element partitions
Brandts, J.; Korotov, S.; Křížek, M.; Axelsson, O.; Karátson, J.
2011-01-01
In this work we present a survey of some geometric results on tetrahedral partitions and their refinements in a unified manner. They can be used for mesh generation and adaptivity in practical calculations by the finite element method (FEM), and also in theoretical finite element (FE) analysis.
An introduction to the UNCLE finite element scheme
International Nuclear Information System (INIS)
Enderby, J.A.
1983-01-01
UNCLE is a completely general finite element scheme which provides common input, output, equation-solving and other facilities for a family of finite element codes for linear and non-linear stress analysis, heat transfer etc. This report describes the concepts on which UNCLE is based and gives a general account of the facilities provided. (author)
Analysis of Tube Drawing Process – A Finite Element Approach ...
African Journals Online (AJOL)
In this paper the effect of die semi angle on drawing load in cold tube drawing has been investigated numerically using the finite element method. The equation governing the stress distribution was derived and solved using Galerkin finite element method. An isoparametric formulation for the governing equation was utilized ...
About the Finite Element Method Applied to Thick Plates
Directory of Open Access Journals (Sweden)
Mihaela Ibănescu
2006-01-01
Full Text Available The present paper approaches of plates subjected to transverse loads, when the shear force and the actual boundary conditions are considered, by using the Finite Element Method. The isoparametric finite elements create real facilities in formulating the problems and great possibilities in creating adequate computer programs.
Simulation of temperature distribution by finite element analysis on ...
Indian Academy of Sciences (India)
on exposure to the synchrotron beam has been simulated by finite element analysis. Design of the cooling mechanism for each of these components has been carried out and estimation of the temperature rise has also been done incorporating the cooling mechanism. Keywords. Synchrotron; EXAFS; finite element analysis.
THE PRACTICAL ANALYSIS OF FINITE ELEMENTS METHOD ERRORS
Directory of Open Access Journals (Sweden)
Natalia Bakhova
2011-03-01
Full Text Available Abstract. The most important in the practical plan questions of reliable estimations of finite elementsmethod errors are considered. Definition rules of necessary calculations accuracy are developed. Methodsand ways of the calculations allowing receiving at economical expenditures of computing work the best finalresults are offered.Keywords: error, given the accuracy, finite element method, lagrangian and hermitian elements.
Finite Element Method for Analysis of Material Properties
DEFF Research Database (Denmark)
Rauhe, Jens Christian
and the finite element method. The material microstructure of the heterogeneous material is non-destructively determined using X-ray microtomography. A software program has been generated which uses the X-ray tomographic data as an input for the mesh generation of the material microstructure. To obtain a proper...... description of the material microstructure the finite element models must contain a large number of elements and this problem is solved by using the preconditioned conjugated gradient solver with an Element-By-Element preconditioner. Finite element analysis provides the volume averaged stresses and strains...... which are used for the determination of the effective properties of the heterogeneous material. Generally, the properties determined using the finite element method coupled with X-ray microtomography are in good agreement with both experimentally determined properties and properties determined using...
Finite Element Analysis of Fluid-Conveying Timoshenko Pipes
Directory of Open Access Journals (Sweden)
Chih-Liang Chu
1995-01-01
Full Text Available A general finite element formulation using cubic Hermitian interpolation for dynamic analysis of pipes conveying fluid is presented. Both the effects of shearing deformations and rotary inertia are considered. The development retains the use of the classical four degrees-of-freedom for a two-node element. The effect of moving fluid is treated as external distributed forces on the support pipe and the fluid finite element matrices are derived from the virtual work done due to the fluid inertia forces. Finite element matrices for both the support pipe and moving fluid are derived and given explicitly. A numerical example is given to demonstrate the validity of the model.
Shear beams in finite element modelling : Software implementation and validation
Schreppers, G.J.; Hendriks, M.A.N.; Boer, A.; Ferreira, D.; Kikstra, W.P.
2015-01-01
Fiber models for beam and shell elements allow for relatively rapid finite element analysis of concrete structures and structural elements. This project aims at the development of the formulation of such elements and a pilot implementation. The reduction of calculation time and degrees of freedom
Lamarche, L.; Degrez, G.; Prince, A.
A method is described that combines the geometric flexibility of finite element methodology with recent developments of high-resolution finite difference schemes for hyperbolic systems of equations. It is proposed to use the standard weighted residual approach to set up the discrete equations. Upwinding is then achieved via a modified quadrature rule. The Gaussian point is chosen to match the finite difference discretization on a model scalar equation. The extension to systems of equations is then obtained following the flux-splitting approach suggested by Steger and Warming (1981) and Van Leer (1982).
Flexible Automatic Discretization for Finite Differences: Eliminating the Human Factor
Pranger, Casper
2017-04-01
In the geophysical numerical modelling community, finite differences are (in part due to their small footprint) a popular spatial discretization method for PDEs in the regular-shaped continuum that is the earth. However, they rapidly become prone to programming mistakes when physics increase in complexity. To eliminate opportunities for human error, we have designed an automatic discretization algorithm using Wolfram Mathematica, in which the user supplies symbolic PDEs, the number of spatial dimensions, and a choice of symbolic boundary conditions, and the script transforms this information into matrix- and right-hand-side rules ready for use in a C++ code that will accept them. The symbolic PDEs are further used to automatically develop and perform manufactured solution benchmarks, ensuring at all stages physical fidelity while providing pragmatic targets for numerical accuracy. We find that this procedure greatly accelerates code development and provides a great deal of flexibility in ones choice of physics.
A modified finite element procedure for underwater shock analysis
International Nuclear Information System (INIS)
Chan, S.K.
1990-01-01
Using the regular finite element method for analyzing wave propagation problems presents difficulties: (a) The finite element mesh gives spurious reflection of the traveling wave and (b) Since a finite element model has to have a finite boundary, the wave is reflected by the outside boundary. However, for underwater shock problems, only the response of the structure is of major interest, not the behavior of the wave itself, and the shock wave can be assumed to be spherical. By taking advantage of the limited scope of the underwater shock problem, a finite element procedure can be developed that eliminates the above difficulties. This procedure not only can give very accurate solutions but it may also include structural nonlinearities and effect of cavitation
On Finite Element Computations of Contact Problems in Micropolar Elasticity
Eremeyev, Victor A.; Skrzat, Andrzej; Stachowicz, Feliks
2016-01-01
Within the linear micropolar elasticity we discuss the development of new finite element and its implementation in commercial software. Here we implement the developed 8-node hybrid isoparametric element into ABAQUS and perform solutions of contact problems. We consider the contact of polymeric stamp modelled within the micropolar elasticity with an elastic substrate. The peculiarities of modelling of contact problems with a user defined finite element in ABAQUS are discussed. The provided co...
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.
Gleadall, Andrew; Pan, Jingzhe; Ding, Lifeng; Kruft, Marc-Anton; Curcó, David
2015-11-01
Molecular dynamics (MD) simulations are widely used to analyse materials at the atomic scale. However, MD has high computational demands, which may inhibit its use for simulations of structures involving large numbers of atoms such as amorphous polymer structures. An atomic-scale finite element method (AFEM) is presented in this study with significantly lower computational demands than MD. Due to the reduced computational demands, AFEM is suitable for the analysis of Young's modulus of amorphous polymer structures. This is of particular interest when studying the degradation of bioresorbable polymers, which is the topic of an accompanying paper. AFEM is derived from the inter-atomic potential energy functions of an MD force field. The nonlinear MD functions were adapted to enable static linear analysis. Finite element formulations were derived to represent interatomic potential energy functions between two, three and four atoms. Validation of the AFEM was conducted through its application to atomic structures for crystalline and amorphous poly(lactide). Copyright © 2015 Elsevier Ltd. All rights reserved.
A two-scale finite element formulation for the dynamic analysis of heterogeneous materials
Energy Technology Data Exchange (ETDEWEB)
Ionita, Axinte [Los Alamos National Laboratory
2008-01-01
In the analysis of heterogeneous materials using a two-scale Finite Element Method (FEM) the usual assumption is that the Representative Volume Element (RVE) of the micro-scale is much smaller than the finite element discretization of the macro-scale. However there are situations in which the RVE becomes comparable with, or even bigger than the finite element. These situations are considered in this article from the perspective of a two-scale FEM dynamic analysis. Using the principle of virtual power, new equations for the fluctuating fields are developed in terms of velocities rather than displacements. To allow more flexibility in the analysis, a scaling deformation tensor is introduced together with a procedure for its determination. Numerical examples using the new approach are presented.
Finite Element Simulation of Blanking Process
Directory of Open Access Journals (Sweden)
Afzal Ahmed
2012-10-01
daya penembusan sebanyak 42%. Daya tebukan yang diukur melalui eksperimen dan simulasi kekal pada kira-kira 90kN melepasi penembusan punch sebanyak 62%. Apabila ketebalan keputusan kunci ditambah, ketinggian retak dikurangkan dan ini meningkatkan kualiti pengosongan.KEYWORDS: simulation; finite element simulation; blanking; computer aided manufacturing
A finite element calculation of flux pumping
Campbell, A. M.
2017-12-01
A flux pump is not only a fascinating example of the power of Faraday’s concept of flux lines, but also an attractive way of powering superconducting magnets without large electronic power supplies. However it is not possible to do this in HTS by driving a part of the superconductor normal, it must be done by exceeding the local critical density. The picture of a magnet pulling flux lines through the material is attractive, but as there is no direct contact between flux lines in the magnet and vortices, unless the gap between them is comparable to the coherence length, the process must be explicable in terms of classical electromagnetism and a nonlinear V-I characteristic. In this paper a simple 2D model of a flux pump is used to determine the pumping behaviour from first principles and the geometry. It is analysed with finite element software using the A formulation and FlexPDE. A thin magnet is passed across one or more superconductors connected to a load, which is a large rectangular loop. This means that the self and mutual inductances can be calculated explicitly. A wide strip, a narrow strip and two conductors are considered. Also an analytic circuit model is analysed. In all cases the critical state model is used, so the flux flow resistivity and dynamic resistivity are not directly involved, although an effective resistivity appears when J c is exceeded. In most of the cases considered here is a large gap between the theory and the experiments. In particular the maximum flux transferred to the load area is always less than the flux of the magnet. Also once the threshold needed for pumping is exceeded the flux in the load saturates within a few cycles. However the analytic circuit model allows a simple modification to allow for the large reduction in I c when the magnet is over a conductor. This not only changes the direction of the pumped flux but leads to much more effective pumping.
Precise magnetostatic field using the finite element method
International Nuclear Information System (INIS)
Nascimento, Francisco Rogerio Teixeira do
2013-01-01
The main objective of this work is to simulate electromagnetic fields using the Finite Element Method. Even in the easiest case of electrostatic and magnetostatic numerical simulation some problems appear when the nodal finite element is used. It is difficult to model vector fields with scalar functions mainly in non-homogeneous materials. With the aim to solve these problems two types of techniques are tried: the adaptive remeshing using nodal elements and the edge finite element that ensure the continuity of tangential components. Some numerical analysis of simple electromagnetic problems with homogeneous and non-homogeneous materials are performed using first, the adaptive remeshing based in various error indicators and second, the numerical solution of waveguides using edge finite element. (author)
Ruiz-Baier, Ricardo; Lunati, Ivan
2016-10-01
We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation
Finite element solution algorithm for incompressible fluid dynamics
Baker, A. J.
1974-01-01
A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the transient motion of a viscous incompressible fluid, i.e., hydrodynamics. Dependent variable transformation renders the differential equation description uniformly elliptic. The finite element algorithm is established using the Galerkin criterion on a local basis within the Method of Weighted Residuals. It is unconstrained with respect to system linearity, computational mesh uniformity or solution domain closure regularity. The finite element matrices are established using a linear 'natural coordinate function' description. Computational solutions using the COMOC computer program illustrate the various features of the algorithm including recirculating flows.
A wave finite element analysis of the passive cochlea
Elliott, Stephen J.; Ni, Guangjian; Mace, Brian R.; Lineton, Ben
2013-01-01
Current models of the cochlea can be characterized as being either based on the assumed propagation of a single slow wave, which provides good insight, or involve the solution of a numerical model, such as in the finite element method, which allows the incorporation of more detailed anatomical features. In this paper it is shown how the wave finite element method can be used to decompose the results of a finite element calculation in terms of wave components, which allows the insight of the w...
Finite Element Based Formulation of Lattice Boltzmann Equation
International Nuclear Information System (INIS)
Jo, Jong Chull; Roh, Kyung Wan; Kwon, Young W.; Kwon, Young W.
2008-01-01
The Lattice Boltzmann Method (LBM) has been developed for application to thermal-fluid problems. Recently, the technique was also applied to fluid-structure interaction problems. Most of those studies considered a regular shape of lattice or mesh like square and cubic grids. In order to apply the LBM to more practical cases, it is necessary to be able to solve complex or irregular shapes of problem domains. There have been different kinds of approaches to address the problems. The most common technique was using the finite volume formulation of the lattice Boltzmann equation. Another approach was a point-wise interpolation technique for irregular grids. Other techniques were based on the finite element method. Generally, the finite element method is very powerful for solving two or three-dimensional complex or irregular shapes of domains using the isoparametric element formulation which is based on a mathematical mapping from a regular shape of element in an imaginary domain to a more general and irregular shape of element in the physical domain. In addition, there are variety of choices of finite elements such as triangular or quadrilateral shapes in 2-D, or tetrahedral, triangular prism, or general six-sided solids in 3-D. As a result, the present study presents a new finite element formulation for the lattice Boltzmann equation using the general weighted residual technique. Among the weighted residual formulations, the collocation method, Galerkin method or method of moments are used to develop the finite element based LBM
A simple triangular finite element for nonlinear thin shells: statics, dynamics and anisotropy
Viebahn, Nils; Pimenta, Paulo M.; Schröder, Jörg
2017-02-01
This work presents a simple finite element implementation of a geometrically exact and fully nonlinear Kirchhoff-Love shell model. Thus, the kinematics are based on a deformation gradient written in terms of the first- and second-order derivatives of the displacements. The resulting finite element formulation provides C^1-continuity using a penalty approach, which penalizes the kinking at the edges of neighboring elements. This approach enables the application of well-known C^0-continuous interpolations for the displacements, which leads to a simple finite element formulation, where the only unknowns are the nodal displacements. On the basis of polyconvex strain energy functions, the numerical framework for the simulation of isotropic and anisotropic thin shells is presented. A consistent plane stress condition is incorporated at the constitutive level of the model. A triangular finite element, with a quadratic interpolation for the displacements and a one-point integration for the enforcement of the C^1-continuity at the element interfaces leads to a robust shell element. Due to the simple nature of the element, even complex geometries can be meshed easily, which include folded and branched shells. The reliability and flexibility of the element formulation is shown in a couple of numerical examples, including also time dependent boundary value problems. A plane reference configuration is assumed for the shell mid-surface, but initially curved shells can be accomplished if one regards the initial configuration as a stress-free deformed state from the plane position, as done in previous works.
High convergence order finite elements with lumped mass matrix
DEFF Research Database (Denmark)
Jensen, Morten skårup
1996-01-01
A method for deriving hexahedral finite elements with lumped mass matrices for three-dimensional problems is presented. These elements meet the theoretical conditions for high order convergence, and two numerical examples based on the three-dimensional scalar wave equation show that this is also...... the case in practice and that their accuracy is comparable to elements with consistent mass matrices....
Reliable finite element methods for self-adjoint singular perturbation ...
African Journals Online (AJOL)
It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundaryvalue singular perturbation problem admits a decomposition into a regular part and a finite ...
Finite element analyses for RF photoinjector gun cavities
International Nuclear Information System (INIS)
Marhauser, F.
2006-01-01
This paper details electromagnetical, thermal and structural 3D Finite Element Analyses (FEA) for normal conducting RF photoinjector gun cavities. The simulation methods are described extensively. Achieved results are presented. (orig.)
Structural Topology Optimization Based on the Smoothed Finite Element Method
Directory of Open Access Journals (Sweden)
Vahid Shobeiri
Full Text Available Abstract In this paper, the smoothed finite element method, incorporated with the level set method, is employed to carry out the topology optimization of continuum structures. The structural compliance is minimized subject to a constraint on the weight of material used. The cell-based smoothed finite element method is employed to improve the accuracy and stability of the standard finite element method. Several numerical examples are presented to prove the validity and utility of the proposed method. The obtained results are compared with those obtained by several standard finite element-based examples in order to access the applicability and effectiveness of the proposed method. The common numerical instabilities of the structural topology optimization problems such as checkerboard pattern and mesh dependency are studied in the examples.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Energy Technology Data Exchange (ETDEWEB)
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Finite element analysis of unnotched charpy impact tests
2008-10-01
This paper describes nonlinear finite element analysis (FEA) to examine the energy to : fracture unnotched Charpy specimens under pendulum impact loading. An oversized, : nonstandard pendulum impactor, called the Bulk Fracture Charpy Machine (BFCM), ...
Finite element analyses of railroad tank car head impacts
2008-09-24
This paper describes engineering analyses of a railroad : tank car impacted at its head by a rigid punch. This type of : collision, referred to as a head impact, is examined using : dynamic, nonlinear finite element analysis (FEA). : Commercial softw...
Finite element analysis of rotating beams physics based interpolation
Ganguli, Ranjan
2017-01-01
This book addresses the solution of rotating beam free-vibration problems using the finite element method. It provides an introduction to the governing equation of a rotating beam, before outlining the solution procedures using Rayleigh-Ritz, Galerkin and finite element methods. The possibility of improving the convergence of finite element methods through a judicious selection of interpolation functions, which are closer to the problem physics, is also addressed. The book offers a valuable guide for students and researchers working on rotating beam problems – important engineering structures used in helicopter rotors, wind turbines, gas turbines, steam turbines and propellers – and their applications. It can also be used as a textbook for specialized graduate and professional courses on advanced applications of finite element analysis.
Finite Element Analysis of the Hierarchical Structure of Human Bone
National Research Council Canada - National Science Library
Dolloff, Katherine
2003-01-01
.... Finally, the effective stiffness of the bone was estimated. In order to determine the stiffness of the collagen fiber, a three-dimensional finite element model was developed and a simple analytical model was derived...
Generalized multiscale finite element method. Symmetric interior penalty coupling
Efendiev, Yalchin R.
2013-12-01
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.
Finite element modelling of helmeted head impact under frontal ...
Indian Academy of Sciences (India)
CSF), brain, tentorium and falx. The finite element model of the helmet consists of shell and foam liner. ... mechanical behaviour of motorcycle helmet. ... the latter authors use a SI (Structural Intensity) approach to study power flow distribution.
Structural analysis with the finite element method linear statics
Oñate, Eugenio
2013-01-01
STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD Linear Statics Volume 1 : The Basis and Solids Eugenio Oñate The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM). The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years. Volume1 presents the basis of the FEM for structural analysis and a detailed description of the finite element formulation for axially loaded bars, plane elasticity problems, axisymmetric solids and general three dimensional solids. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems. The book includes a chapter on miscellaneous topics such as treatment of inclined supports, elas...
Finite element analysis of bending performance on polyurethane composite panel
Jia, Minli; Li, Hongqiao; Wang, Xiaoming
2017-09-01
The finite element analysis model of polyurethane composite panel (simply named PCP) is established by using ABAQUS software. In view of the PCPs made of different thickness of surface board, their bending performance is carried out on finite element analysis, and the load-deflection curves which come from it are compared with the experimental results. The results show that the values between finite element analysis and experiment agree well with each other. It can be deduced that the established finite element model is fit to simulate the bending test of PCPs. The simulation not only has certain reference significance to the optimal design for the bending performance of PCPs, but also to the choice of PCPs in the practical project.
Finite-element method for above-core structures
International Nuclear Information System (INIS)
Kennedy, J.M.; Belytschko, T.B.
1979-12-01
Three-dimensional finite-element models for the treatment of the nonlinear, transient response of a fast breeder reactor's above-core structures are described. For purposes of treating arbitrarily large rotations, node orientations are described by unit vectors and the deformable elements are treated by a corotational formulation in which the coordinate system is embedded in the elements. Deformable elements may be connected either to nodes directly or through rigid bodies. The time integration is carried out by the Newmark β method. These features have been incorporated to form the finite-element program SAFE/RAS (Safety Analysis by Finite Elements/Reactor Analysis and Safety Division). Computations are presented for semianalytical comparisons, simple scoping studies, and Stanford Research Institute (SRI) test comparisons
Application of Mass Lumped Higher Order Finite Elements
International Nuclear Information System (INIS)
J. Chen, H.R. Strauss, S.C. Jardin, W. Park, L.E. Sugiyama, G. Fu, J. Breslau
2005-01-01
There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied
The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion
International Nuclear Information System (INIS)
Moszo, P.; Kristek, J.; Galis, M.; Pazak, P.; Balazovijech, M.
2006-01-01
Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth's structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finite-difference, finite-element, and hybrid finite-difference-finite-element methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. (Author)
Solution of Differential Equation by Means of Finite Element Method
Hayashi, Daigoro; 林, 大五郎
1989-01-01
The finite element method may be defined as the modern "Method of Weighted Residuals" (MWR). This paper describes how to solve the differential equations which are essential in order to explain quantiatively a number of valuable geological and geodynamic problems.The methods to solve linear differential equation, non-linear equation, non-linear non-steady equation, Laplace equation and incompreeible New tonian flow problem are explained by means of the Galerkin finite element method.
Symmetry-preserving finite element schemes: An introductory investigation
Bihlo, Alexander; Valiquette, Francis
2018-01-01
Using the method of equivariant moving frames, we present a procedure for constructing symmetry-preserving finite element methods for second-order ordinary differential equations. Using the method of lines, we then indicate how our constructions can be extended to (1+1)-dimensional evolutionary partial differential equations, using Burgers' equation as an example. Numerical simulations verify that the symmetry-preserving finite element schemes constructed converge at the expected rate and tha...
Examples of finite element mesh generation using SDRC IDEAS
Zapp, John; Volakis, John L.
1990-01-01
IDEAS (Integrated Design Engineering Analysis Software) offers a comprehensive package for mechanical design engineers. Due to its multifaceted capabilities, however, it can be manipulated to serve the needs of electrical engineers, also. IDEAS can be used to perform the following tasks: system modeling, system assembly, kinematics, finite element pre/post processing, finite element solution, system dynamics, drafting, test data analysis, and project relational database.
Non-intrusive finite element reliability analysis methods
Papaioannou, Iason
2014-01-01
This thesis focuses on the modeling of uncertainties in structural systems and on strategies for the reliability assessment of structures analysed by finite element programs. New concepts are introduced for the numerical treatment of spatially varied uncertain quantities through the discretization of the relevant random fields as well as for robust and efficient finite element reliability analysis and updating of the reliability in light of new information. The methods have been implemented i...
Finite element modeling of the filament winding process using ABAQUS
Miltenberger, Louis C.
1992-01-01
A comprehensive stress model of the filament winding fabrication process, previously implemented in the finite element program, WACSAFE, was implemented using the ABAQUS finite element software package. This new implementation, referred to as the ABWACSAFE procedure, consists of the ABAQUS software and a pre/postprocessing routine that was developed to prepare necessary ABAQUS input files and process ABAQUS displacement results for stress and strain computation. The ABWACSAF...
A finite element primer for beginners the basics
Zohdi, Tarek I
2014-01-01
The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:(1) Weighted residual methods and Galerkin approximations,(2) A model problem for one-dimensional?linear elastostatics,(3) Weak formulations in one dimension,(4) Minimum principles in one dimension,(5) Error estimation in one dimension,(5) Construction of Finite Element basis functions in one dimension,(6) Gaussian Quadrature,(7) Iterative solvers and element by element data structures,(8) A model problem for th
FEWA: a Finite Element model of Water flow through Aquifers
International Nuclear Information System (INIS)
Yeh, G.T.; Huff, D.D.
1983-11-01
This report documents the implementation and demonstration of a Finite Element model of Water flow through Aquifers (FEWA). The particular features of FEWA are its versatility and flexibility to deal with as many real-world problems as possible. Point as well as distributed sources/sinks are included to represent recharges/pumpings and rainfall infiltrations. All sources/sinks can be transient or steady state. Prescribed hydraulic head on the Dirichlet boundaries and fluxes on Neumann or Cauchy boundaries can be time-dependent or constant. Source/sink strength over each element and node, hydraulic head at each Dirichlet boundary node, and flux at each boundary segment can vary independently of each other. Either completely confined or completely unconfined aquifers, or partially confined and partially unconfined aquifers can be dealt with effectively. Discretization of a compound region with very irregular curved boundaries is made easy by including both quadrilateral and triangular elements in the formulation. Large-field problems can be solved efficiently by including a pointwise iterative solution strategy as an optional alternative to the direct elimination solution method for the matrix equation approximating the partial differential equation of groundwater flow. FEWA also includes transient flow through confining leaky aquifers lying above and/or below the aquifer of interest. The model is verified against three simple cases to which analytical solutions are available. It is then demonstrated by two examples of how the model can be applied to heterogeneous and anisotropic aquifers with transient boundary conditions, time-dependent sources/sinks, and confining aquitards for a confined aquifer of variable thickness and for a free surface problem in an unconfined aquifer, respectively. 20 references, 25 figures, 8 tables
A Comparison of Continuous Mass-lumped Finite Elements and Finite Differences for 3D
Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.
2012-01-01
The finite-difference method is widely used for time-domain modelling of the wave equation because of its ease of implementation of high-order spatial discretization schemes, parallelization and computational efficiency. However, finite elements on tetrahedral meshes are more accurate in complex
An adaptive discontinuous finite element method for the transport equation
International Nuclear Information System (INIS)
Lang, J.; Walter, A.
1995-01-01
In this paper we introduce a discontinuous finite element method. In our approach, it is possible to combine the advantages of finite element and finite difference methods. The main ingredients are numerical flux approximation and local orthogonal basis functions. The scheme is defined on arbitrary triangulations and two different error indicators are derived. Especially the second one is closely connected to our approach and able to handle arbitrary varying flow directions. Numerical results are given for boundary value problems in two dimensions. They demonstrate the performance of the scheme, combined with the two error indicators
Comparison of 3-D finite elements for incompressible fluid flow
International Nuclear Information System (INIS)
Robichaud, M.; Tanguy, P.A.
1985-01-01
In recent years, the finite element method applied to the solution of incompressible fluid flow has been in constant evolution. In the present state-of-the-art, 2-D problems are solved routinely and reliable results are obtained at a reasonable cost. In 3-D the finite element method is still undergoing active research and many methods have been proposed to solve the Navier-Stokes equations at 'low cost'. These methods have in common the choice of the element which has a trilinear velocity and a discontinuous constant pressure (Q1-PO). The prohibitive cost of 3-D finite element method in fluid flow is the reason for this choice: the Q1-PO is the simplest and the cheapest 3-D element. However, as mentioned in (5) and (6), it generates 'spurious' pressure modes phenomenon called checkerboarding. On regular mesh these spurious modes can be filtered but on distorted mesh the pressure solution is meaningless. (author)
Numerical experiment on finite element method for matching data
International Nuclear Information System (INIS)
Tokuda, Shinji; Kumakura, Toshimasa; Yoshimura, Koichi.
1993-03-01
Numerical experiments are presented on the finite element method by Pletzer-Dewar for matching data of an ordinary differential equation with regular singular points by using model equation. Matching data play an important role in nonideal MHD stability analysis of a magnetically confined plasma. In the Pletzer-Dewar method, the Frobenius series for the 'big solution', the fundamental solution which is not square-integrable at the regular singular point, is prescribed. The experiments include studies of the convergence rate of the matching data obtained by the finite element method and of the effect on the results of computation by truncating the Frobenius series at finite terms. It is shown from the present study that the finite element method is an effective method for obtaining the matching data with high accuracy. (author)
Finite element analysis of soil-sheet pile interaction
Nyby, D. W.
A finite element model which accurately and economically models soil-sheet pile structures was developed. The model was used to analyze cantilever and anchored sheet pile walls. The finite element model includes transition and interface elements. The transition element has the capability of conforming to the displaced shape of the sheet pile elements on one side (cubic element) and soil elements on the other sides (bilinear element). The interface element models the frictional resistance between the soil and the sheet pile. It behaves elastically below a threshold force level (Coulomb friction) and perfectly plastic above this value. The soil is modeled using nonlinear constitutive relations. These relations are used for both the transition elements and the bilinear elements. The economy of the finite element model was increased in two ways. Closed-form integration was used to reduce the computational effort and an equation solver was used which takes advantage of the banded, symmetric, and positive-definite characteristics of the global stiffness matrix.
Finite element analysis of composite concrete-timber beams
Directory of Open Access Journals (Sweden)
N. C. S. FORTI
Full Text Available AbstractIn the search for sustainable construction, timber construction is gaining in popularity around the world. Sustainably harvested wood stores carbon dioxide, while reforestation absorbs yet more CO2. One technique involves the combination of a concrete slab and a timber beam, where the two materials are assembled by the use of flexible connectors. Composite structures provide reduced costs, environmental benefits, a better acoustic performance, when compared to timber structures, and maintain structural safety. Composite structures combine materials with different mechanical properties. Their mechanical performance depends on the efficiency of the connection, which is designed to transmit shear longitudinal forces between the two materials and to prevent vertical detachment. This study contributes with the implementation of a finite element formulation for stress and displacement determination of composite concrete-timber beams. The deduced stiffness matrix and load vector are presented along to numerical examples. Numerical examples are compared to the analytical equations available in Eurocode 5 and to experimental data found in the literature.
Finite Element Aircraft Simulation of Turbulence
1997-02-01
A Simulation of Rotor Blade Element Turbulence (SORBET) model has been : developed for realtime aircraft simulation that accommodates stochastic : turbulence and distributed discrete gusts as a function of the terrain. This : model is applicable to c...
Zhu, Y.; Zhang, Y. X.
2010-08-01
A simple and shear-flexible rectangular composite layered plate element and nonlinear finite element analysis procedures are developed in this paper for nonlinear analysis of fiber reinforced plastic (FRP)-reinforced concrete slabs. The composite layered plate element is constructed based on Mindlin-Reissner plate theory and Timoshenko’s composite beam functions, and transverse shear effects and membrane-bending coupling effects are accounted for. Both geometric nonlinearity and material nonlinearity of the materials, which incorporates tension, compression, tension stiffening and cracking of the concrete, are included in the new model. The developed element and the nonlinear finite element analysis procedures are validated by comparing the computed numerical results of numerical examples with those obtained from experimental investigations and from the commercial finite element analysis package ABAQUS. The element is then employed to investigate the nonlinear structural behavior and the cracking progress of a clamped two-way FRP-reinforced concrete slab. The influences of reinforcement with different materials, ratio and layout in tension or compressive regions on structural behavior of the clamped slabs are investigated by parametric studies.
International Nuclear Information System (INIS)
Al-Akhrass, Dina
2014-01-01
Simulations in solid mechanics exhibit several difficulties, as dealing with incompressibility, with nonlinearities due to finite strains, contact laws, or constitutive laws. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using elements of low order. During the three last decades, many approaches have been proposed in the literature to overcome the incompressibility problem. Among them, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field (displacement - pressure) mixed formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the 'inf-sup' stability condition from the continuous problem. Hence, the interpolation orders in displacement and pressure have to be chosen in a way to satisfy the Brezzi-Babuska stability conditions when using Galerkin approaches. Interpolation orders must be chosen so as to satisfy this condition. Two possibilities are considered: to use stable finite element satisfying this requirement, or to use finite element that does not satisfy this condition, and to add terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite element P2/P1 and P2/P1/P1 are used as reference, and compared to P1/P1 and P1/P1/P1 formulations stabilized with a bubble function or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. A finite strain model based on logarithmic strain is selected. This approach is extended to three and two field mixed formulations with stable or stabilized elements. These approaches are validated on academic cases and used on industrial cases. (author)
A finite element analysis of the distribution velocity in viscous ...
African Journals Online (AJOL)
In this work we use the finite element method to analyze the distribution of velocity in a viscous incompressible fluid flow using Lagrange interpolation function. The results obtained are highly accurate and converge fast to the exact solution as the number of elements increase.
Finite element stress analysis of brick-mortar masonry under ...
African Journals Online (AJOL)
Stress analysis of a brick-mortar couplet as a substitute for brick wall structure has been performed by finite element method, and algorithm for determining the element stiffness matrix for a plane stress problem using the displacement approach was developed. The nodal displacements were derived for the stress in each ...
Finite element solution of the Boussinesq wave equation | Akpobi ...
African Journals Online (AJOL)
In this work, we investigate a Boussinesq-type flow model for nonlinear dispersive waves by developing a computational model based on the finite element discretisation technique. Hermite interpolation functions were used to interpolate approximation elements. The system is modeled using a time dependent equation.
An implicit discontinuous Galerkin finite element model for water waves
van der Vegt, Jacobus J.W.; Ambati, V.R.; Bokhove, Onno
2005-01-01
We discuss a new higher order accurate discontinuous Galerkin finite element method for non-linear free surface gravity waves. The algorithm is based on an arbitrary Lagrangian Eulerian description of the flow field using deforming elements and a moving mesh, which makes it possible to represent
Stress distributions in finite element analysis of concrete gravity dam ...
African Journals Online (AJOL)
Gravity dams are solid structures built of mass concrete material; they maintain their stability against the design loads from the geometric shape, the mass, and the strength of the concrete. The model was meshed with an 8-node biquadratic plane strain quadrilateral (CPE8R) elements, using ABAQUS, a finite element ...
A nonlinear dynamic corotational finite element model for submerged pipes
De Vries, F. H.; Geijselaers, H. J.M.; Van Den Boogaard, A. H.; Huisman, A.
2017-01-01
A three dimensional finite element model is built to compute the motions of a pipe that is being laid on the seabed. This process is geometrically nonlinear, therefore co-rotational beam elements are used. The pipe is subject to static and dynamic forces. Static forces are due to gravity, current
Behaviour of Lagrangian triangular mixed fluid finite elements
Indian Academy of Sciences (India)
The behaviour of mixed fluid finite elements, formulated based on the Lagrangian frame of reference, is investigated to understand the effects of locking due to incompressibility and irrotational constraints. For this purpose, both linear and quadratic mixed triangular fluid elements are formulated. It is found that there exists a ...
Modelling Convergence of Finite Element Analysis of Cantilever Beam
African Journals Online (AJOL)
Convergence studies are carried out by investigating the convergence of numerical results as the number of elements is increased. If convergence is not obtained, the engineer using the finite element method has absolutely no indication whether the results are indicative of a meaningful approximation to the correct solution ...
A set of pathological tests to validate new finite elements
Indian Academy of Sciences (India)
M. Senthilkumar (Newgen Imaging) 1461 1996 Oct 15 13:05:22
End shear. 16. 16. Thick cylinder problem. ∗. Radial pressure. 17. 17. Membrane problem. End shear. 18. 18. Cantilever plate test. Tip moment. 19. End shear. 19 ... Shell finite elements testing. Individual element tests. Patch test. &. FEM convergence. 1989. 1995. 1997. 1998. &. White. & Taylor. Patch test revisited. Zhang.
Behaviour of Lagrangian triangular mixed fluid finite elements
Indian Academy of Sciences (India)
relationship with the penalty finite element approach. Since two constraints are required to be enforced simultaneously, three-field mixed elements involving the displacement and the two Lagrange multipliers, are formulated. The study also includes the effect of bubble functions (or incompatible modes) on the behaviour of ...
Natarajan, Sundararajan; Bordas, Stéphane; Ooi, Ean Tat
2015-01-01
We show both theoretically and numerically a connection between the smoothed finite element method (SFEM) and the virtual element method and use this approach to derive stable, cheap and optimally convergent polyhedral FEM.We show that the stiffness matrix computed with one subcell SFEM is identical to the consistency term of the virtual element method, irrespective of the topology of the element, as long as the shape functions vary linearly on the boundary. Using this connection, we propose ...
Finite element approximation to the even-parity transport equation
International Nuclear Information System (INIS)
Lewis, E.E.
1981-01-01
This paper studies the finite element method, a procedure for reducing partial differential equations to sets of algebraic equations suitable for solution on a digital computer. The differential equation is cast into the form of a variational principle, the resulting domain then subdivided into finite elements. The dependent variable is then approximated by a simple polynomial, and these are linked across inter-element boundaries by continuity conditions. The finite element method is tailored to a variety of transport problems. Angular approximations are formulated, and the extent of ray effect mitigation is examined. Complex trial functions are introduced to enable the inclusion of buckling approximations. The ubiquitous curved interfaces of cell calculations, and coarse mesh methods are also treated. A concluding section discusses limitations of the work to date and suggests possible future directions
Ship Impact Study: Analytical Approaches and Finite Element Modeling
Directory of Open Access Journals (Sweden)
Pawel Woelke
2012-01-01
Full Text Available The current paper presents the results of a ship impact study conducted using various analytical approaches available in the literature with the results obtained from detailed finite element analysis. Considering a typical container vessel impacting a rigid wall with an initial speed of 10 knots, the study investigates the forces imparted on the struck obstacle, the energy dissipated through inelastic deformation, penetration, local deformation patterns, and local failure of the ship elements. The main objective of the paper is to study the accuracy and generality of the predictions of the vessel collision forces, obtained by means of analytical closed-form solutions, in reference to detailed finite element analyses. The results show that significant discrepancies between simplified analytical approaches and detailed finite element analyses can occur, depending on the specific impact scenarios under consideration.
Panczak, Tim; Ring, Steve; Welch, Mark
1999-01-01
Thermal engineering has long been left out of the concurrent engineering environment dominated by CAD (computer aided design) and FEM (finite element method) software. Current tools attempt to force the thermal design process into an environment primarily created to support structural analysis, which results in inappropriate thermal models. As a result, many thermal engineers either build models "by hand" or use geometric user interfaces that are separate from and have little useful connection, if any, to CAD and FEM systems. This paper describes the development of a new thermal design environment called the Thermal Desktop. This system, while fully integrated into a neutral, low cost CAD system, and which utilizes both FEM and FD methods, does not compromise the needs of the thermal engineer. Rather, the features needed for concurrent thermal analysis are specifically addressed by combining traditional parametric surface based radiation and FD based conduction modeling with CAD and FEM methods. The use of flexible and familiar temperature solvers such as SINDA/FLUINT (Systems Improved Numerical Differencing Analyzer/Fluid Integrator) is retained.
On Using Particle Finite Element for Hydrodynamics Problems Solving
Directory of Open Access Journals (Sweden)
E. V. Davidova
2015-01-01
Full Text Available The aim of the present research is to develop software for the Particle Finite Element Method (PFEM and its verification on the model problem of viscous incompressible flow simulation in a square cavity. The Lagrangian description of the medium motion is used: the nodes of the finite element mesh move together with the fluid that allows to consider them as particles of the medium. Mesh cells deform when in time-stepping procedure, so it is necessary to reconstruct the mesh to provide stability of the finite element numerical procedure.Meshing algorithm allows us to obtain the mesh, which satisfies the Delaunay criteria: it is called \\the possible triangles method". This algorithm is based on the well-known Fortune method of Voronoi diagram constructing for a certain set of points in the plane. The graphical representation of the possible triangles method is shown. It is suitable to use generalization of Delaunay triangulation in order to construct meshes with polygonal cells in case of multiple nodes close to be lying on the same circle.The viscous incompressible fluid flow is described by the Navier | Stokes equations and the mass conservation equation with certain initial and boundary conditions. A fractional steps method, which allows us to avoid non-physical oscillations of the pressure, provides the timestepping procedure. Using the finite element discretization and the Bubnov | Galerkin method allows us to carry out spatial discretization.For form functions calculation of finite element mesh with polygonal cells, \
A wave finite element analysis of the passive cochlea.
Elliott, Stephen J; Ni, Guangjian; Mace, Brian R; Lineton, Ben
2013-03-01
Current models of the cochlea can be characterized as being either based on the assumed propagation of a single slow wave, which provides good insight, or involve the solution of a numerical model, such as in the finite element method, which allows the incorporation of more detailed anatomical features. In this paper it is shown how the wave finite element method can be used to decompose the results of a finite element calculation in terms of wave components, which allows the insight of the wave approach to be brought to bear on more complicated numerical models. In order to illustrate the method, a simple box model is considered, of a passive, locally reacting, basilar membrane interacting via three-dimensional fluid coupling. An analytic formulation of the dispersion equation is used initially to illustrate the types of wave one would expect in such a model. The wave finite element is then used to calculate the wavenumbers of all the waves in the finite element model. It is shown that only a single wave type dominates the response until this peaks at the best place in the cochlea, where an evanescent, higher order fluid wave can make a significant contribution.
Finite element analysis of thrust angle contact ball slewing bearing
Deng, Biao; Guo, Yuan; Zhang, An; Tang, Shengjin
2017-12-01
In view of the large heavy slewing bearing no longer follows the rigid ring hupothesis under the load condition, the entity finite element model of thrust angular contact ball bearing was established by using finite element analysis software ANSYS. The boundary conditions of the model were set according to the actual condition of slewing bearing, the internal stress state of the slewing bearing was obtained by solving and calculation, and the calculated results were compared with the numerical results based on the rigid ring assumption. The results show that more balls are loaded in the result of finite element method, and the maximum contact stresses between the ball and raceway have some reductions. This is because the finite element method considers the ferrule as an elastic body. The ring will produce structure deformation in the radial plane when the heavy load slewing bearings are subjected to external loads. The results of the finite element method are more in line with the actual situation of the slewing bearing in the engineering.
Two-dimensional isostatic meshes in the finite element method
Martínez Marín, Rubén; Samartín, Avelino
2002-01-01
In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's...
Finite element modelling of helmeted head impact under frontal ...
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... Finite element models of the head and helmet were used to study contact forces during frontal impact of the head with a rigid surface. The ﬁnite element model of the head consists of skin, skull, cerebro-spinal ﬂuid (CSF), brain, tentorium and falx. The ﬁnite element model of the helmet consists of shell and ...
Gao, Longfei
2018-02-22
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.
Finite Element Method for Capturing Ultra-relativistic Shocks
Richardson, G. A.; Chung, T. J.
2003-01-01
While finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.
Engineering computation of structures the finite element method
Neto, Maria Augusta; Roseiro, Luis; Cirne, José; Leal, Rogério
2015-01-01
This book presents theories and the main useful techniques of the Finite Element Method (FEM), with an introduction to FEM and many case studies of its use in engineering practice. It supports engineers and students to solve primarily linear problems in mechanical engineering, with a main focus on static and dynamic structural problems. Readers of this text are encouraged to discover the proper relationship between theory and practice, within the finite element method: Practice without theory is blind, but theory without practice is sterile. Beginning with elasticity basic concepts and the classical theories of stressed materials, the work goes on to apply the relationship between forces, displacements, stresses and strains on the process of modeling, simulating and designing engineered technical systems. Chapters discuss the finite element equations for static, eigenvalue analysis, as well as transient analyses. Students and practitioners using commercial FEM software will find this book very helpful. It us...
The Finite Element Numerical Modelling of 3D Magnetotelluric
Directory of Open Access Journals (Sweden)
Ligang Cao
2014-01-01
Full Text Available The ideal numerical simulation of 3D magnetotelluric was restricted by the methodology complexity and the time-consuming calculation. Boundary values, the variation of weighted residual equation, and the hexahedral mesh generation method of finite element are three major causes. A finite element method for 3D magnetotelluric numerical modeling is presented in this paper as a solution for the problem mentioned above. In this algorithm, a hexahedral element coefficient matrix for magnetoelluric finite method is developed, which solves large-scale equations using preconditioned conjugate gradient of the first-type boundary conditions. This algorithm is verified using the homogeneous model, and the positive landform model, as well as the low resistance anomaly model.
Finite Element Modelling of Cold Formed Stainless Steel Columns
Directory of Open Access Journals (Sweden)
M. Macdonald
2005-01-01
Full Text Available This paper describes the results obtained from a finite element investigation into the load capacity of column members of lipped channel cross-section, cold formed from Type 304 stainless steel, subjected to concentric and eccentric compression loading. The main aims of this investigation were to determine the effects which the non-linearity of the stress-strain behaviour of the material would have on the column behaviour under concentric or eccentric loading. Stress-strain curves derived from tests and design codes are incorporated into non-linear finite element analyses of eccentrically loaded columns and the results obtained are compared with those obtained on the basis of experiments on stainless steel channel columns with the same properties and dimensions. Comparisons of the finite element results and the test results are also made with existing design specifications and conclusions are drawn on the basis of the comparisons.
Directory of Open Access Journals (Sweden)
P.B. Silva
2013-01-01
Full Text Available Structural spectral elements are formulated using the analytical solution of the applicable elastodynamic equations and, therefore, mesh refinement is not needed to analyze high frequency behavior provided the elastodynamic equations used remain valid. However, for modeling complex structures, standard spectral elements require long and cumbersome analytical formulation. In this work, a method to build spectral finite elements from a finite element model of a slice of a structural waveguide (a structure with one dimension much larger than the other two is proposed. First, the transfer matrix of the structural waveguide is obtained from the finite element model of a thin slice. Then, the wavenumbers and wave propagation modes are obtained from the transfer matrix and used to build the spectral element matrix. These spectral elements can be used to model homogeneous waveguides with constant cross section over long spans without the need of refining the finite element mesh along the waveguide. As an illustrating example, spectral elements are derived for straight uniform rods and beams and used to calculate the forced response in the longitudinal and transverse directions. Results obtained with the spectral element formulation are shown to agree well with results obtained with a finite element model of the whole beam. The proposed approach can be used to generate spectral elements of waveguides of arbitrary cross section and, potentially, of arbitrary order.
AEROTAXI ground static test and finite element model validation
Directory of Open Access Journals (Sweden)
Radu BISCA
2011-06-01
Full Text Available In this presentation, we will concentrate on typical Ground Static Test (GST and Finite Element (FE software comparisons. It is necessary to note, that standard GST are obligatory for any new aircraft configuration. We can mention here the investigations of the AeroTAXITM, a small aircraft configuration, using PRODERA® equipment. A Finite Element Model (FEM of the AeroTAXITM has been developed in PATRAN/NASTRAN®, partly from a previous ANSYS® model. FEM can be used to investigate potential structural modifications or changes with realistic component corrections. Model validation should be part of every modern engineering analysis and quality assurance procedure.
Stochastic Finite Elements in Reliability-Based Structural Optimization
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Engelund, S.
1995-01-01
Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...... to optimization variables can be performed. A computer implementation is described and an illustrative example is given....
Fourier analysis of finite element preconditioned collocation schemes
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
Stochastic Finite Elements in Reliability-Based Structural Optimization
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Engelund, S.
Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...
Preconditioning for Mixed Finite Element Formulations of Elliptic Problems
Wildey, Tim
2013-01-01
In this paper, we discuss a preconditioning technique for mixed finite element discretizations of elliptic equations. The technique is based on a block-diagonal approximation of the mass matrix which maintains the sparsity and positive definiteness of the corresponding Schur complement. This preconditioner arises from the multipoint flux mixed finite element method and is robust with respect to mesh size and is better conditioned for full permeability tensors than a preconditioner based on a diagonal approximation of the mass matrix. © Springer-Verlag Berlin Heidelberg 2013.
Diffusive mesh relaxation in ALE finite element numerical simulations
Energy Technology Data Exchange (ETDEWEB)
Dube, E.I.
1996-06-01
The theory for a diffusive mesh relaxation algorithm is developed for use in three-dimensional Arbitary Lagrange/Eulerian (ALE) finite element simulation techniques. This mesh relaxer is derived by a variational principle for an unstructured 3D grid using finite elements, and incorporates hourglass controls in the numerical implementation. The diffusive coefficients are based on the geometric properties of the existing mesh, and are chosen so as to allow for a smooth grid that retains the general shape of the original mesh. The diffusive mesh relaxation algorithm is then applied to an ALE code system, and results from several test cases are discussed.
FINITE ELEMENT EVALUATION AND OPTIMIZATION OF GEOMETRY WITH DOE
Directory of Open Access Journals (Sweden)
Janko D. Jovanovic
2011-03-01
Full Text Available Since 1960, Taguchi methods have been used for improving the quality of Japanese products with great success. Basic assumption of Taguchi's design for six sigma or robust design is that quality must be designed into a product from the start at both the product and process design stage in order to improve product reliability and manufacturability. This paper deals with case study of product design based on Taguchi's approach that involves parametric optimization of piston rod geometry aiming mass reduction with stress restriction. Finite element analysis software ANSYS Workbench was used to get access to CAD parameters of piston rod within a process of parametric finite element evaluation and optimization.
FINITE ELEMENT MODELING OF THIN CIRCULAR SANDWICH PLATES DEFLECTION
Directory of Open Access Journals (Sweden)
K. S. Kurachka
2014-01-01
Full Text Available A mathematical model of a thin circular sandwich plate being under the vertical load is proposed. The model employs the finite element method and takes advantage of an axisymmetric finite element that leads to the small dimension of the resulting stiffness matrix and sufficient accuracy for practical calculations. The analytical expressions for computing local stiffness matrices are found, which can significantly speed up the process of forming the global stiffness matrix and increase the accuracy of calculations. A software is under development and verification. The discrepancy between the results of the mathematical model and those of analytical formulas for homogeneous thin circularsandwich plates does not exceed 7%.
COMPUTER EXPERIMENTS WITH FINITE ELEMENTS OF HIGHER ORDER
Directory of Open Access Journals (Sweden)
Khomchenko A.
2017-12-01
Full Text Available The paper deals with the problem of constructing the basic functions of a quadrilateral finite element of the fifth order by the means of the computer algebra system Maple. The Lagrangian approximation of such a finite element contains 36 nodes: 20 nodes perimeter and 16 internal nodes. Alternative models with reduced number of internal nodes are considered. Graphs of basic functions and cognitive portraits of lines of zero level are presented. The work is aimed at studying the possibilities of using modern information technologies in the teaching of individual mathematical disciplines.
Finite element, discontinuous Galerkin, and finite difference evolution schemes in spacetime
International Nuclear Information System (INIS)
Zumbusch, G
2009-01-01
Numerical schemes for Einstein's vacuum equation are developed. Einstein's equation in harmonic gauge is second-order symmetric hyperbolic. It is discretized in four-dimensional spacetime by finite differences, finite elements and interior penalty discontinuous Galerkin methods, the latter being related to Regge calculus. The schemes are split into space and time and new time-stepping schemes for wave equations are derived. The methods are evaluated for linear and nonlinear test problems of the Apples-with-Apples collection.
[Finite element analysis on stress change of lumbar spine].
Yan, Jia-zhi; Wu, Zhi-hong; Wang, Xue-song; Xing, Ze-jun; Song, Hai-feng; Zhao, Yu; Zhang, Jian-guo; Wang, Yi-peng; Qiu, Gui-xing
2009-05-05
To build a 3D finite element model of whole lumbar spine and verify its efficiency and analyze the biomechanical change of L3-4 motion segment. L1-L5 segment data were obtained from computed tomography (CT) scans of the lumbar spine of a 40-year-old man with no abnormal findings. A three-dimensional finite element model of the human whole lumbar spine was built in the Mimics and the ABAQUS software. The model was composed of bony vertebrae, articulating facets, intervertebral disc and associated ligaments. The basic stress analysis of L3-4 motion segment was made under the considerations of different material properties of bone, ligaments and facet joints contacting frictional property. The stress on annulus fiber, nucleus pulposus, endplate and facet joints under axial pressure (0.3 MPa, 0.5 MPa, 1.0 MPa, 2.0 MPa & 4.0 MPa) were analyzed. A three-dimensional finite element model of human L3-L4 motion segment has 272, 619 elements, the stresses were higher in the posterior of annulus fiber, the Max pressure stress (S33) distributed in nucleus pulposus and the center of endplate. The stresses increased as axial pressure rose. 3D finite element model of whole lumbar spine and L3-4 motion segment were established successfully and the stress analyses were feasible and reliable.
Comparison study of finite element and basis set methods for finite size scaling
International Nuclear Information System (INIS)
Antillon, Edwin; Moy, Winton; Wei Qi; Kais, Sabre
2009-01-01
We compare two methods of obtaining critical parameters for a quantum Hamiltonian using a finite size scaling approach. A finite element and basis set method were used in conjunction with the finite size scaling to obtain the critical parameters for the Hulthen potential. The critical parameters obtained analytically were the coupling constant λ c =(1/2), the critical exponents for the energy α=2 and for the 'correlation length 'ν=1. The extrapolated results for finite size scaling with the basis set method are λ c =0.499 99, α=1.9960, and ν=0.999 10. The results for the finite element solutions are λ c =0.501 84, α=1.999 93, and ν=1.000 79 for the linear interpolation and λ c =0.500 00, α=2.000 11, and ν=1.000 32 for the Hermite interpolation. The results for each method compare very well with the analytical results obtained for the Hulthen potential. However, the finite element method is easier to implement and may be combined with ab initio and density functional theory to obtain quantum critical parameters for more complex systems.
Advanced finite element simulation with MSC Marc application of user subroutines
Javanbakht, Zia
2017-01-01
This book offers an in-depth insight into the general-purpose finite element program MSC Marc, which is distributed by MSC Software Corporation. It is a specialized program for nonlinear problems (implicit solver) which is common in academia and industry. The primary goal of this book is to provide a comprehensive introduction to a special feature of this software: the user can write user-subroutines in the programming language Fortran, which is the language of all classical finite element packages. This subroutine feature allows the user to replace certain modules of the core code and to implement new features such as constitutive laws or new elements. Thus, the functionality of commercial codes (‘black box’) can easily be extended by linking user written code to the main core of the program. This feature allows to take advantage of a commercial software package with the flexibility of a ‘semi-open’ code. .
Flexible Mould for Precast Concrete Elements
DEFF Research Database (Denmark)
Jepsen, Christian Raun; Kristensen, Mathias Kræmmergaard; Kirkegaard, Poul Henning
2010-01-01
The present paper describes the development of a digitally controlled mou Id that forms a double curved and fair surface directly from the digital CAD model. The primary motivation for the development of the mould is to reduce the cost of constructing double curved, cast elements for architecture......, both in-situ cast and modular. Today, such elements are usually cast in milled formwork that is expensive and produces a lot of waste. Architects are often limited in their freedom of design by the high costs of the existing methods and as a result, the possibilities for drawing and evaluating complex...
Flexible Mould for Precast Concrete Elements
DEFF Research Database (Denmark)
Jepsen, Christian Raun; Kristensen, Mathias Kræmmergaard; Kirkegaard, Poul Henning
2010-01-01
The present paper describes the development of a digitally controlled mou Id that forms a double curved and fair surface directly from the digital CAD model. The primary motivation for the development of the mould is to reduce the cost of constructing double curved, cast elements for architecture...
Fluid structure interaction in electrohydraulic servovalve: a finite element approach
Hiremath, Somashekhar S.; Singaperumal, M.
2010-01-01
Electrohydraulic servovalves (EHSV) promise unique application opportunities and high performance, unmatched by other drive technologies. Typical applications include aerospace, robotic manipulators, motion simulators, injection molding, CNC machines and material testing machines. EHSV available are either a flapper/nozzle type or a jet pipe type. In the present paper an attempt has been made to study the dynamics of jet pipe EHSV with built-in mechanical feedback using Finite Element Method (FEM). In jet pipe EHSV, the dynamics of spool greatly depends on pressure recovery and hence the fluid flow at spool ends. The effect of pressure recovery on spool dynamics is studied using FEM by creating the fluid-structure-interaction. The mechanical parts were created using general purpose finite elements like shell, beam, and solid elements while fluid cavities were created using hydrostatic fluid elements. The analysis was carried out using the commercially available FE code ABAQUS. The jet pipe and spool dynamics are presented in the paper.
Magnetoelastic energy calculations for finite element analysis of superconductors
International Nuclear Information System (INIS)
Akin, J.E.; Stoddart, W.C.T.
1977-01-01
It has been shown that the high current density and magnetic flux density associated with superconductors can make the magnetoelastic energy a significant portion of the total energy in a structural system. The present work presents a procedure for evaluating this magnetoelastic energy for use in the finite element analysis of the structural dynamics and stability of the superconductor. A simple, special case of the element matrices is illustrated
A finite element field solver for dipole modes
International Nuclear Information System (INIS)
Nelson, E.M.
1992-01-01
A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL. (author). 7 refs., 4 figs
A particle finite element method for machining simulations
Sabel, Matthias; Sator, Christian; Müller, Ralf
2014-07-01
The particle finite element method (PFEM) appears to be a convenient technique for machining simulations, since the geometry and topology of the problem can undergo severe changes. In this work, a short outline of the PFEM-algorithm is given, which is followed by a detailed description of the involved operations. The -shape method, which is used to track the topology, is explained and tested by a simple example. Also the kinematics and a suitable finite element formulation are introduced. To validate the method simple settings without topological changes are considered and compared to the standard finite element method for large deformations. To examine the performance of the method, when dealing with separating material, a tensile loading is applied to a notched plate. This investigation includes a numerical analysis of the different meshing parameters, and the numerical convergence is studied. With regard to the cutting simulation it is found that only a sufficiently large number of particles (and thus a rather fine finite element discretisation) leads to converged results of process parameters, such as the cutting force.
Aranha: a 2D mesh generator for triangular finite elements
International Nuclear Information System (INIS)
Fancello, E.A.; Salgado, A.C.; Feijoo, R.A.
1990-01-01
A method for generating unstructured meshes for linear and quadratic triangular finite elements is described in this paper. Some topics on the C language data structure used in the development of the program Aranha are also presented. The applicability for adaptive remeshing is shown and finally several examples are included to illustrate the performance of the method in irregular connected planar domains. (author)
Finite Element Method for Linear Multiterm Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Abdallah A. Badr
2012-01-01
Full Text Available We consider the linear multiterm fractional differential equation (fDE. Existence and uniqueness of the solution of such equation are discussed. We apply the finite element method (FEM to obtain the numerical solution of this equation using Galerkin approach. A comparison, through examples, between our techniques and other previous numerical methods is established.
Finite Element Method for Linear Multiterm Fractional Differential Equations
Badr, Abdallah A.
2012-01-01
We consider the linear multiterm fractional differential equation (fDE). Existence and uniqueness of the solution of such equation are discussed. We apply the finite element method (FEM) to obtain the numerical solution of this equation using Galerkin approach. A comparison, through examples, between our techniques and other previous numerical methods is established.
Finite Element Vibration and Dynamic Response Analysis of Engineering Structures
Directory of Open Access Journals (Sweden)
Jaroslav Mackerle
2000-01-01
Full Text Available This bibliography lists references to papers, conference proceedings, and theses/dissertations dealing with finite element vibration and dynamic response analysis of engineering structures that were published from 1994 to 1998. It contains 539 citations. The following types of structures are included: basic structural systems; ground structures; ocean and coastal structures; mobile structures; and containment structures.
A Finite Element Approach to Modeling Abrasive Wear Modes
Woldman, M.; van der Heide, Emile; Tinga, Tiedo; Masen, Marc Arthur
2016-01-01
Machine components operating in sandy environments will wear because of the abrasive interaction with sand particles. In this work, a method is derived to predict the amount of wear caused by such abrasive action, in order to improve the maintenance concept of the components. A finite element model
Finite element concept to derive isostatic residual maps ...
Indian Academy of Sciences (India)
lies are isolated so as to construct the isostatic residual maps. Very accurate geophysical studies have ... Finite element concept; isostatic anomaly; Gorda Plate; Sierra Nevada. Proc. Indian Acad. Sci. (Earth Planet. Sci.), 110 .... The continuous line is obtained by regression analysis. The broken line shows the. FEA regional ...
An Orthogonal Residual Procedure for Nonlinear Finite Element Equations
DEFF Research Database (Denmark)
Krenk, S.
A general and robust solution procedure for nonlinear finite element equations with limit points is developed. At each equilibrium iteration the magnitude of the load is adjusted such that the residual force is orthogonal to the current displacement increment from the last equilibrium state...
Finite Element Analysis of Boron Diffusion in Wooden Poles
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Hoffmeyer, P.; Bechgaard, C.
2003-01-01
The problem of describing the migration of dissolved boron in wood is treated with special reference to the commonly used remedial treatment of wooden poles. The governing equations are derived and discussed together with some of the material parameters required. The equations are solved by the f...... by the finite element method and, finally, results showing the effect of different treatment strategies are presented....
2-D Finite Element Analysis of Massive RC Structures
DEFF Research Database (Denmark)
Saabye Ottosen, Niels
1982-01-01
Nonlinear analysis of concrete structures using finite elements is discussed. The applications include a thick-walled top-closure for a pressure vessel as well as the delicate problems of beams failing in shear. The top-closure analysis evaluates the effect of two different failure criteria...
A 2-dimensional finite element simulation of cooling in castings ...
African Journals Online (AJOL)
In this work we present a 2 dimensional finite element simulation of the cooling process in castings. A one way coupling +technique was used to predict the behavior of thermal strains and stresses from the temperature history of casting. The temperature distribution across the casting at different times, the cooling pattern of ...
Finite element analysis of boron diffusion in wooden Poles
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Hoffmeyer, Preben; Bechgaard, Carl
2004-01-01
The problem of describing the migration of dissolved boron in wood is treated with special reference to the commonly used remedial treatment of wooden poles. The governing equations are derived and discussed together with some of the material parameters required. The equations are solved by the f...... by the finite element method and, finally, results showing the effect of different treatment strategies are presented....
The Development of Piezoelectric Accelerometers Using Finite Element Analysis
DEFF Research Database (Denmark)
Liu, Bin
1999-01-01
This paper describes the application of Finite Element (FE) approach for the development of piezoelectric accelerometers. An accelerometer is simulated using the FE approach as an example. Good agreement is achieved between simulated results and calibrated results. It is proved that the FE modeling...
Efficient implicit finite element analysis of sheet forming processes
van den Boogaard, Antonius H.; Meinders, Vincent T.; Huetink, Han
2003-01-01
The computation time for implicit finite element analyses tends to increase disproportionally with increasing problem size. This is due to the repeated solution of linear sets of equations, if direct solvers are used. By using iterative linear equation solvers the total analysis time can be reduced
Bending analysis of laminated composite plates using finite element ...
African Journals Online (AJOL)
In this paper, a number of finite element analyses have been carried out for various side-to-thickness ratios, aspect ratios and modulus ratios to study the effect of transverse shear deformation on deflection and stresses of laminated composite plates subjected to uniformly distributed load. The numerical results showed, ...
Finite Element Analysis of Boron Diffusion in Wooden Poles
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Hoffmeyer, Preben; Bechgaard, Carl
2004-01-01
The problem of describing the migration of dissolved boron in wood is treated with special reference to the commonly used remedial treatment of wooden poles. The governing equations are derived and discussed together with some of the material parameters required. The equations are solved by the f...... by the finite element method and, finally, results showing the effect of different treatment strategies are presented....
Discontinuous Galerkin finite element methods for hyperbolic differential equations
van der Vegt, Jacobus J.W.; van der Ven, H.; Boelens, O.J.; Boelens, O.J.; Toro, E.F.
2002-01-01
In this paper a suryey is given of the important steps in the development of discontinuous Galerkin finite element methods for hyperbolic partial differential equations. Special attention is paid to the application of the discontinuous Galerkin method to the solution of the Euler equations of gas
Finite element simulation of laser transmission welding of dissimilar ...
African Journals Online (AJOL)
Now-a-days, metal to plastic micro-welding is of great interest in the field of biomedical and electronics applications. Laser transmission welding (LTW) has emerged as the most suitable technique for such applications. In this paper, a three-dimensional finite element (FE) thermal model is developed to simulate the laser ...
Design, development and use of the finite element machine
Adams, L. M.; Voigt, R. C.
1983-01-01
Some of the considerations that went into the design of the Finite Element Machine, a research asynchronous parallel computer are described. The present status of the system is also discussed along with some indication of the type of results that were obtained.
Finite element modeling of intermuscular interactions and myofascial force transmission
Yucesoy, C.A.; Koopman, Hubertus F.J.M.; Huijing, P.A.J.B.M.; Grootenboer, H.J.
2001-01-01
A finite element muscle model to study the principles of intermuscular myofascial force transmission is developed. The results obtained explain force differences at the distal and proximal tendons of muscles that have mechanical interaction. This is in agreement with experimental findings in other
Finite element analysis of thermoelastic instability with intermittent contact
Geijselaers, Hubertus J.M.; Koning, A.J.E.
2000-01-01
The equations that describe the development of corrugations on block braked wheel treads caused by thermoelastic instability are discretized using the finite element method. The perturbations of temperatures and distortions are described by an amplitude function, which is spatially fixed multiplied
Finite element and perturbative study of buffered leaky planar waveguides
Uranus, H.P.; Hoekstra, Hugo; van Groesen, Embrecht W.C.
2005-01-01
The effects of the presence of a high-index medium in the proximity of planar waveguiding structures that makes up buffered leaky waveguides, were studied using a finite element method (FEM) leaky mode solver and a perturbation method. Various phenomena observed in the FEM results were interpreted
An implicit discontinuous Galerkin finite element model for water waves
van der Vegt, Jacobus J.W.; Tomar, S.K.; Yao, Z.H.; Yuan, M.W.; Zhong, W.X.
2004-01-01
An overview is given of a discontinuous Galerkin finite element method for linear free surface water waves. The method uses an implicit time integration method which is unconditionally stable and does not suffer from the frequently encountered mesh dependent saw-tooth type instability at the free
Space-time discontinuous Galerkin finite element methods
van der Vegt, Jacobus J.W.; Deconinck, H.; Ricchiuto, M.
2006-01-01
In these notes an introduction is given to space-time discontinuous Galerkin (DG) finite element methods for hyperbolic and parabolic conservation laws on time dependent domains. the space-time DG discretization is explained in detail, including the definition of the numerical fluxes and
Hands on applied finite element analysis application with ANSYS
Arslan, Mehmet Ali
2015-01-01
Hands on Applied Finite Element Analysis Application with Ansys is truly an extraordinary book that offers practical ways of tackling FEA problems in machine design and analysis. In this book, 35 good selection of example problems have been presented, offering students the opportunity to apply their knowledge to real engineering FEA problem solutions by guiding them with real life hands on experience.
The future of the finite element method in geotechnics
Brinkgreve, R.B.J.
2012-01-01
In this presentation a vision is given on tlie fiiture of the finite element method (FEM) for geotechnical engineering and design. In the past 20 years the FEM has proven to be a powerful method for estimating deformation, stability and groundwater flow in geoteclmical stmctures. Much has been
A direct implementation for influence lines in finite element software
DEFF Research Database (Denmark)
Jepsen, Michael S.; Damkilde, Lars
2014-01-01
The use of influence lines is a recognized method for determining the critical design load conditions and this paper shows a direct method for applying influence lines in any structural finite element software. The main idea is to equate displacement or angular discontinuities with nodal forces...
Finite element modelling of fibre-reinforced brittle materials
Kullaa, J.
1997-01-01
The tensile constitutive behaviour of fibre-reinforced brittle materials can be extended to two or three dimensions by using the finite element method with crack models. The three approaches in this study include the smeared and discrete crack concepts and a multi-surface plasticity model. The
Finite element analysis of tubular joints in offshore structures ...
African Journals Online (AJOL)
... representing a 2-D model of the joint between the brace and the chord walls. This was subsequently followed but finite element analysis of six tubular joints. A global analysis was initially undertaken, then the submodel analysis carried in the areas of stress concentration. Journal of Civil Engineering, JKUAT (2001) Vol 6, ...
Piezoelectric Accelerometers Modification Based on the Finite Element Method
DEFF Research Database (Denmark)
Liu, Bin; Kriegbaum, B.
2000-01-01
The paper describes the modification of piezoelectric accelerometers using a Finite Element (FE) method. Brüel & Kjær Accelerometer Type 8325 is chosen as an example to illustrate the advanced accelerometer development procedure. The deviation between the measurement and FE simulation results...
A Monte Carlo adapted finite element method for dislocation ...
Indian Academy of Sciences (India)
P Zakian
2017-10-10
Oct 10, 2017 ... simulations are proposed. Various comparisons are examined to illustrate the capability of both methods for random simulation of faults. Keywords. Monte Carlo simulation; stochastic modeling; split node technique; finite element method; earthquake fault dislocation. 1. Introduction. In material science, a ...
Reliability-Based Shape Optimization using Stochastic Finite Element Methods
DEFF Research Database (Denmark)
Enevoldsen, Ib; Sørensen, John Dalsgaard; Sigurdsson, G.
1991-01-01
stochastic fields (e.g. loads and material parameters such as Young's modulus and the Poisson ratio). In this case stochastic finite element techniques combined with FORM analysis can be used to obtain measures of the reliability of the structural systems, see Der Kiureghian & Ke (6) and Liu & Der Kiureghian...
Finite Element Analysis of a Free-Standing Staircase | Ajagbe ...
African Journals Online (AJOL)
The existing approximate analytical methods of analyzing free-standing stairs fail to predict the distribution of any stress resultant and the actual three dimensional behavior of the stair slab system. A more rationale but simple and accurate method of analysis based on finite element method is presented. Plate flexural ...
Finite element modelling of elastic intraplate stresses due to ...
Indian Academy of Sciences (India)
Finite element modelling of elastic intraplate stresses due to heterogeneities in crustal density and mechanical properties for the Jabalpur earthquake region, central India. A Manglik1,∗. , S Thiagarajan. 1. , A V Mikhailova. 2 and Yu Rebetsky. 2. 1. National Geophysical Research Institute, Uppal Road, Hyderabad 500 007, ...
Finite element concept to derive isostatic residual maps ...
Indian Academy of Sciences (India)
A new space-domain operator based on the shape function concept of finite element analysis has been developed to derive the residual maps of the Gorda Plate of western United States. The technique does not require explicit assumptions on isostatic models. Besides delineating the Gorda Plate boundary, the residual ...
Superconvergence for tetrahedral quadratic finite element methods for elliptic equations
Brandts, J.H.; Krizek, M.
2005-01-01
For a model elliptic boundary value problem we will prove that on strongly regular families of uniform tetrahedral partitions of the domain, the gradient of the quadratic finite element approximation is superclose to the gradient of the quadratic Lagrange interpolant of the exact solution. This
A mixed finite element method for particle simulation in lasertron
International Nuclear Information System (INIS)
Le Meur, G.
1987-03-01
A particle simulation code is being developed with the aim to treat the motion of charged particles in electromagnetic devices, such as Lasertron. The paper describes the use of mixed finite element methods in computing the field components, without derivating them from scalar or vector potentials. Graphical results are shown
Finite element model to study two dimensional unsteady state ...
African Journals Online (AJOL)
Kunal Pathak
2015-10-20
Oct 20, 2015 ... Excess buffer;. Finite element method. Abstract The calcium signaling plays a crucial role in expansion and contraction of cardiac myo- cytes. This calcium signaling is achieved by calcium diffusion, buffering mechanisms and influx in cardiac myocytes. The various calcium distribution patterns required for ...
Finite element simulations of two rock mechanics tests
International Nuclear Information System (INIS)
Dahlke, H.J.; Lott, S.A.
1986-04-01
Rock mechanics tests are performed to determine in situ stress conditions and material properties of an underground rock mass. To design stable underground facilities for the permanent storage of high-level nuclear waste, determination of these properties and conditions is a necessary first step. However, before a test and its associated equipment can be designed, the engineer needs to know the range of expected values to be measured by the instruments. Sensitivity studies by means of finite element simulations are employed in this preliminary design phase to evaluate the pertinent parameters and their effects on the proposed measurements. The simulations, of two typical rock mechanics tests, the plate bearing test and the flat-jack test, by means of the finite element analysis, are described. The plate bearing test is used to determine the rock mass deformation modulus. The flat-jack test is used to determine the in situ stress conditions of the host rock. For the plate bearing test, two finite element models are used to simulate the classic problem of a load on an elastic half space and the actual problem of a plate bearing test in an underground tunnel of circular cross section. For the flat-jack simulation, a single finite element model is used to simulate both horizontal and vertical slots. Results will be compared to closed-form solutions available in the literature
Finite Element Modelling Of Solidification Of Zinc Alloy | Osinkolu ...
African Journals Online (AJOL)
The solidification process of Zinc alloy is modelled by solving heat transfer equations with the aid of finite element method (FEM) using appropriate boundary conditions at the mould walls. The commercial software, Matlab, has been used to model the solidification process. The temperature profiles for each casting condition ...
Deflation in preconditioned conjugate gradient methods for Finite Element Problems
Vermolen, F.J.; Vuik, C.; Segal, A.
2002-01-01
We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods applied to a Finite Element discretization for an elliptic equation. Our set-up is a Poisson problem in two dimensions with continuous or discontinuous
Bending analysis of laminated composite plates using finite element ...
African Journals Online (AJOL)
user
In the past, the structural behavior of plates and shells using the finite element method has been studied by a variety of approaches. Choudhary and Tungikar ... (2011) presented the nonlinear static analysis of a rectangular laminated composite thick plate resting on nonlinear two-parameter elastic foundation with cubic.
Can finite element models detect clinically inferior cemented hip implants?
Stolk, J.; Maher, S.A.; Verdonschot, N.J.J.; Prendergast, P.J.; Huiskes, R.
2003-01-01
Rigorous preclinical testing of cemented hip prostheses against the damage accumulation failure scenario will reduce the incidence of aseptic loosening. For that purpose, a finite element simulation is proposed that predicts damage accumulation in the cement mantle and prosthetic migration. If the
Finite element analysis of one–dimensional hydrodynamic ...
African Journals Online (AJOL)
In this research work, we consider the one dimensional hydrodynamic dispersion of a reactive solute in electroosmotic flow. We present results demonstrating the utility of finite element methods to simulate and visualize hydrodynamic dispersion in the electroosmotic flow. From examination of concentration profile, effective ...
Finite element concept to derive isostatic residual maps-Application ...
Indian Academy of Sciences (India)
A new space-domain operator based on the shape function concept of finite element analysis has been developed to derive the residual maps of the Gorda Plate of western United States. The technique does not require explicit assumptions on isostatic models. Besides delineating the Gorda Plate boundary, the residual ...
Finite element analysis of bone loss around failing implants
Wolff, J.E.H.; Narra, N.; Antalainen, A.K.; Valasek, J.; Kaiser, J.; Sandor, G.K.; Marcian, P.
2014-01-01
Dental implants induce diverse forces on their surrounding bone. However, when excessive unphysiological forces are applied, resorption of the neighbouring bone may occur. The aim of this study was to assess possible causes of bone loss around failing dental implants using finite element analysis. A
Appendix F : finite element analysis of end region.
2013-03-01
FE (finite element) modeling was conducted to 1) provide a better understanding of the : elastic behavior of the end region prior to cracking and 2) to evaluate the effects of bearing pad : stiffness and width on end region elastic stresses. The FEA ...
Finite element investigation of the prestressed jointed concrete ...
African Journals Online (AJOL)
Precast prestressed concrete pavement (PCP) technology is of recent origin, and the information on PCP performance is not available in literature. This research presents a finite-element analysis of the potential benefits of prestressing on the jointed concrete pavements (JCP). With using a 3-dimensional (3D) ...
Material Models for the Human Torso Finite Element Model
2018-04-04
ARL-TR-8338 ● Apr 2018 US Army Research Laboratory Material Models for the Human Torso Finite Element Model by Carolyn E...longer needed. Do not return it to the originator. ARL-TR-8338 ● Apr 2018 US Army Research Laboratory Material Models for the...Weapons and Materials Research Directorate, ARL Approved for public release; distribution is unlimited. ii REPORT
finite element model for predicting residual stresses in shielded
African Journals Online (AJOL)
eobe
Diffractometer (XRD 6000). From the Finite Element Model Simulation, the transverse residual stress in the x ... Keywords: Residual stress, 3D FEM, Shielded manual metal arc welding, Low Carbon Steel (ASTM A36), X-Ray diffraction, degree of ..... I. ''Residual stress effects on fatigue life of welded structures using LEFM'',.
Finite element analyses of wood laminated composite poles
Cheng Piao; Todd F. Shupe; R.C. Tang; Chung Y. Hse
2005-01-01
Finite element analyses using ANSYS were conducted on orthotropic, polygonal, wood laminated composite poles subjected to a body force and a concentrated load at the free end. Deflections and stress distributions of small-scale and full-size composite poles were analyzed and compared to the results obtained in an experimental study. The predicted deflection for both...
GRIZ: Visualization of finite element analysis results on unstructured grids
International Nuclear Information System (INIS)
Dovey, D.; Loomis, M.D.
1994-01-01
GRIZ is a general-purpose post-processing application that supports interactive visualization of finite element analysis results on three-dimensional unstructured grids. GRIZ includes direct-to-videodisc animation capabilities and is being used as a production tool for creating engineering animations
CSIR Research Space (South Africa)
Suliman, Ridhwaan
2015-01-01
Full Text Available A fully-coupled partitioned finite volume–finite volume and hybrid finite volume–finite element fluid-structure interaction scheme is presented. The fluid domain is modelled as a viscous incompressible isothermal region governed by the Navier...
Dedicated finite elements for electrode thin films on quartz resonators.
Srivastava, Sonal A; Yong, Yook-Kong; Tanaka, Masako; Imai, Tsutomu
2008-08-01
The accuracy of the finite element analysis for thickness shear quartz resonators is a function of the mesh resolution; the finer the mesh resolution, the more accurate the finite element solution. A certain minimum number of elements are required in each direction for the solution to converge. This places a high demand on memory for computation, and often the available memory is insufficient. Typically the thickness of the electrode films is very small compared with the thickness of the resonator itself; as a result, electrode elements have very poor aspect ratios, and this is detrimental to the accuracy of the result. In this paper, we propose special methods to model the electrodes at the crystal interface of an AT cut crystal. This reduces the overall problem size and eliminates electrode elements having poor aspect ratios. First, experimental data are presented to demonstrate the effects of electrode film boundary conditions on the frequency-temperature curves of an AT cut plate. Finite element analysis is performed on a mesh representing the resonator, and the results are compared for testing the accuracy of the analysis itself and thus validating the results of analysis. Approximations such as lumping and Guyan reduction are then used to model the electrode thin films at the electrode interface and their results are studied. In addition, a new approximation called merging is proposed to model electrodes at the electrode interface.
Isogeometric finite element approximation of minimal surfaces based on extended loop subdivision
Pan, Qing; Chen, Chong; Xu, Guoliang
2017-08-01
In this paper, we investigate the formulation of isogeometric analysis for minimal surface models on planar bounded domains by extended Loop surface subdivision approach. The exactness of the physical domain of interest is fixed on the coarsest level of the triangular discretization with any topological structure, which is thought of as the initial control mesh of Loop subdivision. By performing extended Loop subdivision, the control mesh can be repeatedly refined, and the geometry is described as an infinite set of quartic box-spline while maintaining its original exactness. The limit function representation of extended Loop subdivision forms our finite element space, which possesses C1 smoothness and the flexibility of mesh topology. We establish its inverse inequalities which resemble the ones of general finite element spaces. We develop the approximation estimate with the aid of H1 convergence property of the corresponding linear models. It enables us to overcome the difficulty of proving the boundedness of the gradient of finite element solutions appearing in the coefficient of minimal surface models. Numerical examples are given with the comparison to the classical linear finite element method which is consistent with our theoretical results.
Creating a Test-Validated Finite-Element Model of the X-56A Aircraft Structure
Pak, Chan-Gi; Truong, Samson
2014-01-01
Small modeling errors in a finite-element model will eventually induce errors in the structural flexibility and mass, thus propagating into unpredictable errors in the unsteady aerodynamics and the control law design. One of the primary objectives of the X-56A Multi-Utility Technology Testbed aircraft is the flight demonstration of active flutter suppression and, therefore, in this study, the identification of the primary and secondary modes for the structural model tuning based on the flutter analysis of the X-56A aircraft. The ground-vibration test-validated structural dynamic finite-element model of the X-56A aircraft is created in this study. The structural dynamic finite-element model of the X-56A aircraft is improved using a model-tuning tool. In this study, two different weight configurations of the X-56A aircraft have been improved in a single optimization run. Frequency and the cross-orthogonality (mode shape) matrix were the primary focus for improvement, whereas other properties such as c.g. location, total weight, and off-diagonal terms of the mass orthogonality matrix were used as constraints. The end result was an improved structural dynamic finite-element model configuration for the X-56A aircraft. Improved frequencies and mode shapes in this study increased average flutter speeds of the X-56A aircraft by 7.6% compared to the baseline model.
Finite element analysis of degraded concrete structures - Workshop proceedings
International Nuclear Information System (INIS)
1999-09-01
This workshop is related to the finite element analysis of degraded concrete structures. It is composed of three sessions. The first session (which title is: the use of finite element analysis in safety assessments) comprises six papers which titles are: Historical Development of Concrete Finite Element Modeling for Safety Evaluation of Accident-Challenged and Aging Concrete Structures; Experience with Finite Element Methods for Safety Assessments in Switzerland; Stress State Analysis of the Ignalina NPP Confinement System; Prestressed Containment: Behaviour when Concrete Cracking is Modelled; Application of FEA for Design and Support of NPP Containment in Russia; Verification Problems of Nuclear Installations Safety Software of Strength Analysis (NISS SA). The second session (title: concrete containment structures under accident loads) comprises seven papers which titles are: Two Application Examples of Concrete Containment Structures under Accident Load Conditions Using Finite Element Analysis; What Kind of Prediction for Leak rates for Nuclear Power Plant Containments in Accidental Conditions; Influence of Different Hypotheses Used in Numerical Models for Concrete At Elevated Temperatures on the Predicted Behaviour of NPP Core Catchers Under Severe Accident Conditions; Observations on the Constitutive Modeling of Concrete Under Multi-Axial States at Elevated Temperatures; Analyses of a Reinforced Concrete Containment with Liner Corrosion Damage; Program of Containment Concrete Control During Operation for the Temelin Nuclear Power Plant; Static Limit Load of a Deteriorated Hyperbolic Cooling Tower. The third session (concrete structures under extreme environmental load) comprised five papers which titles are: Shear Transfer Mechanism of RC Plates After Cracking; Seismic Back Calculation of an Auxiliary Building of the Nuclear Power Plant Muehleberg, Switzerland; Seismic Behaviour of Slightly Reinforced Shear Wall Structures; FE Analysis of Degraded Concrete
Plane-wave basis finite elements and boundary elements for three-dimensional wave scattering.
Perrey-Debain, E; Laghrouche, O; Bettess, P; Trevelyan, J
2004-03-15
Classical finite-element and boundary-element formulations for the Helmholtz equation are presented, and their limitations with respect to the number of variables needed to model a wavelength are explained. A new type of approximation for the potential is described in which the usual finite-element and boundary-element shape functions are modified by the inclusion of a set of plane waves, propagating in a range of directions evenly distributed on the unit sphere. Compared with standard piecewise polynomial approximation, the plane-wave basis is shown to give considerable reduction in computational complexity. In practical terms, it is concluded that the frequency for which accurate results can be obtained, using these new techniques, can be up to 60 times higher than that of the conventional finite-element method, and 10 to 15 times higher than that of the conventional boundary-element method.
Investigations on Actuator Dynamics through Theoretical and Finite Element Approach
Directory of Open Access Journals (Sweden)
Somashekhar S. Hiremath
2010-01-01
Full Text Available This paper gives a new approach for modeling the fluid-structure interaction of servovalve component-actuator. The analyzed valve is a precision flow control valve-jet pipe electrohydraulic servovalve. The positioning of an actuator depends upon the flow rate from control ports, in turn depends on the spool position. Theoretical investigation is made for No-load condition and Load condition for an actuator. These are used in finite element modeling of an actuator. The fluid-structure-interaction (FSI is established between the piston and the fluid cavities at the piston end. The fluid cavities were modeled with special purpose hydrostatic fluid elements while the piston is modeled with brick elements. The finite element method is used to simulate the variation of cavity pressure, cavity volume, mass flow rate, and the actuator velocity. The finite element analysis is extended to study the system's linearized response to harmonic excitation using direct solution steady-state dynamics. It was observed from the analysis that the natural frequency of the actuator depends upon the position of the piston in the cylinder. This is a close match with theoretical and simulation results. The effect of bulk modulus is also presented in the paper.
Flexible ferroelectric element based on van der Waals heteroepitaxy.
Jiang, Jie; Bitla, Yugandhar; Huang, Chun-Wei; Do, Thi Hien; Liu, Heng-Jui; Hsieh, Ying-Hui; Ma, Chun-Hao; Jang, Chi-Yuan; Lai, Yu-Hong; Chiu, Po-Wen; Wu, Wen-Wei; Chen, Yi-Chun; Zhou, Yi-Chun; Chu, Ying-Hao
2017-06-01
We present a promising technology for nonvolatile flexible electronic devices: A direct fabrication of epitaxial lead zirconium titanate (PZT) on flexible mica substrate via van der Waals epitaxy. These single-crystalline flexible ferroelectric PZT films not only retain their performance, reliability, and thermal stability comparable to those on rigid counterparts in tests of nonvolatile memory elements but also exhibit remarkable mechanical properties with robust operation in bent states (bending radii down to 2.5 mm) and cycling tests (1000 times). This study marks the technological advancement toward realizing much-awaited flexible yet single-crystalline nonvolatile electronic devices for the design and development of flexible, lightweight, and next-generation smart devices with potential applications in electronics, robotics, automotive, health care, industrial, and military systems.
Finite element and discontinuous Galerkin methods for transient wave equations
Cohen, Gary
2017-01-01
This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem ...
FEM and BIEM - A new infinite hybrid finite element
International Nuclear Information System (INIS)
Drakaliev, P.
1993-01-01
The finite element method (MFE) and the boundary integral equation method (BIEM) are general approximation procedures applicable to a wide variety of engineering problems. Each of them has many variants and each possesses certain merits and limitations of its own. The FEM may be easier to apply in domains with anisotropic or nonlinear behaviour. On the other hand the BEM is more attractive for unbounded domains or regions of high stress concentration. Therefore, the idea of combining both numerical techniques is of great interest in many practical problems, especially in solid and fluid mechanics, such as soil-structure and structure-fluid interaction problems. In the developments to follow an energy approach for symmetrizing the indirect BIEM is being used to obtain the stiffness matrix for the infinite or semi-infinite elastic medium. Thus the subdomain is considered as an infinite super element with an arbitrary shaped boundary and can be easily implemented into existing finite element codes
Block-iterative finite element computations for incompressible flow problems
International Nuclear Information System (INIS)
Tezduyar, T.E.; Liou, J.; Glowinski, R.; Nguyen, T.; Poole, S.
1988-01-01
A block-iterative finite element procedure is presented for two-dimensional fluid dynamics computations on multiply-connected domains based on the vorticity-stream function formulation of the incompressible Navier-Stokes equations. The difficulty associated with the convection term in the vorticity transport equation is addressed by using a streamline-upwind/Petrov-Galerkin scheme. Element-by-element preconditioned iteration techniques with high degree of vectorization and high computational speed are employed to solve the linear equation system for each block. The authors conclude that performance evaluations show the potential of these techniques to be used for large-scale computations
Solution of Fokker–Planck equation by finite element and finite ...
Indian Academy of Sciences (India)
Abstract. The response of a structural system to white noise excitation (delta- correlated) constitutes a Markov vector process whose transitional probability den- sity function (TPDF) is governed by both the forward Fokker–Planck and backward. Kolmogorov equations. Numerical solution of these equations by finite element ...
Solution of Fokker–Planck equation by finite element and finite ...
Indian Academy of Sciences (India)
hindered by the problem of dimensionality. In this paper numerical solution of the stationary and transient form of the Fokker–Planck (FP) equation corresponding to two state nonlinear systems is obtained by standard sequential finite element method. (FEM) using C0 shape function and Crank–Nicholson time integration ...
Finite element simulations of surface effect on Rayleigh waves
He, Jin; Zhao, Jinling
2018-03-01
Rayleigh waves influenced by surface effect are investigated by using finite element methods, in which eigenfrequency analysis are performed on a model composed of a half-space covered by the surface effect dominated domain. For a given wavelength, the frequency of the Rayleigh wave is obtained as the eigenfrequency of the model satisfying Floquet periodic boundary conditions. The thickness of the surface effect can be set to be infinitely small or a finite value in the finite element methods. The curvature-dependent out-of-plane force induced by surface tension as described by the generalized Young-Laplace equation is realized through geometric nonlinear analysis. The finite element simulations show that the assumptions of small curvature and infinitely small thickness of the surface effect widely used in theoretical approaches become invalid when Rayleigh waves are highly influenced by the surface effect. This work gives a more accurate insight into the surface effect on Rayleigh waves and provides a potential method for measuring the thickness of the surface effect from the dispersion curves of surface effect influenced Rayleigh wave velocities.
Finite-element-analysis of fields radiated from ICRF antenna
International Nuclear Information System (INIS)
Yamanaka, Kaoru; Sugihara, Ryo.
1984-01-01
The electromagnetic fields radiated from a loop antenna on which an oscillating current flows across the static magnetic field B 0 are calculated in several simple geometries by the finite element method (FEM) and by analytical methods in a cross section of a plasma cylinder. The wave number along B 0 is assumed to be finite. Good agreement between FEM and the analytical solutions is obtained, demonstrating the accuracy of the FEM solutions. The method is used to calculate the fields from a half-turn antenna, and acceptable results are obtained. (author)
Solution of Exterior Helmholtz Problems Using Finite and Infinite Elements
Shirron, Joseph James
This dissertation discusses methods for the computation of solutions of the Helmholtz equation in unbounded domains. Two classes of methods are considered: one in which the infinite exterior domain is truncated and finite elements are used to discretize the resultant computational domain, and another in which the exterior domain is discretized by infinite elements. For the first class of methods a generalized Robin boundary condition is imposed on the truncating surface to replace the Sommerfeld radiation condition at infinity and to ensure uniqueness of the solution. Several of these approximate radiation conditions are discussed and a comparison is presented to illustrate their efficacy. For the second class of methods finite elements are used to discretize the exterior domain out to an enclosing circle or prolate spheroid, then infinite elements are used to discretize the remaining unbounded domain. Strikingly different approximation and convergence behavior is observed depending on whether a bilinear or sesquilinear form is chosen for the variational formulation of the problem. Convergence analysis for the infinite element methods is presented for both two and three spatial dimensions. A solution method based on the idea of domain decomposition is also discussed, as are various techniques for obtaining the solution in the far field. Numerical experiments for problems of acoustic scattering by bodies of revolution convincingly demonstrate the superiority in terms of computational expense of the infinite element methods over boundary element methods.
Solution of the neutronics code dynamic benchmark by finite element method
Avvakumov, A. V.; Vabishchevich, P. N.; Vasilev, A. O.; Strizhov, V. F.
2016-10-01
The objective is to analyze the dynamic benchmark developed by Atomic Energy Research for the verification of best-estimate neutronics codes. The benchmark scenario includes asymmetrical ejection of a control rod in a water-type hexagonal reactor at hot zero power. A simple Doppler feedback mechanism assuming adiabatic fuel temperature heating is proposed. The finite element method on triangular calculation grids is used to solve the three-dimensional neutron kinetics problem. The software has been developed using the engineering and scientific calculation library FEniCS. The matrix spectral problem is solved using the scalable and flexible toolkit SLEPc. The solution accuracy of the dynamic benchmark is analyzed by condensing calculation grid and varying degree of finite elements.
An object-oriented class design for the generalized finite element method programming
Directory of Open Access Journals (Sweden)
Dorival Piedade Neto
Full Text Available The Generalized Finite Element Method (GFEM is a numerical method based on the Finite Element Method (FEM, presenting as its main feature the possibility of improving the solution by means of local enrichment functions. In spite of its advantages, the method demands a complex data structure, which can be especially benefited by the Object-Oriented Programming (OOP. Even though the OOP for the traditional FEM has been extensively described in the technical literature, specific design issues related to the GFEM are yet little discussed and not clearly defined. In the present article it is described an Object-Oriented (OO class design for the GFEM, aiming to achieve a computational code that presents a flexible class structure, circumventing the difficulties associated to the method characteristics. The proposed design is evaluated by means of some numerical examples, computed using a code implemented in Python programming language.
Chortis, Dimitris I
2013-01-01
This book concerns the development of novel finite elements for the structural analysis of composite beams and blades. The introduction of material damping is also an important aspect of composite structures and it is presented here in terms of their static and dynamic behavior. The book thoroughly presents a new shear beam finite element, which entails new blade section mechanics, capable of predicting structural blade coupling due to composite coupling and/or internal section geometry. Theoretical background is further expanded towards the inclusion of nonlinear structural blade models and damping mechanics for composite structures. The models effectively include geometrically nonlinear terms due to large displacements and rotations, improve the modeling accuracy of very large flexible blades, and enable the modeling of rotational stiffening and buckling, as well as, nonlinear structural coupling. Validation simulations on specimen level study the geometric nonlinearities effect on the modal frequencies and...
Finite element fluid modeling of axisymmetric magnetized boundary plasma with recycling neutrals
International Nuclear Information System (INIS)
Zanino, R.
1992-01-01
Finite elements should provide a natural and flexible method for fluid modeling of the tokamak SOL, in particular when the SOL geometry is complex, and/or the poloidal magnetic field is very inclined to the limiter/divertor target. Here we present a Galerkin finite element code, FELS, for transport modeling of a 2-fluid magnetized boundary plasma in an axisymmetry domain, in the presence of recycling neutrals. The classical collisional plasma dynamics along magnetic field lines is taken into account, and a simple diffusive Ansatz is used for the fluxes across magnetic surfaces; electric currents and diamagnetic flows are neglected for the time being. An analytical fluid model is used for the recycling neutrals. Results are shown and discussed for the case of a simple geometry. (orig.)
All-electron Kohn–Sham density functional theory on hierarchic finite element spaces
International Nuclear Information System (INIS)
Schauer, Volker; Linder, Christian
2013-01-01
In this work, a real space formulation of the Kohn–Sham equations is developed, making use of the hierarchy of finite element spaces from different polynomial order. The focus is laid on all-electron calculations, having the highest requirement onto the basis set, which must be able to represent the orthogonal eigenfunctions as well as the electrostatic potential. A careful numerical analysis is performed, which points out the numerical intricacies originating from the singularity of the nuclei and the necessity for approximations in the numerical setting, with the ambition to enable solutions within a predefined accuracy. In this context the influence of counter-charges in the Poisson equation, the requirement of a finite domain size, numerical quadratures and the mesh refinement are examined as well as the representation of the electrostatic potential in a high order finite element space. The performance and accuracy of the method is demonstrated in computations on noble gases. In addition the finite element basis proves its flexibility in the calculation of the bond-length as well as the dipole moment of the carbon monoxide molecule
Finite Element Framework for Computational Fluid Dynamics in FEBio.
Ateshian, Gerard A; Shim, Jay J; Maas, Steve A; Weiss, Jeffrey A
2018-02-01
The mechanics of biological fluids is an important topic in biomechanics, often requiring the use of computational tools to analyze problems with realistic geometries and material properties. This study describes the formulation and implementation of a finite element framework for computational fluid dynamics (CFD) in FEBio, a free software designed to meet the computational needs of the biomechanics and biophysics communities. This formulation models nearly incompressible flow with a compressible isothermal formulation that uses a physically realistic value for the fluid bulk modulus. It employs fluid velocity and dilatation as essential variables: The virtual work integral enforces the balance of linear momentum and the kinematic constraint between fluid velocity and dilatation, while fluid density varies with dilatation as prescribed by the axiom of mass balance. Using this approach, equal-order interpolations may be used for both essential variables over each element, contrary to traditional mixed formulations that must explicitly satisfy the inf-sup condition. The formulation accommodates Newtonian and non-Newtonian viscous responses as well as inviscid fluids. The efficiency of numerical solutions is enhanced using Broyden's quasi-Newton method. The results of finite element simulations were verified using well-documented benchmark problems as well as comparisons with other free and commercial codes. These analyses demonstrated that the novel formulation introduced in FEBio could successfully reproduce the results of other codes. The analogy between this CFD formulation and standard finite element formulations for solid mechanics makes it suitable for future extension to fluid-structure interactions (FSIs).
Finite element analysis of structures through unified formulation
Carrera, Erasmo; Petrolo, Marco; Zappino, Enrico
2014-01-01
The finite element method (FEM) is a computational tool widely used to design and analyse complex structures. Currently, there are a number of different approaches to analysis using the FEM that vary according to the type of structure being analysed: beams and plates may use 1D or 2D approaches, shells and solids 2D or 3D approaches, and methods that work for one structure are typically not optimized to work for another. Finite Element Analysis of Structures Through Unified Formulation deals with the FEM used for the analysis of the mechanics of structures in the case of linear elasticity. The novelty of this book is that the finite elements (FEs) are formulated on the basis of a class of theories of structures known as the Carrera Unified Formulation (CUF). It formulates 1D, 2D and 3D FEs on the basis of the same ''fundamental nucleus'' that comes from geometrical relations and Hooke''s law, and presents both 1D and 2D refined FEs that only have displacement variables as in 3D elements. It also covers 1D...
Dynamic analysis of an axially moving beam subject to inner pressure using finite element method
Energy Technology Data Exchange (ETDEWEB)
Hua, Hongliang; Qiu, Ming; Liao, Zhenqiang [Nanjing University of Science and Technology, Nanjing (China)
2017-06-15
A dynamic model of an axially moving flexible beam subject to an inner pressure is present. The coupling principle between a flexible beam and inner pressure is analyzed first, and the potential energy of the inner pressure due to the beam bending is derived using the principle of virtual work. A 1D hollow beam element contain inner pressure is established. The finite element method and Lagrange’s equation are used to derive the motion equations of the axially moving system. The dynamic responses are analyzed by Newmark-β time integration method. Based on the computed dynamic responses, the effects of inner pressure on beam dynamics are discussed. Some interesting phenomenon is observed.
FECAP - FINITE ELEMENT COMPOSITE ANALYSIS PROGRAM FOR A MICROCOMPUTER
Bowles, D. E.
1994-01-01
Advanced composite materials have gained use in the aerospace industry over the last 20 years because of their high specific strength and stiffness, and low coefficient of thermal expansion. Design of composite structures requires the analysis of composite material behavior. The Finite Element Composite Analysis Program, FECAP, is a special purpose finite element analysis program for analyzing composite material behavior with a microcomputer. Composite materials, in regard to this program, are defined as the combination of at least two distinct materials to form one nonhomogeneous anisotropic material. FECAP assumes a state of generalized plane strain exists in a material consisting of two or more orthotropic phases, subjected to mechanical and/or thermal loading. The finite element formulation used in FECAP is displacement based and requires the minimization of the total potential energy for each element with respect to the unknown variables. This procedure leads to a set of linear simultaneous equations relating the unknown nodal displacements to the applied loads. The equations for each element are assembled into a global system, the boundary conditions are applied, and the system is solved for the nodal displacements. The analysis may be performed using either 4-mode linear or 8-mode quadratic isoparametric elements. Output includes the nodal displacements, and the element stresses and strains. FECAP was written for a Hewlett Packard HP9000 Series 200 Microcomputer with the HP Basic operating system. It was written in HP BASIC 3.0 and requires approximately 0.5 Mbytes of RAM in addition to what is required for the operating system. A math coprocessor card is highly recommended. FECAP was developed in 1988.
Sensitive analysis of a finite element model of orthogonal cutting
Brocail, J.; Watremez, M.; Dubar, L.
2011-01-01
This paper presents a two-dimensional finite element model of orthogonal cutting. The proposed model has been developed with Abaqus/explicit software. An Arbitrary Lagrangian-Eulerian (ALE) formulation is used to predict chip formation, temperature, chip-tool contact length, chip thickness, and cutting forces. This numerical model of orthogonal cutting will be validated by comparing these process variables to experimental and numerical results obtained by Filice et al. [1]. This model can be considered to be reliable enough to make qualitative analysis of entry parameters related to cutting process and frictional models. A sensitivity analysis is conducted on the main entry parameters (coefficients of the Johnson-Cook law, and contact parameters) with the finite element model. This analysis is performed with two levels for each factor. The sensitivity analysis realised with the numerical model on the entry parameters has allowed the identification of significant parameters and the margin identification of parameters.
Exemplifying Quantum Systems in a Finite Element Basis
International Nuclear Information System (INIS)
Young, Toby D.
2009-01-01
This paper presents a description of the abstractions required for the expression and solution of the linear single-particle Schroedinger equation in a finite element basis. This paper consists of two disparate themes: First, to layout and establish the foundations of finite element analysis as an approximate numerical solution to extendable quantum mechanical systems; and second, to promote a high-performance open-source computational model for the approximate numerical solution to quantum mechanical systems. The structural foundation of the one-and two-dimensional time-independent Schroedinger equation describing an infinite potential well is explored and a brief overview of the hierarchal design of the computational library written in C++ is given.
Domain Decomposition Solvers for Frequency-Domain Finite Element Equations
Copeland, Dylan
2010-10-05
The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.
Piping noise transmission loss calculations using finite element analysis
Eberhart, Richard; Catron, Fred W.; Fagerlund, Allen C.; Karczub, Denis G.; Mann, J. Adin
2005-09-01
The prediction of noise radiated by piping downstream of a control valve is subject to various uncertainties. One of the significant sources of uncertainty is the pipe-wall transmission loss. Due to the difficulties in experimentally measuring pipe-wall transmission loss accurately, and practical difficulties of taking into account pipe length and boundary conditions, an analytical approach for the calculation of transmission loss is required. The feasibility of uncoupled structural-acoustic finite element based calculations of transmission loss is being investigated for this purpose. By developing the use of finite element based calculations of transmission loss, it is hoped to provide a simple analysis procedure to quantify the effects of pipe length and boundary conditions on the noise level downstream of control valves in practical piping systems. It should also assist in the refinement of analytical/statistical calculations of transmission loss and noise radiation.
Finite element analysis of fretting contact for nonhomogenous materials
Korkmaz, Y. M.; Coker, D.
2018-01-01
Fretting problem arises in the case of relatively small sliding motion between contacting surfaces. Fatigue life of the components that are in contact with each other, especially in rotorcraft may be significantly reduced due to fretting. The purpose of this study is to investigate material inhomogeneity near the contact region on the fretting problem in a cylindrical on flat contact configuration. A finite element (FE) model was constructed by using commercial finite element package ABAQUSTMto study partial sliding and stress concentrations. In order to investigate the effect of material inhomogeneity, the fretting contact is analyzed by introducing voids near the contact region. The void size and an array of voids is introduced into the substrate. The results are compared in terms of pressure, shear traction, tangential stress magnitudes and relative slip between the contacting materials.
The finite element method and applications in engineering using ANSYS
Madenci, Erdogan
2015-01-01
This textbook offers theoretical and practical knowledge of the finite element method. The book equips readers with the skills required to analyze engineering problems using ANSYS®, a commercially available FEA program. Revised and updated, this new edition presents the most current ANSYS® commands and ANSYS® screen shots, as well as modeling steps for each example problem. This self-contained, introductory text minimizes the need for additional reference material by covering both the fundamental topics in finite element methods and advanced topics concerning modeling and analysis. It focuses on the use of ANSYS® through both the Graphics User Interface (GUI) and the ANSYS® Parametric Design Language (APDL). Extensive examples from a range of engineering disciplines are presented in a straightforward, step-by-step fashion. Key topics include: • An introduction to FEM • Fundamentals and analysis capabilities of ANSYS® • Fundamentals of discretization and approximation functions • Modeling techniq...
Stress of tee joints by the finite element method
International Nuclear Information System (INIS)
Gantayat, A.N.; Powell, G.H.
1973-02-01
A series of three computer programs for the stress and thermal stress analysis of tee joints to ASA B16.9 is described. Detailed user's guides to the programs are presented, and the results of analyses are compared with experimental measurements obtained elsewhere. An investigation to select the most appropriate finite element for inclusion in the programs is described. The finite element theory, for both stress and transient heat flow analysis, is presented in detail. Listings of input data for sample problems are included. It is concluded that results in good agreement with experiment can be obtained, but that further studies of the effects of mesh refinement remain to be carried out. (auth)
Parallel, adaptive finite element methods for conservation laws
Biswas, Rupak; Devine, Karen D.; Flaherty, Joseph E.
1994-01-01
We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.
Finite element model of magnetoconvection of a ferrofluid
International Nuclear Information System (INIS)
Snyder, S.M.; Cader, Tahir; Finlayson, B.A.
2003-01-01
Combined natural and magnetic convective heat transfer through a ferrofluid in a cubic enclosure is simulated numerically. The momentum equation includes a magnetic term that arises when a magnetic fluid is in the presence of a magnetic field gradient and a temperature gradient. In order to validate the theory, the wall temperature isotherms and Nusselt numbers are compared to experimental work of Sawada et al. (Int. J. Appl. Electromagn. Mater. 4 (1994) 329). Results are obtained using standard computational fluid dynamics codes, with modifications to account for the Langevin factor when needed. The CFD code FIDAP uses the finite element method, sometimes with a user-defined subroutine. The CFD code FEMLAB uses the finite element method with a user-supplied body force
A finite element model of ferroelectric/ferroelastic polycrystals
Energy Technology Data Exchange (ETDEWEB)
HWANG,STEPHEN C.; MCMEEKING,ROBERT M.
2000-02-17
A finite element model of polarization switching in a polycrystalline ferroelectric/ferroelastic ceramic is developed. It is assumed that a crystallite switches if the reduction in potential energy of the polycrystal exceeds a critical energy barrier per unit volume of switching material. Each crystallite is represented by a finite element with the possible dipole directions assigned randomly subject to crystallographic constraints. The model accounts for both electric field induced (i.e. ferroelectric) switching and stress induced (i.e. ferroelastic) switching with piezoelectric interactions. Experimentally measured elastic, dielectric, and piezoelectric constants are used consistently, but different effective critical energy barriers are selected phenomenologically. Electric displacement versus electric field, strain versus electric field, stress versus strain, and stress versus electric displacement loops of a ceramic lead lanthanum zirconate titanate (PLZT) are modeled well below the Curie temperature.
Finite Element Analysis of Electrically Excited Quartz Tuning Fork Devices
Oria, Roger; Otero, Jorge; González, Laura; Botaya, Luis; Carmona, Manuel; Puig-Vidal, Manel
2013-01-01
Quartz Tuning Fork (QTF)-based Scanning Probe Microscopy (SPM) is an important field of research. A suitable model for the QTF is important to obtain quantitative measurements with these devices. Analytical models have the limitation of being based on the double cantilever configuration. In this paper, we present an electromechanical finite element model of the QTF electrically excited with two free prongs. The model goes beyond the state-of-the-art of numerical simulations currently found in the literature for this QTF configuration. We present the first numerical analysis of both the electrical and mechanical behavior of QTF devices. Experimental measurements obtained with 10 units of the same model of QTF validate the finite element model with a good agreement. PMID:23722828
Finite Element Analysis of Electrically Excited Quartz Tuning Fork Devices
Directory of Open Access Journals (Sweden)
Manel Puig-Vidal
2013-05-01
Full Text Available Quartz Tuning Fork (QTF-based Scanning Probe Microscopy (SPM is an important field of research. A suitable model for the QTF is important to obtain quantitative measurements with these devices. Analytical models have the limitation of being based on the double cantilever configuration. In this paper, we present an electromechanical finite element model of the QTF electrically excited with two free prongs. The model goes beyond the state-of-the-art of numerical simulations currently found in the literature for this QTF configuration. We present the first numerical analysis of both the electrical and mechanical behavior of QTF devices. Experimental measurements obtained with 10 units of the same model of QTF validate the finite element model with a good agreement.
Finite-element analysis of flawed and unflawed pipe tests
International Nuclear Information System (INIS)
James, R.J.; Nickell, R.E.; Sullaway, M.F.
1989-12-01
Contemporary versions of the general purpose, nonlinear finite element program ABAQUS have been used in structural response verification exercises on flawed and unflawed austenitic stainless steel and ferritic steel piping. Among the topics examined, through comparison between ABAQUS calculations and test results, were: (1) the effect of using variations in the stress-strain relationship from the test article material on the calculated response; (2) the convergence properties of various finite element representations of the pipe geometry, using shell, beam and continuum models; (3) the effect of test system compliance; and (4) the validity of ABAQUS J-integral routines for flawed pipe evaluations. The study was culminated by the development and demonstration of a ''macroelement'' representation for the flawed pipe section. The macroelement can be inserted into an existing piping system model, in order to accurately treat the crack-opening and crack-closing static and dynamic response. 11 refs., 20 figs., 1 tab
Assembly of finite element methods on graphics processors
Cecka, Cris
2010-08-23
Recently, graphics processing units (GPUs) have had great success in accelerating many numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are created and analyzed. Multiple strategies for efficient use of global, shared, and local memory, methods to achieve memory coalescing, and optimal choice of parameters are introduced. We find that with appropriate preprocessing and arrangement of support data, the GPU coprocessor using single-precision arithmetic achieves speedups of 30 or more in comparison to a well optimized double-precision single core implementation. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite element discretization. © 2010 John Wiley & Sons, Ltd.
An adaptive finite element method for steady and transient problems
International Nuclear Information System (INIS)
Benner, R.E. Jr.; Davis, H.T.; Scriven, L.E.
1987-01-01
Distributing integral error uniformly over variable subdomains, or finite elements, is an attractive criterion by which to subdivide a domain for the Galerkin/finite element method when localized steep gradients and high curvatures are to be resolved. Examples are fluid interfaces, shock fronts and other internal layers, as well as fluid mechanical and other boundary layers, e.g. thin-film states at solid walls. The uniform distribution criterion is developed into an adaptive technique for one-dimensional problems. Nodal positions can be updated simultaneously with nodal values during Newton iteration, but it is usually better to adopt nearly optimal nodal positions during Newton iteration upon nodal values. Three illustrative problems are solved: steady convection with diffusion, gradient theory of fluid wetting on a solid surface and Buckley-Leverett theory of two phase Darcy flow in porous media
Finite-element modelling of multilayer X-ray optics.
Cheng, Xianchao; Zhang, Lin
2017-05-01
Multilayer optical elements for hard X-rays are an attractive alternative to crystals whenever high photon flux and moderate energy resolution are required. Prediction of the temperature, strain and stress distribution in the multilayer optics is essential in designing the cooling scheme and optimizing geometrical parameters for multilayer optics. The finite-element analysis (FEA) model of the multilayer optics is a well established tool for doing so. Multilayers used in X-ray optics typically consist of hundreds of periods of two types of materials. The thickness of one period is a few nanometers. Most multilayers are coated on silicon substrates of typical size 60 mm × 60 mm × 100-300 mm. The high aspect ratio between the size of the optics and the thickness of the multilayer (10 7 ) can lead to a huge number of elements for the finite-element model. For instance, meshing by the size of the layers will require more than 10 16 elements, which is an impossible task for present-day computers. Conversely, meshing by the size of the substrate will produce a too high element shape ratio (element geometry width/height > 10 6 ), which causes low solution accuracy; and the number of elements is still very large (10 6 ). In this work, by use of ANSYS layer-functioned elements, a thermal-structural FEA model has been implemented for multilayer X-ray optics. The possible number of layers that can be computed by presently available computers is increased considerably.
Finite-element modelling of multilayer X-ray optics
Energy Technology Data Exchange (ETDEWEB)
Cheng, Xianchao; Zhang, Lin
2017-04-11
Multilayer optical elements for hard X-rays are an attractive alternative to crystals whenever high photon flux and moderate energy resolution are required. Prediction of the temperature, strain and stress distribution in the multilayer optics is essential in designing the cooling scheme and optimizing geometrical parameters for multilayer optics. The finite-element analysis (FEA) model of the multilayer optics is a well established tool for doing so. Multilayers used in X-ray optics typically consist of hundreds of periods of two types of materials. The thickness of one period is a few nanometers. Most multilayers are coated on silicon substrates of typical size 60 mm × 60 mm × 100–300 mm. The high aspect ratio between the size of the optics and the thickness of the multilayer (10^{7}) can lead to a huge number of elements for the finite-element model. For instance, meshing by the size of the layers will require more than 10^{16}elements, which is an impossible task for present-day computers. Conversely, meshing by the size of the substrate will produce a too high element shape ratio (element geometry width/height > 10^{6}), which causes low solution accuracy; and the number of elements is still very large (10^{6}). In this work, by use of ANSYS layer-functioned elements, a thermal-structural FEA model has been implemented for multilayer X-ray optics. The possible number of layers that can be computed by presently available computers is increased considerably.
A parallel finite element simulator for ion transport through three-dimensional ion channel systems.
Tu, Bin; Chen, Minxin; Xie, Yan; Zhang, Linbo; Eisenberg, Bob; Lu, Benzhuo
2013-09-15
A parallel finite element simulator, ichannel, is developed for ion transport through three-dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson-Nernst-Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I - V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α-Hemolysin (α-HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size-modified PNP (SMPNP) model on VDAC and α-HL. It is shown that the size effects in SMPNP can
Finite Element CURVIB method for fluid-structure interaction simulations of tissue heart valves
Gilmanov, Anvar; Stolarski, Henryk; Le, Trung; Sotiropoulos, Fotis
2012-11-01
A new fluid-structure interaction (FSI) model is developed for solving the three-dimensional unsteady Navier-Stokes equations in domains with arbitrarily complex tissues undergoing large deformation. The method employs the sharp-interface CURVIB method [L. Ge, F. Sotiropoulos, JCP, 225 (2007) 1782-1809] for handling complex moving boundaries, with a finite element (FE) model, which can handle large structural/tissue deformations using the nonlinear Kirckhhoff thin shells theory. A new treatment of the flexible immersed body is introduced to handle the thin body surfaces. A version of Aitken's acceleration for strong fluid-structure coupling is used to calculate the responses of the flexible bodies to the applied fluid load. The new, rotation-free finite element formulation for large deformations of thin shells has been extensively tested and validated for a range of relevant problems. The coupled FE-CURVIB FSI model is validated for vortex induced oscillations of a flexible cantilever and applied to simulate physiologic pulsatile flows through a tissue aortic heart valve in an anatomic artery geometry. The results show the good convergence property of the new FSI algorithm and demonstrate its promise for a broad range of biological applications.
On angle conditions in the finite element method
Czech Academy of Sciences Publication Activity Database
Brandts, J.; Hannukainen, A.; Korotov, S.; Křížek, Michal
2011-01-01
Roč. 56, - (2011), s. 81-95 ISSN 1575-9822 R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional research plan: CEZ:AV0Z10190503 Keywords : simplicial finite elements * minimum and maximum angle condition * ball conditions Subject RIV: BA - General Mathematics http://www.sema.org.es/ojs/index.php?journal=journal&page=article&op=viewArticle&path%5B%5D=612
Finite element realization of the UH model for unsaturated soils
International Nuclear Information System (INIS)
Luo Ting; Zhang Panpan; Yao Yangping; Liu Yuemiao
2014-01-01
Gaomiaozi bentonite which is the buffer/backfill materials of the HLW geological repository will be overconsolidated and unsaturated in a long period. The study of the model for overconsolidated unsaturated soils and its finite element application is of practical value. Based on the user subroutines, the UH model for unsaturated soils is developed in ABAQUS. Numerical simulations of triaxial test are performed using this program. The results obtained show a good agreement with the analytic solutions and the experimental data. (authors)
A finite element method for SSI time history calculations
International Nuclear Information System (INIS)
Ni, X.M.; Gantenbein, F.; Petit, M.
1989-01-01
The method which is proposed is based on a finite element modelisation for the soil and the structure and a time history calculation. It has been developed for plane and axisymmetric geometries. The principle of this method will be presented, then applications will be given, first to a linear calculation for which results will be compared to those obtained by standard methods. Then results for a non linear behavior will be described
High speed inviscid compressible flow by the finite element method
Zienkiewicz, O. C.; Loehner, R.; Morgan, K.
1984-01-01
The finite element method and an explicit time stepping algorithm which is based on Taylor-Galerkin schemes with an appropriate artificial viscosity is combined with an automatic mesh refinement process which is designed to produce accurate steady state solutions to problems of inviscid compressible flow in two dimensions. The results of two test problems are included which demonstrate the excellent performance characteristics of the proposed procedures.
Investigations on Actuator Dynamics through Theoretical and Finite Element Approach
Somashekhar S. Hiremath; M. Singaperumal
2010-01-01
This paper gives a new approach for modeling the fluid-structure interaction of servovalve component-actuator. The analyzed valve is a precision flow control valve-jet pipe electrohydraulic servovalve. The positioning of an actuator depends upon the flow rate from control ports, in turn depends on the spool position. Theoretical investigation is made for No-load condition and Load condition for an actuator. These are used in finite element modeling of an actuator. The fluid-structure-interact...
Finite element analysis of time-independent superconductivity
International Nuclear Information System (INIS)
Shuler, J.J.
1993-01-01
The focus of the thesis research is the development of electromagnetic (EM) finite elements based upon a generalized four-potential variational principle. The final goal of this research is to formulate, develop and validate finite element models that can accurately capture electromagnetic, thermal and material phase changes in a superconductor. The use of the four-potential variational principle allows for downstream coupling of electromagnetic fields with the thermal, mechanical and quantum effects exhibited by superconducting materials. The use to variational methods to model an electromagnetic system allows for a greater range of applications than just the superconducting problem. In fact, the four-potential variational principle can be used to solve a broader range of EM problems than any of the currently available formulations. It also reduces the number of independent variables from six to four while easily dealing with conductor/insulator interfaces. This methodology has been applied to a range of EM field problems. Seven problems are presented here. These applications show the power of the four-potential variational method, when augmented by Lagrange multiplier weighted constraint equations, to solve diverse EM field problems. All of the finite element models predict EM quantities exceptionally well and match the expected physical behavior. The results obtained with these finite element models display in previously unseen detail the physics of the superconducting charge carriers within the boundary layer of a Ginzburg-Landau superconductor. These results are compared to the physics of a low viscosity fluid problem. From this analogy, a physical argument is advanced about superconductors. This argument is that the small resistance that exists within a superconductor is similar in origin to the viscous effects of fluids and can be attributed to collisions that occur between moving and static charge carriers
Finite element computation of natural convection in enclosures
International Nuclear Information System (INIS)
Kushwaha, H.S.
1982-01-01
Compared to U-V-P-T formulation and stream-vorticity temperature formulation, penalty function formulation is simple and computationally competitive. Incremental New-Raphons method employed in this study is effective and efficient. From this study it is established that very fine mesh is not required for a low Rayleigh number considered in this study. The upwinding finite element may be necessary to avoid oscillations for higher Rayleigh numbers. (author)
Applications of finite element simulation in orthopedic and trauma surgery
Herrera, Antonio; Ibarz, Elena; Cegoñino, José; Lobo-Escolar, Antonio; Puértolas, Sergio; López, Enrique; Mateo, Jesús; Gracia, Luis
2012-01-01
Research in different areas of orthopedic and trauma surgery requires a methodology that allows both a more economic approach and the ability to reproduce different situations in an easy way. Simulation models have been introduced recently in bioengineering and could become an essential tool in the study of any physiological unity, regardless of its complexity. The main problem in modeling with finite elements simulation is to achieve an accurate reproduction of the anatomy and a perfect corr...
Finite Element Analysis of a Natural Fiber (Maize) Composite Beam
Bavan, D. Saravana; Kumar, G. C. Mohan
2013-01-01
Natural fiber composites are termed as biocomposites or green composites. These fibers are green, biodegradable, and recyclable and have good properties such as low density and low cost when compared to synthetic fibers. The present work is investigated on the finite element analysis of the natural fiber (maize) composite beam, processed by means of hand lay-up method. Composite beam material is composed of stalk-based fiber of maize and unsaturated polyester resin polymer as matrix with meth...
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
A verification procedure for MSC/NASTRAN Finite Element Models
Stockwell, Alan E.
1995-01-01
Finite Element Models (FEM's) are used in the design and analysis of aircraft to mathematically describe the airframe structure for such diverse tasks as flutter analysis and actively controlled landing gear design. FEM's are used to model the entire airplane as well as airframe components. The purpose of this document is to describe recommended methods for verifying the quality of the FEM's and to specify a step-by-step procedure for implementing the methods.
A code for obtaining temperature distribution by finite element method
International Nuclear Information System (INIS)
Bloch, M.
1984-01-01
The ELEFIB Fortran language computer code using finite element method for calculating temperature distribution of linear and two dimensional problems, in permanent region or in the transient phase of heat transfer, is presented. The formulation of equations uses the Galerkin method. Some examples are shown and the results are compared with other papers. The comparative evaluation shows that the elaborated code gives good values. (M.C.K.) [pt
Progress in Finite Element Modeling of the Lower Extremities
2015-06-01
an assembly architecture that is currently under development. 15. SUBJECT TERMS lower extremities, FEM , accelerative loading, biological...is on lower-leg injuries due to an underbody blast event beneath a vehicle. During such an event, the explosive gases and soil impart momentum to the...parsed by an external finite element method ( FEM ) solver. The program is written in C++ and heavily makes use of operator overloading, function
Convergence of a residual based artificial viscosity finite element method
Nazarov, Murtazo
2013-02-01
We present a residual based artificial viscosity finite element method to solve conservation laws. The Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We prove convergence of the method, applied to a scalar conservation law in two space dimensions, toward an unique entropy solution for implicit time stepping schemes. © 2012 Elsevier B.V. All rights reserved.
Piezoelectric theory for finite element analysis of ultrasonic motors
Energy Technology Data Exchange (ETDEWEB)
Emery, J.D.; Mentesana, C.P.
1997-06-01
The authors present the fundamental equations of piezoelectricity and references. They show how a second form of the equations and a second set of coefficients can be found, through inversions involving the elasticity tensor. They show how to compute the clamped permittivity matrix from the unclamped matrix. The authors list the program pzansys.ftn and present examples of its use. This program does the conversions and calculations needed by the finite element program ANSYS.
Building Finite Element Models to Investigate Zebrafish Jaw Biomechanics.
Brunt, Lucy H; Roddy, Karen A; Rayfield, Emily J; Hammond, Chrissy L
2016-12-03
Skeletal morphogenesis occurs through tightly regulated cell behaviors during development; many cell types alter their behavior in response to mechanical strain. Skeletal joints are subjected to dynamic mechanical loading. Finite element analysis (FEA) is a computational method, frequently used in engineering that can predict how a material or structure will respond to mechanical input. By dividing a whole system (in this case the zebrafish jaw skeleton) into a mesh of smaller 'finite elements', FEA can be used to calculate the mechanical response of the structure to external loads. The results can be visualized in many ways including as a 'heat map' showing the position of maximum and minimum principal strains (a positive principal strain indicates tension while a negative indicates compression. The maximum and minimum refer the largest and smallest strain). These can be used to identify which regions of the jaw and therefore which cells are likely to be under particularly high tensional or compressional loads during jaw movement and can therefore be used to identify relationships between mechanical strain and cell behavior. This protocol describes the steps to generate Finite Element models from confocal image data on the musculoskeletal system, using the zebrafish lower jaw as a practical example. The protocol leads the reader through a series of steps: 1) staining of the musculoskeletal components, 2) imaging the musculoskeletal components, 3) building a 3 dimensional (3D) surface, 4) generating a mesh of Finite Elements, 5) solving the FEA and finally 6) validating the results by comparison to real displacements seen in movements of the fish jaw.
Finite elements for partial differential equations: An introductory survey
International Nuclear Information System (INIS)
Succi, S.
1988-03-01
After presentation of the basic ideas behind the theory of the Finite Element Method, the application of the method to three equations of particular interest in Physics and Engineering is discussed in some detail, namely, a one-dimensional Sturm-Liouville problem, a two-dimensional linear Fokker-Planck equation and a two-dimensional nonlinear Navier-Stokes equation. 6 refs, 8 figs
Wave Scattering in Heterogeneous Media using the Finite Element Method
2016-10-21
C.P. Vendhan (2014) Rigid-object water- entry impact dynamics: finite-element/ smoothed particle hydrodynamics modeling and experimental validation, J...domain. Time harmonic FSI problems have an interesting feature namely, the hydrodynamic /acoustic problem can be solved first for each of the assumed...assumed to be inviscid. For the same reason, acoustic/ hydrodynamic pressure p is the only load acting on the structure at the fluid-solid interface
Imposing orthogonality to hierarchic higher-order finite elements
Czech Academy of Sciences Publication Activity Database
Šolín, P.; Vejchodský, Tomáš; Zítka, M.; Ávila, F.
2007-01-01
Roč. 76, 1-3 (2007), s. 211-217 ISSN 0378-4754 R&D Projects: GA ČR GP201/04/P021 Institutional research plan: CEZ:AV0Z10190503 Keywords : optimal shape functions * energetic inner product * Laplace equation * symmetric linear elliptic problems * numerical experiments * hp-finite element method Subject RIV: BA - General Mathematics Impact factor: 0.738, year: 2007
Finite groups with three conjugacy class sizes of some elements
Indian Academy of Sciences (India)
Abstract. Let G be a finite group. We prove as follows: Let G be a p-solvable group for a fixed prime p. If the conjugacy class sizes of all elements of primary and biprimary orders of G are {1, pa, n} with a and n two positive integers and (p, n) = 1, then G is p-nilpotent or G has abelian Sylow p-subgroups. Keywords. Conjugacy ...
Rigorous characterization of photonic devices by finite element method
Rahman, B. M. A.; Kejalakshmy, N.
2015-01-01
A review on the characterisations of photonics devices by using the frequency domain modal solution, junction analysis and beam propagation methods and additionally time-domain approach, but all based on the numerically efficient finite element method is presented. Numerically simulated results for various photonic devices such as uniform optical waveguides, photonic crystal fibres, high-speed optical modulators, spot-size converters, compact power splitters, metalclad terahertz waveguides, photonic crystals and nonlinear acousto-optical interactions in optical waveguide are presented.
Finite Element Analysis Of Reasonable Foundation For Supporting Silo's Tower
Nurdin, Sukiman
2011-01-01
The limitation of soil data due to poor soil investigation process is a common problem in civil engineering project. The finite element method was used to analyse the compatibility of foundation to support silos in Liverpool Docks. Both shallow foundation and pile foundation were considered. The results of the analyses are presented by comparing analytical and numerical solution. Parametric study was considered for each case. There are different results for two types of shallow foundation tha...
A finite element method for flow problems in blast loading
International Nuclear Information System (INIS)
Forestier, A.; Lepareux, M.
1984-06-01
This paper presents a numerical method which describes fast dynamic problems in flow transient situations as in nuclear plants. A finite element formulation has been chosen; it is described by a preprocessor in CASTEM system: GIBI code. For these typical flow problems, an A.L.E. formulation for physical equations is used. So, some applications are presented: the well known problem of shock tube, the same one in 2D case and a last application to hydrogen detonation
Three dimensional mathematical model of tooth for finite element analysis
Directory of Open Access Journals (Sweden)
Puškar Tatjana
2010-01-01
Full Text Available Introduction. The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects in programmes for solid modeling. Objective. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. Methods. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analyzing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body into simple geometric bodies (cylinder, cone, pyramid,.... Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Results. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Conclusion Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.
[Three dimensional mathematical model of tooth for finite element analysis].
Puskar, Tatjana; Vasiljević, Darko; Marković, Dubravka; Jevremović, Danimir; Pantelić, Dejan; Savić-Sević, Svetlana; Murić, Branka
2010-01-01
The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects) in programmes for solid modeling. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analysing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body) into simple geometric bodies (cylinder, cone, pyramid,...). Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.
OPTIMIZATION OF EQUIPMENT "RAKECUP TYPE " USING FINITE ELEMENT ANALYSIS
Directory of Open Access Journals (Sweden)
ŞOMOIAG Adrian
2011-06-01
Full Text Available It has been designed a new solution technological constructive of navvy equipment like rake cup attachable to the excavator arm. Cup shape and size were determined after repeated attempts for a specific cup, with the technological requirements required by the designer, the attempts being made in AutoCAD, 2D - 3D, until the desired results, based on the calculations. Finally, the structure was optimized to load applications from the cup, using finite element analysis method.
Thermohydraulic analysis in pipelines using the finite element method
International Nuclear Information System (INIS)
Costa, L.E.; Idelsohn, S.R.
1984-01-01
The Finite Element Method (FEM) is employed for the numerical solution of fluid flow problems with combined heat transfer mechanisms. Boussinesq approximations are used for the solution of the governing equations. The application of the FEM leads to a set of simultaneous nonlinear equations. The development of the method, for the solution of bidimensional and axisymmetric problems, is presented. Examples of fluid flow in pipes, including natural and forced convection, are solved with the proposed method and discussed in the paper. (Author) [pt
Evaluation of a Nonlinear Finite Element Program - ABAQUS.
1983-03-15
review of detailed program architecture . Instead, discussion is focused on the overall coding structure and its data base design. This is in contrast to...conditions, etc.; material model information; and plotting of undeformed geometry. Hisotry Input-These include data related to analysis procedure...efficiency of a finite element software is affected by several factors. These include: 01 i) Program architecture and coding style ii) Numerical
Free vibration analysis of dragonfly wings using finite element method
M Darvizeh; A Darvizeh; H Rajabi; A Rezaei
2016-01-01
In the present work, investigations on the microstructure and mechanicalproperties of the dragonfly wing are carried out and numerical modelingbased on Finite Element Method (FEM) is developed to predict Flightcharacteristics of dragonfly wings. Vibrational behavior of wings typestructures is immensely important in analysis, design and manufacturing ofsimilar engineering structures. For this purpose natural frequencies andmode shapes are calculated. In addition, the kind of deformation in eac...
Finite element analysis of the cyclic indentation of bilayer enamel
Jia, Yunfei; Xuan, Fu-zhen; Chen, Xiaoping; Yang, Fuqian
2014-04-01
Tooth enamel is often subjected to repeated contact and often experiences contact deformation in daily life. The mechanical strength of the enamel determines the biofunctionality of the tooth. Considering the variation of the rod arrangement in outer and inner enamel, we approximate enamel as a bilayer structure and perform finite element analysis of the cyclic indentation of the bilayer structure, to mimic the repeated contact of enamel during mastication. The dynamic deformation behaviour of both the inner enamel and the bilayer enamel is examined. The material parameters of the inner and outer enamel used in the analysis are obtained by fitting the finite element results with the experimental nanoindentation results. The penetration depth per cycle at the quasi-steady state is used to describe the depth propagation speed, which exhibits a two-stage power-law dependence on the maximum indentation load and the amplitude of the cyclic load, respectively. The continuous penetration of the indenter reflects the propagation of the plastic zone during cyclic indentation, which is related to the energy dissipation. The outer enamel serves as a protective layer due to its great resistance to contact deformation in comparison to the inner enamel. The larger equivalent plastic strain and lower stresses in the inner enamel during cyclic indentation, as calculated from the finite element analysis, indicate better crack/fracture resistance of the inner enamel.
Discontinuous finite element treatment of duct problems in transport calculations
International Nuclear Information System (INIS)
Mirza, A. M.; Qamar, S.
1998-01-01
A discontinuous finite element approach is presented to solve the even-parity Boltzmann transport equation for duct problems. Presence of ducts in a system results in the streaming of particles and hence requires the employment of higher order angular approximations to model the angular flux. Conventional schemes based on the use of continuous trial functions require the same order of angular approximations to be used everywhere in the system, resulting in wastage of computational resources. Numerical investigations for the test problems presented in this paper indicate that the discontinuous finite elements eliminate the above problems and leads to computationally efficient and economical methods. They are also found to be more suitable for treating the sharp changes in the angular flux at duct-observer interfaces. The new approach provides a single-pass alternate to extrapolation and interactive schemes which need multiple passes of the solution strategy to acquire convergence. The method has been tested with the help of two case studies, namely straight and dog-leg duct problems. All results have been verified against those obtained from Monte Carlo simulations and K/sup +/ continuous finite element method. (author)
Documentation of SPECTROM-55: A finite element thermohydrogeological analysis program
International Nuclear Information System (INIS)
Osnes, J.D.; Ratigan, J.L.; Loken, M.C.; Parrish, D.K.
1989-01-01
SPECTROM-55 is a finite element computer program for analyses of coupled heat and fluid transfer through fully saturated porous media. The code is part of the SPECTROM (Special Purpose Engineering Codes for Thermal/ROck Mechanics) series of special purpose finite element programs, that address the many unique rock mechanics problems resulting from storage of radioactive waste in geologic formations. This document presents the theoretical basis for the mathematical model, the finite element formulation of the problem, and a description of the input data for the program along with details about program support and continuing documentation. The program is especially suited for analyses of the regional hydrogeology in the vicinity of a heat-generating nuclear waste repository. These applications typically involved forced and free convection in a ground-water flow system. The program provides transient or steady-state temperatures, pressures, and fluid velocities resulting from the application of a variety of initial and boundary conditions to bodies with complicated shapes. The boundary conditions include constant heat and fluid fluxes, convective heat transfer, constant temperature, and constant pressure. Initial temperatures and pressures can be specified. Composite systems of anisotropic materials, such as geologic strata, can be defined in either planar or axisymmetric configurations. Constant or varying volumetric heat generation, such as decaying heat generation from radioactive waste, can be specified
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.
Finite element modeling of TFTR poloidal field coils
International Nuclear Information System (INIS)
Baumgartner, J.A.; O'Toole, J.A.
1986-01-01
The Tokamak Fusion Test Reactor (TFTR) Poloidal Field (PF) coils were originally analyzed to TFTR design conditions. The coils have been reanalyzed by PPPL and Grumman to determine operating limits under as-built conditions. Critical stress levels, based upon data obtained from the reanalysis of each PF coil, are needed for input to the TFTR simulation code algorithms. The primary objective regarding structural integrity has been to ascertain the magnitude and location of critical internal stresses in each PF coil due to various combinations of electromagnetic and thermally induced loads. For each PF coil, a global finite element model (FEM) of a coil sector is being analyzed to obtain the basic coil internal loads and displacements. Subsequent fine mesh local models of the coil lead stem and lead spur regions produce the magnitudes and locations of peak stresses. Each copper turn and its surrounding insulation are modeled using solid finite elements. The corresponding electromagnetic and thermal analyses are similarly modeled. A series of test beams were developed to determine the best combination of MSC/NASTRAN-type finite elements for use in PF coil analysis. The results of this analysis compare favorably with those obtained by the earlier analysis which was limited in scope
Statistical osteoporosis models using composite finite elements: a parameter study.
Wolfram, Uwe; Schwen, Lars Ole; Simon, Ulrich; Rumpf, Martin; Wilke, Hans-Joachim
2009-09-18
Osteoporosis is a widely spread disease with severe consequences for patients and high costs for health care systems. The disease is characterised by a loss of bone mass which induces a loss of mechanical performance and structural integrity. It was found that transverse trabeculae are thinned and perforated while vertical trabeculae stay intact. For understanding these phenomena and the mechanisms leading to fractures of trabecular bone due to osteoporosis, numerous researchers employ micro-finite element models. To avoid disadvantages in setting up classical finite element models, composite finite elements (CFE) can be used. The aim of the study is to test the potential of CFE. For that, a parameter study on numerical lattice samples with statistically simulated, simplified osteoporosis is performed. These samples are subjected to compression and shear loading. Results show that the biggest drop of compressive stiffness is reached for transverse isotropic structures losing 32% of the trabeculae (minus 89.8% stiffness). The biggest drop in shear stiffness is found for an isotropic structure also losing 32% of the trabeculae (minus 67.3% stiffness). The study indicates that losing trabeculae leads to a worse drop of macroscopic stiffness than thinning of trabeculae. The results further demonstrate the advantages of CFEs for simulating micro-structured samples.
Finite Element Analysis of a Natural Fiber (Maize Composite Beam
Directory of Open Access Journals (Sweden)
D. Saravana Bavan
2013-01-01
Full Text Available Natural fiber composites are termed as biocomposites or green composites. These fibers are green, biodegradable, and recyclable and have good properties such as low density and low cost when compared to synthetic fibers. The present work is investigated on the finite element analysis of the natural fiber (maize composite beam, processed by means of hand lay-up method. Composite beam material is composed of stalk-based fiber of maize and unsaturated polyester resin polymer as matrix with methyl ethyl ketone peroxide (MEKP as a catalyst and Cobalt Octoate as a promoter. The material was modeled and resembled as a structural beam using suitable assumption and analyzed by means of finite element method using ANSYS software for determining the deflection and stress properties. Morphological analysis and X-ray diffraction (XRD analysis for the fiber were examined by means of scanning electron microscope (SEM and X-ray diffractometer. From the results, it has been found that the finite element values are acceptable with proper assumptions, and the prepared natural fiber composite beam material can be used for structural engineering applications.
TAURUS, Post-processor of 3-D Finite Elements Plots
International Nuclear Information System (INIS)
Brown, B.E.; Hallquist, J.O.; Kennedy, T.
2002-01-01
Description of program or function: TAURUS reads the binary plot files generated by the LLNL three-dimensional finite element analysis codes, NIKE3D (NESC 9725), DYNA3D (NESC 9909), TACO3D (NESC 9838), TOPAZ3D (NESC9599) and GEMINI and plots contours, time histories, and deformed shapes. Contours of a large number of quantities may be plotted on meshes consisting of plate, shell, and solid type elements. TAURUS can compute a variety of strain measures, reaction forces along constrained boundaries, and momentum. TAURUS has three phases: initialization, geometry display with contouring, and time history processing
Reliability-Based Shape Optimization using Stochastic Finite Element Methods
DEFF Research Database (Denmark)
Enevoldsen, Ib; Sørensen, John Dalsgaard; Sigurdsson, G.
1991-01-01
stochastic fields (e.g. loads and material parameters such as Young's modulus and the Poisson ratio). In this case stochastic finite element techniques combined with FORM analysis can be used to obtain measures of the reliability of the structural systems, see Der Kiureghian & Ke (6) and Liu & Der Kiureghian...... (7). In this paper a reliability-based shape optimization problem is formulated with the total expected cost as objective function and some requirements for the reliability measures (element or systems reliability measures) as constraints, see section 2. As design variables sizing variables...
Analysis of Piezoelectric Solids using Finite Element Method
Aslam, Mohammed; Nagarajan, Praveen; Remanan, Mini
2018-03-01
Piezoelectric materials are extensively used in smart structures as sensors and actuators. In this paper, static analysis of three piezoelectric solids is done using general-purpose finite element software, Abaqus. The simulation results from Abaqus are compared with the results obtained using numerical methods like Boundary Element Method (BEM) and meshless point collocation method (PCM). The BEM and PCM are cumbersome for complex shape and complicated boundary conditions. This paper shows that the software Abaqus can be used to solve the governing equations of piezoelectric solids in a much simpler and faster way than the BEM and PCM.
Periodic Boundary Conditions in the ALEGRA Finite Element Code
International Nuclear Information System (INIS)
Aidun, John B.; Robinson, Allen C.; Weatherby, Joe R.
1999-01-01
This document describes the implementation of periodic boundary conditions in the ALEGRA finite element code. ALEGRA is an arbitrary Lagrangian-Eulerian multi-physics code with both explicit and implicit numerical algorithms. The periodic boundary implementation requires a consistent set of boundary input sets which are used to describe virtual periodic regions. The implementation is noninvasive to the majority of the ALEGRA coding and is based on the distributed memory parallel framework in ALEGRA. The technique involves extending the ghost element concept for interprocessor boundary communications in ALEGRA to additionally support on- and off-processor periodic boundary communications. The user interface, algorithmic details and sample computations are given
Calibration of a finite element composite delamination model by experiments
DEFF Research Database (Denmark)
Gaiotti, M.; Rizzo, C.M.; Branner, Kim
2013-01-01
This paper deals with the mechanical behavior under in plane compressive loading of thick and mostly unidirectional glass fiber composite plates made with an initial embedded delamination. The delamination is rectangular in shape, causing the separation of the central part of the plate into two...... distinct sub-laminates. The work focuses on experimental validation of a finite element model built using the 9-noded MITC9 shell elements, which prevent locking effects and aiming to capture the highly non linear buckling features involved in the problem. The geometry has been numerically defined...
Finite volume and finite element methods applied to 3D laminar and turbulent channel flows
Louda, Petr; Sváček, Petr; Kozel, Karel; Příhoda, Jaromír
2014-12-01
The work deals with numerical simulations of incompressible flow in channels with rectangular cross section. The rectangular cross section itself leads to development of various secondary flow patterns, where accuracy of simulation is influenced by numerical viscosity of the scheme and by turbulence modeling. In this work some developments of stabilized finite element method are presented. Its results are compared with those of an implicit finite volume method also described, in laminar and turbulent flows. It is shown that numerical viscosity can cause errors of same magnitude as different turbulence models. The finite volume method is also applied to 3D turbulent flow around backward facing step and good agreement with 3D experimental results is obtained.
Finite volume and finite element methods applied to 3D laminar and turbulent channel flows
Energy Technology Data Exchange (ETDEWEB)
Louda, Petr; Příhoda, Jaromír [Institute of Thermomechanics, Czech Academy of Sciences, Prague (Czech Republic); Sváček, Petr; Kozel, Karel [Czech Technical University in Prague, Fac. of Mechanical Engineering (Czech Republic)
2014-12-10
The work deals with numerical simulations of incompressible flow in channels with rectangular cross section. The rectangular cross section itself leads to development of various secondary flow patterns, where accuracy of simulation is influenced by numerical viscosity of the scheme and by turbulence modeling. In this work some developments of stabilized finite element method are presented. Its results are compared with those of an implicit finite volume method also described, in laminar and turbulent flows. It is shown that numerical viscosity can cause errors of same magnitude as different turbulence models. The finite volume method is also applied to 3D turbulent flow around backward facing step and good agreement with 3D experimental results is obtained.
Flow Over Backward Facing Step with Inclined Wall Solved by Finite Volume and Finite Element Method
Louda, Petr; Sváček, Petr; Kozel, Karel; Příhoda, Jaromír
2010-09-01
The work deals with numerical solution of 2D incompressible flow over backward facing step. The inclination angles of the upper wall of the channel were chosen as in measurements by Driver and Seegmiller [1]. Two numerical methods are considered. One is finite volume method, the other one is finite element method. Turbulence is modeled using two-equation turbulence models of k-ω type. The influence of outlet boundary condition is discussed and do-nothing-like condition found suitable also for finite volume method. The comparison of both methods is presented for laminar as well as turbulent cases, including experimental results. The differences of the results are studied using one turbulence model and both numerical methods or one method and more turbulence models. It is found that sensitivity of the computation to these circumstances increases for higher inclination angles (diffuser flow).
Finite element analysis of magnetically induced vibrations of conductive plates
International Nuclear Information System (INIS)
Lee, J.S.; Prevost, J.H.; Lee, P.C.Y.
1990-01-01
The coupling effect between the electromagnetic field and mechanical response of a conducting structure is of importance in high energy devices such as fusion reactors. This paper is concerned with numerical modeling of the dynamic field-structure interaction. After the theory of magneto-elasticity for nonferrous conductors is reviewed briefly, a finite element numerical model for fully coupled analysis of the field-structure interaction in conductor plates is developed and corroborated numerically. In developing coupled magneto-plate elements the magnetic field vector rather than the potentials is employed as the primary unknown in electromagnetic field calculation and attention is paid to the performance of the structural elements as well as the electromagnetic elements. Thus the resulting continuum-based, consistent finite element model requires only Cdeg-continuity both in electromagnetic aspect and mechanical aspect. For time integration of the coupled nonlinear system of equations, a partitioned analysis scheme is developed and its numerical implementation details are also presented. Then the proposed numerical model is applied to perform fully coupled analysis of the magnetically induced vibrations of the conducting plates in transient magnetic fields. The Fusion Electromagnetic Induction Experiments (FELIX) are modeled and the numerical results are shown to be in ver good agreement with the measured field data. (orig.)
Finite element analysis of FRP-strengthened RC beams
Directory of Open Access Journals (Sweden)
Teeraphot Supaviriyakit
2004-05-01
Full Text Available This paper presents a non-linear finite element analysis of reinforced concrete beam strengthened with externally bonded FRP plates. The finite element modeling of FRP-strengthened beams is demonstrated. Concrete and reinforcing bars are modeled together as 8-node isoparametric 2D RC element. The FRP plate is modeled as 8-node isoparametric 2D elastic element. The glue is modeled as perfect compatibility by directly connecting the nodes of FRP with those of concrete since there is no failure at the glue layer. The key to the analysis is the correct material models of concrete, steel and FRP. Cracks and steel bars are modeled as smeared over the entire element. Stress-strain properties of cracked concrete consist of tensile stress model normal to crack, compressive stress model parallel to crack and shear stress model tangential to crack. Stressstrain property of reinforcement is assumed to be elastic-hardening to account for the bond between concrete and steel bars. FRP is modeled as elastic-brittle material. From the analysis, it is found that FEM can predict the load-displacement relation, ultimate load and failure mode of the beam correctly. It can also capture the cracking process for both shear-flexural peeling and end peeling modes similar to the experiment.
Application of finite element numerical technique to nuclear reactor geometries
International Nuclear Information System (INIS)
Rouai, N. M.
1995-01-01
Determination of the temperature distribution in nuclear elements is of utmost importance to ensure that the temperature stays within safe limits during reactor operation. This paper discusses the use of Finite element numerical technique (FE) for the solution of the two dimensional heat conduction equation in geometries related to nuclear reactor cores. The FE solution stats with variational calculus which considers transforming the heat conduction equation into an integral equation I(O) and seeks a function that minimizes this integral and hence gives the solution to the heat conduction equation. In this paper FE theory as applied to heat conduction is briefly outlined and a 2-D program is used to apply the theory to simple shapes and to two gas cooled reactor fuel elements. Good results are obtained for both cases with reasonable number of elements. 7 figs
International Nuclear Information System (INIS)
Ackroyd, R.T.
1987-01-01
A least squares principle is described which uses a penalty function treatment of boundary and interface conditions. Appropriate choices of the trial functions and vectors employed in a dual representation of an approximate solution established complementary principles for the diffusion equation. A geometrical interpretation of the principles provides weighted residual methods for diffusion theory, thus establishing a unification of least squares, variational and weighted residual methods. The complementary principles are used with either a trial function for the flux or a trial vector for the current to establish for regular meshes a connection between finite element, finite difference and nodal methods, which can be exact if the mesh pitches are chosen appropriately. Whereas the coefficients in the usual nodal equations have to be determined iteratively, those derived via the complementary principles are given explicitly in terms of the data. For the further development of the connection between finite element, finite difference and nodal methods, some hybrid variational methods are described which employ both a trial function and a trial vector. (author)
Generalization of mixed multiscale finite element methods with applications
Energy Technology Data Exchange (ETDEWEB)
Lee, C S [Texas A & M Univ., College Station, TX (United States)
2016-08-01
Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixed multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii
Finite element analysis of inclined nozzle-plate junctions
International Nuclear Information System (INIS)
Dixit, K.B.; Seth, V.K.; Krishnan, A.; Ramamurthy, T.S.; Dattaguru, B.; Rao, A.K.
1979-01-01
Estimation of stress concentration at nozzle to plate or shell junctions is a significant problem in the stress analysis of nuclear reactors. The topic is a subject matter of extensive investigations and earlier considerable success has been reported on analysis for the cases when the nozzle is perpendicular to the plate or is radial to the shell. Analytical methods for the estimation of stress concentrations for the practical situations when the intersecting nozzle is inclined to the plate or is non-radial to the shell is rather scanty. Specific complications arise in dealing with the junction region when the nozzle with circular cross-section meets the non-circular cut-out on the plate or shell. In this paper a finite element analysis is developed for inclined nozzles and results are presented for nozzle-plate junctions. A method of analysis is developed with a view to achieving simultaneously accuracy of results and simplicity in the choice of elements and their connectivity. The circular nozzle is treated by axisymmetric conical shell elements. The nozzle portion in the region around the junction and the flat plate is dealt with by triangular flat shell elements. Special transition elements are developed for joining the flat shell elements with the axisymmetric elements under non-axisymmetric loading. A substructure method of analysis is adopted which achieves considerable economy in handling the structure and also conveniently combines the different types of elements in the structure. (orig.)
Quiza, Ramón; Davim, J Paulo
2012-01-01
Artificial intelligence (AI) techniques and the finite element method (FEM) are both powerful computing tools, which are extensively used for modeling and optimizing manufacturing processes. The combination of these tools has resulted in a new flexible and robust approach as several recent studies have shown. This book aims to review the work already done in this field as well as to expose the new possibilities and foreseen trends. The book is expected to be useful for postgraduate students and researchers, working in the area of modeling and optimization of manufacturing processes.
Bause, Markus; Radu, Florin A; Köcher, Uwe
2017-01-01
Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods in space for simulating transport processes have been demonstrated in a wide class of works. We consider a family of continuous Galerkin-Petrov time discretization schemes that is combined with a mixed finite element approximation of the spatial variables. The existence and uniqueness of the semidiscrete approximation and of the fully discrete solution are established. For this, the Banach-Nečas-Babuška theorem is applied in a non-standard way. Error estimates with explicit rates of convergence are proved for the scalar and vector-valued variable. An optimal order estimate in space and time is proved by duality techniques for the scalar variable. The convergence rates are analyzed and illustrated by numerical experiments, also on stochastically perturbed meshes.
Modeling Intracochlear Magnetic Stimulation: A Finite-Element Analysis.
Mukesh, S; Blake, D T; McKinnon, B J; Bhatti, P T
2017-08-01
This study models induced electric fields, and their gradient, produced by pulsatile current stimulation of submillimeter inductors for cochlear implantation. Using finite-element analysis, the lower chamber of the cochlea, scala tympani, is modeled as a cylindrical structure filled with perilymph bounded by tissue, bone, and cochlear neural elements. Single inductors as well as an array of inductors are modeled. The coil strength (~100 nH) and excitation parameters (peak current of 1-5 A, voltages of 16-20 V) are based on a formative feasibility study conducted by our group. In that study, intracochlear micromagnetic stimulation achieved auditory activation as measured through the auditory brainstem response in a feline model. With respect to the finite element simulations, axial symmetry of the inductor geometry is exploited to improve computation time. It is verified that the inductor coil orientation greatly affects the strength of the induced electric field and thereby the ability to affect the transmembrane potential of nearby neural elements. Furthermore, upon comparing an array of micro-inductors with a typical multi-site electrode array, magnetically excited arrays retain greater focus in terms of the gradient of induced electric fields. Once combined with further in vivo analysis, this modeling study may enable further exploration of the mechanism of magnetically induced, and focused neural stimulation.
Energy Technology Data Exchange (ETDEWEB)
Bochev, Pavel Blagoveston
2011-06-01
We develop a new formulation of the Control Volume Finite Element Method (CVFEM) with a multidimensional Scharfetter-Gummel (SG) upwinding for the drift-diffusion equations. The formulation uses standard nodal elements for the concentrations and expands the flux in terms of the lowest-order Nedelec H(curl; {Omega})-compatible finite element basis. The SG formula is applied to the edges of the elements to express the Nedelec element degree of freedom on this edge in terms of the nodal degrees of freedom associated with the endpoints of the edge. The resulting upwind flux incorporates the upwind effects from all edges and is defined at the interior of the element. This allows for accurate evaluation of integrals on the boundaries of the control volumes for arbitrary quadrilateral elements. The new formulation admits efficient implementation through a standard loop over the elements in the mesh followed by loops over the element nodes (associated with control volume fractions in the element) and element edges (associated with flux degrees of freedom). The quantities required for the SG formula can be precomputed and stored for each edge in the mesh for additional efficiency gains. For clarity the details are presented for two-dimensional quadrilateral grids. Extension to other element shapes and three dimensions is straightforward.
The Blended Finite Element Method for Multi-fluid Plasma Modeling
2016-07-01
Briefing Charts 3. DATES COVERED (From - To) 07 June 2016 - 01 July 2016 4. TITLE AND SUBTITLE The Blended Finite Element Method for Multi-fluid Plasma...BLENDED FINITE ELEMENT METHOD FOR MULTI-FLUID PLASMA MODELING Éder M. Sousa1, Uri Shumlak2 1ERC INC., IN-SPACE PROPULSION BRANCH (RQRS) AIR FORCE RESEARCH...MULTI-FLUID PLASMA MODEL 2 BLENDED FINITE ELEMENT METHOD Blended Finite Element Method Nodal Continuous Galerkin Modal Discontinuous Galerkin Model
Progress on hybrid finite element methods for scattering by bodies of revolution
Collins, Jeffery D.; Volakis, John L.
1992-01-01
Progress on the development and implementation of hybrid finite element methods for scattering by bodies of revolution are described. It was found that earlier finite element-boundary integral formulations suffered from convergence difficulties when applied to large and thin bodies of revolution. An alternative implementation is described where the finite element method is terminated with an absorbing termination boundary. In addition, an alternative finite element-boundary integral implementation is discussed for improving the convergence of the original code.
Finite element based inversion for time-harmonic electromagnetic problems
Schwarzbach, Christoph; Haber, Eldad
2013-05-01
In this paper we address the inverse problem and present some recent advances in numerical methods to recover the subsurface electrical conductivity from time-harmonic electromagnetic data. We rigorously formulate and discretize both the forward and the inverse problem in the finite element framework. To solve the forward problem, we derive a finite element discretization of the first-order system of Maxwell's equations in terms of the electric field and the magnetic induction. We show that our approach is equivalent to the standard discretization of the vector Helmholtz equation in terms of the electric field and that the discretization of magnetic induction of the same approximation order is hidden in the standard discretization. We implement the forward solver on unstructured tetrahedral meshes using edge elements. Unstructured meshes are not only capable of representing complex geometry. They can also reduce the overall problem size and, thus, the size of the system of linear equations arising from the forward problem such that direct methods for its solution using a sparse matrix factorization become feasible. The inverse problem is formulated as a regularized output least squares problem. We consider two regularization functions. First, we derive a smoothness regularizer using a primal-dual mixed finite element formulation which generalizes the standard Laplacian operator for a piecewise constant conductivity model on unstructured meshes. Secondly, we derive a total variation regularizer for the same class of models. For the choice of the regularization parameter we revisit the so-called dynamic regularization and compare it to a standard regularization scheme with fixed regularization parameter. The optimization problem is solved by the Gauss-Newton method which can be efficiently implemented using sparse matrix-vector operations and exploiting the sparse matrix factorization of the forward problem system matrix. A synthetic data example from marine
Electrostatic and magnetostatic numerical analysis using nodal and edge finite element
International Nuclear Information System (INIS)
Nascimento, Francisco Rogerio T. do; Jospin, Reinaldo Jacques
2013-01-01
The main objective of this work is to simulate electromagnetic fields using the Finite Element Method. Even in the easiest case of electrostatic and magnetostatic numerical simulation some problems appear when the nodal finite element is used. It is difficult to model vector fields with scalar functions mainly in non-homogeneous materials. With the aim to solve these problems two types of techniques are tried: the nodal elements and the edge finite element that ensure the continuity of tangential components. Some simple electromagnetic numerical analysis problems like waveguides, with homogeneous and non-homogeneous materials, are performed using first the nodal finite elements and then the edge finite elements. (author)
Electrical defibrillation optimization: An automated, iterative parallel finite-element approach
Energy Technology Data Exchange (ETDEWEB)
Hutchinson, S.A.; Shadid, J.N. [Sandia National Lab., Albuquerque, NM (United States); Ng, K.T. [New Mexico State Univ., Las Cruces, NM (United States); Nadeem, A. [Univ. of Pittsburgh, PA (United States)
1997-04-01
To date, optimization of electrode systems for electrical defibrillation has been limited to hand-selected electrode configurations. In this paper we present an automated approach which combines detailed, three-dimensional (3-D) finite element torso models with optimization techniques to provide a flexible analysis and design tool for electrical defibrillation optimization. Specifically, a parallel direct search (PDS) optimization technique is used with a representative objective function to find an electrode configuration which corresponds to the satisfaction of a postulated defibrillation criterion with a minimum amount of power and a low possibility of myocardium damage. For adequate representation of the thoracic inhomogeneities, 3-D finite-element torso models are used in the objective function computations. The CPU-intensive finite-element calculations required for the objective function evaluation have been implemented on a message-passing parallel computer in order to complete the optimization calculations in a timely manner. To illustrate the optimization procedure, it has been applied to a representative electrode configuration for transmyocardial defibrillation, namely the subcutaneous patch-right ventricular catheter (SP-RVC) system. Sensitivity of the optimal solutions to various tissue conductivities has been studied. 39 refs., 9 figs., 2 tabs.
Two-dimensional finite element neutron diffusion analysis using hierarchic shape functions
International Nuclear Information System (INIS)
Carpenter, D.C.
1997-01-01
Recent advances have been made in the use of p-type finite element method (FEM) for structural and fluid dynamics problems that hold promise for reactor physics problems. These advances include using hierarchic shape functions, element-by-element iterative solvers and more powerful mapping techniques. Use of the hierarchic shape functions allows greater flexibility and efficiency in implementing energy-dependent flux expansions and incorporating localized refinement of the solution space. The irregular matrices generated by the p-type FEM can be solved efficiently using element-by-element conjugate gradient iterative solvers. These solvers do not require storage of either the global or local stiffness matrices and can be highly vectorized. Mapping techniques based on blending function interpolation allow exact representation of curved boundaries using coarse element grids. These features were implemented in a developmental two-dimensional neutron diffusion program based on the use of hierarchic shape functions (FEM2DH). Several aspects in the effective use of p-type analysis were explored. Two choices of elemental preconditioning were examined--the proper selection of the polynomial shape functions and the proper number of functions to use. Of the five shape function polynomials tested, the integral Legendre functions were the most effective. The serendipity set of functions is preferable over the full tensor product set. Two global preconditioners were also examined--simple diagonal and incomplete Cholesky. The full effectiveness of the finite element methodology was demonstrated on a two-region, two-group cylindrical problem but solved in the x-y coordinate space, using a non-structured element grid. The exact, analytic eigenvalue solution was achieved with FEM2DH using various combinations of element grids and flux expansions
3D finite element simulations of high velocity projectile impact
Directory of Open Access Journals (Sweden)
Ožbolt Joško
2015-01-01
Full Text Available An explicit three-dimensional (3D finite element (FE code is developed for the simulation of high velocity impact and fragmentation events. The rate sensitive microplane material model, which accounts for large deformations and rate effects, is used as a constitutive law. In the code large deformation frictional contact is treated by forward incremental Lagrange multiplier method. To handle highly distorted and damaged elements the approach based on the element deletion is employed. The code is then used in 3D FE simulations of high velocity projectile impact. The results of the numerical simulations are evaluated and compared with experimental results. It is shown that it realistically predicts failure mode and exit velocities for different geometries of plain concrete slab. Moreover, the importance of some relevant parameters, such as contact friction, rate sensitivity, bulk viscosity and deletion criteria are addressed.
Acoustic Finite Element Calculations in the Time Domain
DEFF Research Database (Denmark)
Jensen, Morten Skaarup
The use of the finite element method (FEM) for making predictions for acoustic fields in the time domain is investigated. First, an introduction to FEM for acoustics is given. This includes a description of important present day algorithms and a derivation of FEM. The overall performance...... of these algorithms is then examined with particular emphasis on accuracy and computational costs. It is shown that the most important error is one that takes the form of a falsely predicted dispersion. The dispersion error can be reduced by using smaller elements and time steps, but this is very costly. Attempts...... and consequences of the dispersion error has been obtained. This led to a new method for determining the optimum element and time step size. The method is valuable because the present way of doing this is not theoretically well-founded....
SPLAI: Computational Finite Element Model for Sensor Networks
Directory of Open Access Journals (Sweden)
Ruzana Ishak
2006-01-01
Full Text Available Wireless sensor network refers to a group of sensors, linked by a wireless medium to perform distributed sensing task. The primary interest is their capability in monitoring the physical environment through the deployment of numerous tiny, intelligent, wireless networked sensor nodes. Our interest consists of a sensor network, which includes a few specialized nodes called processing elements that can perform some limited computational capabilities. In this paper, we propose a model called SPLAI that allows the network to compute a finite element problem where the processing elements are modeled as the nodes in the linear triangular approximation problem. Our model also considers the case of some failures of the sensors. A simulation model to visualize this network has been developed using C++ on the Windows environment.
Analysis of a non-standard mixed finite element method with applications to superconvergence
Brandts, J.H.
2009-01-01
We show that a non-standard mixed finite element method proposed by Barrios and Gatica in 2007, is a higher order perturbation of the least-squares mixed finite element method. Therefore, it is also superconvergent whenever the least-squares mixed finite element method is superconvergent.
Finite-element numerical modeling of atmospheric turbulent boundary layer
Lee, H. N.; Kao, S. K.
1979-01-01
A dynamic turbulent boundary-layer model in the neutral atmosphere is constructed, using a dynamic turbulent equation of the eddy viscosity coefficient for momentum derived from the relationship among the turbulent dissipation rate, the turbulent kinetic energy and the eddy viscosity coefficient, with aid of the turbulent second-order closure scheme. A finite-element technique was used for the numerical integration. In preliminary results, the behavior of the neutral planetary boundary layer agrees well with the available data and with the existing elaborate turbulent models, using a finite-difference scheme. The proposed dynamic formulation of the eddy viscosity coefficient for momentum is particularly attractive and can provide a viable alternative approach to study atmospheric turbulence, diffusion and air pollution.
Finite element method for neutron diffusion problems in hexagonal geometry
International Nuclear Information System (INIS)
Wei, T.Y.C.; Hansen, K.F.
1975-06-01
The use of the finite element method for solving two-dimensional static neutron diffusion problems in hexagonal reactor configurations is considered. It is investigated as a possible alternative to the low-order finite difference method. Various piecewise polynomial spaces are examined for their use in hexagonal problems. The central questions which arise in the design of these spaces are the degree of incompleteness permissible and the advantages of using a low-order space fine-mesh approach over that of a high-order space coarse-mesh one. There is also the question of the degree of smoothness required. Two schemes for the construction of spaces are described and a number of specific spaces, constructed with the questions outlined above in mind, are presented. They range from a complete non-Lagrangian, non-Hermite quadratic space to an incomplete ninth order space. Results are presented for two-dimensional problems typical of a small high temperature gas-cooled reactor. From the results it is concluded that the space used should at least include the complete linear one. Complete spaces are to be preferred to totally incomplete ones. Once function continuity is imposed any additional degree of smoothness is of secondary importance. For flux shapes typical of the small high temperature gas-cooled reactor the linear space fine-mesh alternative is to be preferred to the perturbation quadratic space coarse-mesh one and the low-order finite difference method is to be preferred over both finite element schemes
Improved inhomogeneous finite elements for fabric reinforced composite mechanics analysis
Foye, R. L.
1992-01-01
There is a need to do routine stress/failure analysis of fabric reinforced composite microstructures to provide additional confidence in critical applications and guide materials development. Conventional methods of 3-D stress analysis are time consuming to set up, run and interpret. A need exists for simpler methods of modeling these structures and analyzing the models. The principal difficulty is the discrete element mesh generation problem. Inhomogeneous finite elements are worth investigating for application to these problems because they eliminate the mesh generation problem. However, there are penalties associated with these elements. Their convergence rates can be slow compared to homogeneous elements. Also, there is no accepted method for obtaining detailed stresses in the constituent materials of each element. This paper shows that the convergence rate can be significantly improved by a simple device which substitutes homogeneous elements for the inhomogeneous ones. The device is shown to work well in simple one and two dimensional problems. However, demonstration of the application to more complex two and three dimensional problems remains to be done. Work is also progressing toward more realistic fabric microstructural geometries.
Shape Optimization of Unconstrained Viscoelastic Layers Using Continuum Finite Elements
Lumsdaine, A.; Scott, R. A.
1998-09-01
Of the many methods available for achieving effective vibration damping, adding viscoelastic lamina is a significant technique for vibration and reduction. Recently, the desire to apportion this material in a way that will take the greatest advantage of its dissipative characteristics has led to studies in optimization. Optimal design for viscoelastically damped laminated beams and plates undergoing harmonic excitation has been examined in the literature, both for constrained and unconstrained damping layers. However to the authors' knowledge, previous optimization studies have not used continuum based finite elements to model the structure, as is done here. The problem examined is the shape optimization of an unconstrained damping layer on an elastic structure, assuming a constant volume of damping material as a design constraint. The objective is to minimize the peak displacement. Several boundary conditions are examined for beam and plate type structures. The peak displacement and the loss factor of the optimized structure are compared with the uniform layer structure. Also, results obtained using realistic (frequency dependent) and constant viscoelastic material data are compared. The structures are modelled using continuum based elements in the ABAQUS Finite Element Code. The optimization code uses a Sequential Quadratic Programming algorithm. For most of the structures examined, order of magnitude improvement is seen as a result of optimizing the shape of the damping layer. Peak displacements are reduced by up to 98%. These results are quite robust, with the optimized damping layer achieving significantly better damping performance for a wide variety of cases examined.
Theoretical determination of nozzle admittances using a finite element method
Sigman, R. K.; Zinn, B. T.
1979-01-01
A finite element method (FEM) is used to predict the admittances of axisymmetric nozzles. The flow in the nozzle is assumed to be isentropic and the disturbances are assumed to be small so that linear analyses apply. An approximate two dimensional compressible flow model is used to describe the steady flow in the nozzle. The propagation of acoustic disturbances is governed by the complete linear acoustic wave equation. This partial differential wave equation is transformed to an integral equation using Galerkin's method and Green's theorem is applied so that the acoustic boundary conditions can be introduced through the boundary residuals. A two dimensional finite element method using linear triangular elements is used to solve the integral acoustic equation. A one dimensional FEM is used to solve the reduced nozzle acoustic equation developed by Crocco and the solution is used to verify the sufficiency of the boundary residual formation. It is shown that agreement between predicted values of the admittance and experimental data is quite good.
Numerical algorithms for finite element computations on arrays of microprocessors
Ortega, J. M.
1981-01-01
The development of a multicolored successive over relaxation (SOR) program for the finite element machine is discussed. The multicolored SOR method uses a generalization of the classical Red/Black grid point ordering for the SOR method. These multicolored orderings have the advantage of allowing the SOR method to be implemented as a Jacobi method, which is ideal for arrays of processors, but still enjoy the greater rate of convergence of the SOR method. The program solves a general second order self adjoint elliptic problem on a square region with Dirichlet boundary conditions, discretized by quadratic elements on triangular regions. For this general problem and discretization, six colors are necessary for the multicolored method to operate efficiently. The specific problem that was solved using the six color program was Poisson's equation; for Poisson's equation, three colors are necessary but six may be used. In general, the number of colors needed is a function of the differential equation, the region and boundary conditions, and the particular finite element used for the discretization.
A curved finite element for general thin shell structures
International Nuclear Information System (INIS)
Jones, R.F. Jr.
1978-01-01
This work describes the development of a curved quadrilateral shell finite element which demonstrates very good convergence properties. A general description is used in deriving the element so that it may be applied to any thin shell problem. The element is shown to be very efficient. It has a total of 36 degrees-of-freedom with 9 at each of the corners of the element. There are several distinct advantages that the element offers for practical applications. Most of the shell elements that have been presented in the past are limited to problems in which the coordinates on the shell surface are orthogonal. The element that is described in the paper is derived using a general description so that it may be applied to any thin shell problem including those in which the shell coordinates are not orthogonal. The degree-of-freedom at each of the four nodes are the three Cartesian displacements and their first derivatives with respect to the two surface coordinates. The imposition of boundary conditions is simplified since each of the degrees-of-freedom can be can be associated with a quantity which has a simple physical meaning. During the course of the derivation of the element, the strain displacement relationships are derived in a very simple manner consistent with Love's first approximation for thin shells. The derivation in the paper starts from basic principles and should help to shed some light on the proper form for the bending strain. Two primary contributions are presented in this work. The first is the presentation of a procedure for the development of a general quadrilateral shell element. The second is the simple derivation of the bending strain for the thin shells which apparently has not been presented previously. (Auth.)
Pak, Chan-Gi; Truong, Samson S.
2014-01-01
Small modeling errors in the finite element model will eventually induce errors in the structural flexibility and mass, thus propagating into unpredictable errors in the unsteady aerodynamics and the control law design. One of the primary objectives of Multi Utility Technology Test Bed, X-56A, aircraft is the flight demonstration of active flutter suppression, and therefore in this study, the identification of the primary and secondary modes for the structural model tuning based on the flutter analysis of X-56A. The ground vibration test validated structural dynamic finite element model of the X-56A is created in this study. The structural dynamic finite element model of the X-56A is improved using a model tuning tool. In this study, two different weight configurations of the X-56A have been improved in a single optimization run.
Tadepalli, Srinivas C; Erdemir, Ahmet; Cavanagh, Peter R
2011-08-11
Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation. Copyright © 2011. Published by Elsevier Ltd.
3-D finite element simulation for ultrasonic propagation in tooth.
Sun, Xiaoqing; Witzel, Erich A; Bian, Hongxin; Kang, Shaoying
2008-07-01
Ultrasonic testing of the tooth has been suggested as an alternative method of identifying dental pathology. Due to the complex geometry and low transmission efficiency of ultrasonic signals in tooth structures, it is difficult to establish one-to-one correspondence between ultrasonic behaviour and specific tooth pathologies both in vitro and in vivo. In order to facilitate ultrasonic diagnosis in dental applications, finite element modeling (FEM) was used to simulate ultrasonic wave propagation in teeth with several dental conditions. 3-D finite element tooth models were developed. The geometry of the tooth models was defined by 3-D images generated by scanning real tooth samples using an X-ray computerized tomography machine. Poro-elastic material was used to simulate the mechanical behaviour of the dentine. Numerical simulations of ultrasonic wave propagation were performed on the 3-D FEM models altered to mimic various dental conditions. The software ABAQUS was used as the calculator in the simulation. Excellent replication of ultrasonic behaviours by the FEM simulation was demonstrated through comparison of the simulation results with those of the actual ultrasonic testing on tooth specimens. Pathologies, such as caries, were also simulated on the finite element models. The unique influence of each dental condition on the patterns of ultrasonic waves propagating through the tooth (A-scan) was observed. Through FEM simulation, the influence of a particular dental pathology on ultrasonic wave pattern can be studied without the impact of other parameters. This will lead to a better understanding of how ultrasound could be applied to the diagnosis of pathology within teeth.
Generalized Potential Energy Finite Elements for Modeling Molecular Nanostructures.
Chatzieleftheriou, Stavros; Adendorff, Matthew R; Lagaros, Nikos D
2016-10-24
The potential energy of molecules and nanostructures is commonly calculated in the molecular mechanics formalism by superimposing bonded and nonbonded atomic energy terms, i.e. bonds between two atoms, bond angles involving three atoms, dihedral angles involving four atoms, nonbonded terms expressing the Coulomb and Lennard-Jones interactions, etc. In this work a new, generalized numerical simulation is presented for studying the mechanical behavior of three-dimensional nanostructures at the atomic scale. The energy gradient and Hessian matrix of such assemblies are usually computed numerically; a potential energy finite element model is proposed herein where these two components are expressed analytically. In particular, generalized finite elements are developed that express the interactions among atoms in a manner equivalent to that invoked in simulations performed based on the molecular dynamics method. Thus, the global tangent stiffness matrix for any nanostructure is formed as an assembly of the generalized finite elements and is directly equivalent to the Hessian matrix of the potential energy. The advantages of the proposed model are identified in terms of both accuracy and computational efficiency. In the case of popular force fields (e.g., CHARMM), the computation of the Hessian matrix by implementing the proposed method is of the same order as that of the gradient. This analysis can be used to minimize the potential energy of molecular systems under nodal loads in order to derive constitutive laws for molecular systems where the entropy and solvent effects are neglected and can be approximated as solids, such as double stranded DNA nanostructures. In this context, the sequence dependent stretch modulus for some typical base pairs step is calculated.
Directory of Open Access Journals (Sweden)
Shunde Yin
2018-03-01
Simulation of thermal fracturing during cold CO2 injection involves the coupled processes of heat transfer, mass transport, rock deforming as well as fracture propagation. To model such a complex coupled system, a fully coupled finite element framework for thermal fracturing simulation is presented. This framework is based on the theory of non-isothermal multiphase flow in fracturing porous media. It takes advantage of recent advances in stabilized finite element and extended finite element methods. The stabilized finite element method overcomes the numerical instability encountered when the traditional finite element method is used to solve the convection dominated heat transfer equation, while the extended finite element method overcomes the limitation with traditional finite element method that a model has to be remeshed when a fracture is initiated or propagating and fracturing paths have to be aligned with element boundaries.
An introduction to the mathematical theory of finite elements
Oden, J T
2011-01-01
This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations.J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and co
Applications of finite-element scaling analysis in primatology.
Richtsmeier, J T
1989-01-01
The study of biological shape in three dimensions using landmark data can now be accomplished using several alternative methods. This report focuses on the use of finite-element scaling analysis in primate craniofacial morphology. The method is particularly useful in its ability to localize the differences between forms, thereby indicating those loci that differ most between specimens. Several examples of this feature are provided from primatological research. Particulars of the methods are also discussed in an attempt to provide the reader with cautionary knowledge for prudent application of the method in future research.
Assessing performance and validating finite element simulations using probabilistic knowledge
Energy Technology Data Exchange (ETDEWEB)
Dolin, Ronald M.; Rodriguez, E. A. (Edward A.)
2002-01-01
Two probabilistic approaches for assessing performance are presented. The first approach assesses probability of failure by simultaneously modeling all likely events. The probability each event causes failure along with the event's likelihood of occurrence contribute to the overall probability of failure. The second assessment method is based on stochastic sampling using an influence diagram. Latin-hypercube sampling is used to stochastically assess events. The overall probability of failure is taken as the maximum probability of failure of all the events. The Likelihood of Occurrence simulation suggests failure does not occur while the Stochastic Sampling approach predicts failure. The Likelihood of Occurrence results are used to validate finite element predictions.
The Iris biometric feature segmentation using finite element method
Directory of Open Access Journals (Sweden)
David Ibitayo LANLEGE
2015-05-01
Full Text Available This manuscript presents a method for segmentation of iris images based on a deformable contour (active contour paradigm. The deformable contour is a novel approach in image segmentation. A type of active contour is the Snake. Snake is a parametric curve defined within the domain of the image. Snake properties are specified through a function called energy functional. This means they consist of packets of energy which expressed as partial Differential Equations. The partial Differential Equation is the controlling engine of the active contour since this project, the Finite Element Method (Standard Galerkin Method implementation for deformable model is presented.
Free vibration analysis of dragonfly wings using finite element method
Directory of Open Access Journals (Sweden)
M Darvizeh
2016-04-01
Full Text Available In the present work, investigations on the microstructure and mechanicalproperties of the dragonfly wing are carried out and numerical modelingbased on Finite Element Method (FEM is developed to predict Flightcharacteristics of dragonfly wings. Vibrational behavior of wings typestructures is immensely important in analysis, design and manufacturing ofsimilar engineering structures. For this purpose natural frequencies andmode shapes are calculated. In addition, the kind of deformation in eachmode shape evaluated and the ratio between numerical natural frequencyand experimental natural frequency presented as damping ratio. Theresults obtain from present method are in good agreement with sameexperimental methods.
Towards time domain finite element analysis of gravity gradient noise
International Nuclear Information System (INIS)
Beker, M G; Brand, J F J van den; Hennes, E; Rabeling, D S
2010-01-01
Gravity gradient noise generated by seismic displacements constitute a limiting factor for the sensitivity of ground based gravitational wave detectors at frequencies below 10 Hz. We present a finite element framework to calculate the soil response to various excitations. The accompanying gravity gradients as a result of the seismic displacement field can then be evaluated. The framework is first shown to accurately model seismic waves in homogenous media. Calculations of the gravity gradient noise are then shown to be in agreement with previous analytical results. Finally results of gravity gradient noise from a single pulse excitation of a homogenous medium are discussed.
Piezoelectric Analysis of Saw Sensor Using Finite Element Method
Directory of Open Access Journals (Sweden)
Vladimír KUTIŠ
2013-06-01
Full Text Available In this contribution modeling and simulation of surface acoustic waves (SAW sensor using finite element method will be presented. SAW sensor is made from piezoelectric GaN layer and SiC substrate. Two different analysis types are investigated - modal and transient. Both analyses are only 2D. The goal of modal analysis, is to determine the eigenfrequency of SAW, which is used in following transient analysis. In transient analysis, wave propagation in SAW sensor is investigated. Both analyses were performed using FEM code ANSYS.
[Finite Element Analysis of Intravascular Stent Based on ANSYS Software].
Shi, Gengqiang; Song, Xiaobing
2015-10-01
This paper adopted UG8.0 to bulid the stent and blood vessel models. The models were then imported into the finite element analysis software ANSYS. The simulation results of ANSYS software showed that after endothelial stent implantation, the velocity of the blood was slow and the fluctuation of velocity was small, which meant the flow was relatively stable. When blood flowed through the endothelial stent, the pressure gradually became smaller, and the range of the pressure was not wide. The endothelial shear stress basically unchanged. In general, it can be concluded that the endothelial stents have little impact on the flow of blood and can fully realize its function.
Nonlinear Finite Element Analysis of Pull-Out Test
DEFF Research Database (Denmark)
Saabye Ottesen, N
1981-01-01
A specific pull-out test used to determine in-situ concrete compressive strength is analyzed. This test consists of a steel disc that is extracted from the structure. The finite element analysis considers cracking as well as strain hardening and softening in the pre- and post-failure region......, respectively. The aim is to attain a clear insight into structural behavior. Special attention is given to the failure mode. Severe cracking occurs and the stress distribution is very inhomogeneous. However, large compressive forces run from the disc in a rather narrow band towards the support...
Finite element method for time-space-fractional Schrodinger equation
Directory of Open Access Journals (Sweden)
Xiaogang Zhu
2017-07-01
Full Text Available In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.
A finite element method for extended KdV equations
Directory of Open Access Journals (Sweden)
Karczewska Anna
2016-09-01
Full Text Available The finite element method (FEM is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov–Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.
Finite Element Modeling Techniques for Analysis of VIIP
Feola, Andrew J.; Raykin, J.; Gleason, R.; Mulugeta, Lealem; Myers, Jerry G.; Nelson, Emily S.; Samuels, Brian C.; Ethier, C. Ross
2015-01-01
Visual Impairment and Intracranial Pressure (VIIP) syndrome is a major health concern for long-duration space missions. Currently, it is thought that a cephalad fluid shift in microgravity causes elevated intracranial pressure (ICP) that is transmitted along the optic nerve sheath (ONS). We hypothesize that this in turn leads to alteration and remodeling of connective tissue in the posterior eye which impacts vision. Finite element (FE) analysis is a powerful tool for examining the effects of mechanical loads in complex geometries. Our goal is to build a FE analysis framework to understand the response of the lamina cribrosa and optic nerve head to elevations in ICP in VIIP.
Visualizing Higher Order Finite Elements: FY05 Yearly Report.
Energy Technology Data Exchange (ETDEWEB)
Thompson, David; Pebay, Philippe Pierre
2005-11-01
This report contains an algorithm for decomposing higher-order finite elementsinto regions appropriate for isosurfacing and proves the conditions under which thealgorithm will terminate. Finite elements are used to create piecewise polynomialapproximants to the solution of partial differential equations for which no analyticalsolution exists. These polynomials represent fields such as pressure, stress, and mo-mentim. In the past, these polynomials have been linear in each parametric coordinate.Each polynomial coefficient must be uniquely determined by a simulation, and thesecoefficients are called degrees of freedom. When there are not enough degrees of free-dom, simulations will typically fail to produce a valid approximation to the solution.Recent work has shown that increasing the number of degrees of freedom by increas-ing the order of the polynomial approximation (instead of increasing the number offinite elements, each of which has its own set of coefficients) can allow some typesof simulations to produce a valid approximation with many fewer degrees of freedomthan increasing the number of finite elements alone. However, once the simulation hasdetermined the values of all the coefficients in a higher-order approximant, tools donot exist for visual inspection of the solution.This report focuses on a technique for the visual inspection of higher-order finiteelement simulation results based on decomposing each finite element into simplicialregions where existing visualization algorithms such as isosurfacing will work. Therequirements of the isosurfacing algorithm are enumerated and related to the placeswhere the partial derivatives of the polynomial become zero. The original isosurfacingalgorithm is then applied to each of these regions in turn.3 AcknowledgementThe authors would like to thank David Day and Louis Romero for their insight into poly-nomial system solvers and the LDRD Senior Council for the opportunity to pursue thisresearch. The authors were
Evaluation of Concrete Cylinder Tests Using Finite Elements
DEFF Research Database (Denmark)
Saabye Ottosen, Niels
1984-01-01
Nonlinear axisymmetric finite element analyses are performed on the uniaxial compressive test of concrete cylinders. The models include thick steel loading plates, and cylinders with height‐to‐diameter ratios (h/d) ranging from 1‐3 are treated. A simple constitutive model of the concrete...... cylinders the strain softening is more pronounced along the surface of the cylinder middle, whereas longer cylinders exhibit a more uniform distribution of strain softening. The failure modes for force and displacement controlled tests are found to be similar. If long cylinders are to provide the true...
Beam section stiffness properties usig 3D finite elements
DEFF Research Database (Denmark)
Couturier, Philippe; Krenk, Steen; Høgsberg, Jan Becker
2013-01-01
The cross-section properties of a beam is characterized by a six by six stiffness matrix, relating the six generalized strains to the conjugate section forces. The problem is formulated as a single-layer finite element model of a slice of the beam, on which the six deformation modes are imposed v...... Lagrange multipliers. The Lagrange multipliers represent the constraining forces, and thus combine to form the cross-section stiffness matrix. The theory is illustrated by a simple isotropic cross-section....
Finite element analysis of the stiffness of fabric reinforced composites
Foye, R. L.
1992-01-01
The objective of this work is the prediction of all three dimensional elastic moduli of textile fabric reinforced composites. The analysis is general enough for use with complex reinforcing geometries and capable of subsequent improvements. It places no restrictions on fabric microgeometry except that the unit cell be determinate and rectangular. The unit cell is divided into rectangular subcells in which the reinforcing geometries are easier to define and analyze. The analysis, based on inhomogeneous finite elements, is applied to a variety of weave, braid, and knit reinforced composites. Some of these predictions are correlated to test data.
Finite element method for simulation of the semiconductor devices
International Nuclear Information System (INIS)
Zikatanov, L.T.; Kaschiev, M.S.
1991-01-01
An iterative method for solving the system of nonlinear equations of the drift-diffusion representation for the simulation of the semiconductor devices is worked out. The Petrov-Galerkin method is taken for the discretization of these equations using the bilinear finite elements. It is shown that the numerical scheme is a monotonous one and there are no oscillations of the solutions in the region of p-n transition. The numerical calculations of the simulation of one semiconductor device are presented. 13 refs.; 3 figs
A Dual Orthogonality Procedure for Nonlinear Finite Element Equations
DEFF Research Database (Denmark)
Krenk, S.; Hededal, O.
In the orthogonal residual procedure for solution of nonlinear finite element equations the load is adjusted in each equilibrium iteration to satisfy an orthogonality condition to the current displacement increment. It is here shown that the quasi-newton formulation of the orthogonal residual...... method consists of a simple one-term correction of the displacement subincrement, and that this correction leads to orthogonality between the corrected displacement subincrement and the current increment of the internal force vector, thus defining a dual orthogonality algorithm. It is demonstrated how...
Comparing finite elements and finite differences for developing diffusive models of glioma growth.
Roniotis, Alexandros; Marias, Kostas; Sakkalis, Vangelis; Stamatakos, Georgios; Zervakis, Michalis
2010-01-01
Glioma is the most aggressive type of brain tumor. Several mathematical models have been developed during the last two decades, towards simulating the mechanisms that govern the development of glioma. The most common models use the diffusion-reaction equation (DRE) for simulating the spatiotemporal variation of tumor cell concentration. The proposed diffusive models have mainly used finite differences (FDs) or finite elements (FEs) for the approximation of the solution of the partial differential DRE. This paper presents experimental results on the comparison of the FEs and FDs, especially focused on the glioma model case. It is studied how the different meshes of brain can affect computational consistency, simulation time and efficiency of the model. The experiments have been studied on a test case, for which there is a known algebraic expression of the solution. Thus, it is possible to calculate the error that the different models yield.
A stabilized finite element method for finite-strain three-field poroelasticity
Berger, Lorenz; Bordas, Rafel; Kay, David; Tavener, Simon
2017-07-01
We construct a stabilized finite-element method to compute flow and finite-strain deformations in an incompressible poroelastic medium. We employ a three-field mixed formulation to calculate displacement, fluid flux and pressure directly and introduce a Lagrange multiplier to enforce flux boundary conditions. We use a low order approximation, namely, continuous piecewise-linear approximation for the displacements and fluid flux, and piecewise-constant approximation for the pressure. This results in a simple matrix structure with low bandwidth. The method is stable in both the limiting cases of small and large permeability. Moreover, the discontinuous pressure space enables efficient approximation of steep gradients such as those occurring due to rapidly changing material coefficients or boundary conditions, both of which are commonly seen in physical and biological applications.
Finite element simulation of thermal, elastic and plastic phenomena in fuel elements
International Nuclear Information System (INIS)
Soba, Alejandro; Denis, Alicia C.
1999-01-01
Taking as starting point an irradiation experiment of the first Argentine MOX fuel prototype, performed at the HFR reactor of Petten, Holland, the deformation suffered by the fuel element materials during burning has been numerically studied. Analysis of the pellet-cladding interaction is made by the finite element method. The code determines the temperature distribution and analyzes elastic and creep deformations, taking into account the dependency of the physical parameters of the problem on temperature. (author)
Generalized mixed finite element method for 3D elasticity problems
Qing, Guanghui; Mao, Junhui; Liu, Yanhong
2017-06-01
Without applying any stable element techniques in the mixed methods, two simple generalized mixed element (GME) formulations were derived by combining the minimum potential energy principle and Hellinger-Reissner (H-R) variational principle. The main features of the GME formulations are that the common C0 -continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.
Efficient smoothed finite element time domain analysis for photonic devices.
Atia, Khaled S R; Heikal, A M; Obayya, S S A
2015-08-24
In this paper, a new finite element method (FEM) is proposed to analyse time domain wave propagation in photonic devices. Dissimilar to conventional FEM, efficient "inter-element" matrices are accurately formed through smoothing the field derivatives across element boundaries. In this sense, the new approach is termed "smoothed FEM" (SFETD). For time domain analysis, the propagation is made via the time domain beam propagation method (TD-BPM). Relying on first order elements, our suggested SFETD-BPM enjoys accuracy levels comparable to second-order conventional FEM; thanks to the element smoothing. The proposed method numerical performance is tested through applicating on analysis of a single mode slab waveguide, optical grating structure, and photonic crystal cavity. It is clearly demonstrated that our method is not only accurate but also more computationally efficient (far few run time, and memory requirements) than the conventional FEM approach. The SFETD-BPM is also extended to deal with the very challenging problem of dispersive materials. The material dispersion is smartly utilized to enhance the quality factor of photonic crystal cavity.
Finite-element model of the active organ of Corti
Elliott, Stephen J.; Baumgart, Johannes
2016-01-01
The cochlear amplifier that provides our hearing with its extraordinary sensitivity and selectivity is thought to be the result of an active biomechanical process within the sensory auditory organ, the organ of Corti. Although imaging techniques are developing rapidly, it is not currently possible, in a fully active cochlea, to obtain detailed measurements of the motion of individual elements within a cross section of the organ of Corti. This motion is predicted using a two-dimensional finite-element model. The various solid components are modelled using elastic elements, the outer hair cells (OHCs) as piezoelectric elements and the perilymph and endolymph as viscous and nearly incompressible fluid elements. The model is validated by comparison with existing measurements of the motions within the passive organ of Corti, calculated when it is driven either acoustically, by the fluid pressure or electrically, by excitation of the OHCs. The transverse basilar membrane (BM) motion and the shearing motion between the tectorial membrane and the reticular lamina are calculated for these two excitation modes. The fully active response of the BM to acoustic excitation is predicted using a linear superposition of the calculated responses and an assumed frequency response for the OHC feedback. PMID:26888950
Stress and Deformation Analysis in Base Isolation Elements Using the Finite Element Method
Directory of Open Access Journals (Sweden)
Claudiu Iavornic
2011-01-01
Full Text Available In Modern tools as Finite Element Method can be used to study the behavior of elastomeric isolation systems. The simulation results obtained in this way provide a large series of data about the behavior of elastomeric isolation bearings under different types of loads and help in taking right decisions regarding geometrical optimizations needed for improve such kind of devices.
The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion
International Nuclear Information System (INIS)
Moczo, P.; Kristek, J.; Pazak, P.; Balazovjech, M.; Moczo, P.; Kristek, J.; Galis, M.
2007-01-01
Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth's structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finite difference (FD), finite-element (FE), and hybrid FD-FE methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. We present alternative formulations of equation of motion for a smooth elastic continuum. We then develop alternative formulations for a canonical problem with a welded material interface and free surface. We continue with a model of an earthquake source. We complete the general theoretical introduction by a chapter on the constitutive laws for elastic and viscoelastic media, and brief review of strong formulations of the equation of motion. What follows is a block of chapters on the finite-difference and finite-element methods. We develop FD targets for the free surface and welded material interface. We then present various FD schemes for a smooth continuum, free surface, and welded interface. We focus on the staggered-grid and mainly optimally-accurate FD schemes. We also present alternative formulations of the FE method. We include the FD and FE implementations of the traction-at-split-nodes method for simulation of dynamic rupture propagation. The FD modeling is applied to the model of the deep sedimentary Grenoble basin, France. The FD and FE methods are combined in the hybrid FD-FE method. The hybrid
A finite element approach for predicting nozzle admittances
Sigman, R. K.; Zinn, B. T.
1983-01-01
A finite element method is used to predict the admittances of axisymmetric nozzles. It is assumed that the flow in the nozzle is isentropic and the disturbances are small so that linear analyses apply. An approximate, two dimensional compressible model is used to describe the steady flow in the nozzle. The propagation of acoustic disturbances is governed by the complete linear wave equation. The differential form of the acoustic equation is transformed to an integral equation by using Galerkin's method, and Green's theorem is applied so that the acoustic boundary conditions can be introduced through the boundary residuals. The boundary conditions are described for both straight and curved sonic lines. A two dimensional FEM with linear elements is used to solve the acoustic equation. A one dimensional FEM is also used to solve the reduced equation of Crocco, and the solution verifies the sufficiency of the boundary residual formulation. Comparison between computed admittances and experimental data is shown to be quite good.
Theoretical determination of nozzle admittances using a finite element approach
Sigman, R. K.; Zinn, B. T.
1980-01-01
A finite element method is used to predict the admittances of axisymmetric nozzles. It is assumed that the flow in the nozzle is isentropic and irrotational, and the disturbances are small so that linear analyses apply. An approximate, two dimensional compressible model is used to describe the steady flow in the nozzle. The propagation of acoustic disturbances is governed by the complete linear wave equation. The differential form of the acoustic equation is transformed to an integral equation using Galerkin's method, and Green's theorem is applied so that the acoustic boundary conditions can be introduced through the boundary residuals. A two-dimensional FEM using linear elements is used to solve the acoustic equation. A one dimensional FEM is also used to solve the reduced equation of Crocco, and the solution verifies the sufficiency of the boundary residual formulation. Comparison between computed admittances and experimental data is shown to be quite good.
Finite element analysis of nonisothermal polymer processing operations
Douglas, C.; Roylance, D.
1982-01-01
A finite element formulation for the analysis of polymer processing is presented and its use in some typical situation including entry flow, transient Couette flow, and the Graetz (forced convection) problem is illustrated. The element formulations are constructed on the premise that momentum convection can be neglected (polymer melt flows typically have very low Reynolds' numbers), but that convective heat transfer may be significant (high Peclet numbers). Nonisothermal effects are considered important in polymer processing, due in part to the significant heating which may occur due to viscous dissipation, and also to the very strong influence of temperature on fluid viscosity. The flow is treated as Newtonian with the flow field being coupled to the heat transfer equation only through the viscous heat generation.
OXYGEN PRESSURE REGULATOR DESIGN AND ANALYSIS THROUGH FINITE ELEMENT MODELING
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Asterios KOSMARAS
2017-05-01
Full Text Available Oxygen production centers produce oxygen in high pressure that needs to be defused. A regulator is designed and analyzed in the current paper for medical use in oxygen production centers. This study aims to design a new oxygen pressure regulator and perform an analysis using Finite Element Modeling in order to evaluate its working principle. In the design procedure,the main elements and the operating principles of a pressure regulator are taking into account. The regulator is designed and simulations take place in order to assessthe proposed design. Stress analysis results are presented for the main body of the regulator, as well as, flow analysis to determine some important flow characteristics in the inlet and outlet of the regulator.
Automation Tools for Finite Element Analysis of Adhesively Bonded Joints
Tahmasebi, Farhad; Brodeur, Stephen J. (Technical Monitor)
2002-01-01
This article presents two new automation creation tools that obtain stresses and strains (Shear and peel) in adhesively bonded joints. For a given adhesively bonded joint Finite Element model, in which the adhesive is characterised using springs, these automation tools read the corresponding input and output files, use the spring forces and deformations to obtain the adhesive stresses and strains, sort the stresses and strains in descending order, and generate plot files for 3D visualisation of the stress and strain fields. Grids (nodes) and elements can be numbered in any order that is convenient for the user. Using the automation tools, trade-off studies, which are needed for design of adhesively bonded joints, can be performed very quickly.
Hybrid Fundamental Solution Based Finite Element Method: Theory and Applications
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Changyong Cao
2015-01-01
Full Text Available An overview on the development of hybrid fundamental solution based finite element method (HFS-FEM and its application in engineering problems is presented in this paper. The framework and formulations of HFS-FEM for potential problem, plane elasticity, three-dimensional elasticity, thermoelasticity, anisotropic elasticity, and plane piezoelectricity are presented. In this method, two independent assumed fields (intraelement filed and auxiliary frame field are employed. The formulations for all cases are derived from the modified variational functionals and the fundamental solutions to a given problem. Generation of elemental stiffness equations from the modified variational principle is also described. Typical numerical examples are given to demonstrate the validity and performance of the HFS-FEM. Finally, a brief summary of the approach is provided and future trends in this field are identified.
QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2014-01-01
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n -gon, our construction produces 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n ( n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.
Fracture and Fragmentation of Simplicial Finite Elements Meshes using Graphs
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Mota, A; Knap, J; Ortiz, M
2006-10-18
An approach for the topological representation of simplicial finite element meshes as graphs is presented. It is shown that by using a graph, the topological changes induced by fracture reduce to a few, local kernel operations. The performance of the graph representation is demonstrated and analyzed, using as reference the 3D fracture algorithm by Pandolfi and Ortiz [22]. It is shown that the graph representation initializes in O(N{sub E}{sup 1.1}) time and fractures in O(N{sub I}{sup 1.0}) time, while the reference implementation requires O(N{sub E}{sup 2.1}) time to initialize and O(N{sub I}{sup 1.9}) time to fracture, where NE is the number of elements in the mesh and N{sub I} is the number of interfaces to fracture.
A nonlinear dynamic corotational finite element model for submerged pipes
de Vries, F. H.; Geijselaers, H. J. M.; van den Boogaard, A. H.; Huisman, A.
2017-12-01
A three dimensional finite element model is built to compute the motions of a pipe that is being laid on the seabed. This process is geometrically nonlinear, therefore co-rotational beam elements are used. The pipe is subject to static and dynamic forces. Static forces are due to gravity, current and buoyancy. The dynamic forces exerted by the water are incorporated using Morison’s equation. The dynamic motions are computed using implicit time integration. For this the Hilber-Hughes-Taylor method is selected. The Newton-Raphson iteration scheme is used to solve the equations in every time step. During laying, the pipe is connected to the pipe laying vessel, which is subject to wave motion. Response amplitude operators are used to determine the motions of the ship and thus the motions of the top end of the pipe.
Dynamic analysis of suspension cable based on vector form intrinsic finite element method
Qin, Jian; Qiao, Liang; Wan, Jiancheng; Jiang, Ming; Xia, Yongjun
2017-10-01
A vector finite element method is presented for the dynamic analysis of cable structures based on the vector form intrinsic finite element (VFIFE) and mechanical properties of suspension cable. Firstly, the suspension cable is discretized into different elements by space points, the mass and external forces of suspension cable are transformed into space points. The structural form of cable is described by the space points at different time. The equations of motion for the space points are established according to the Newton’s second law. Then, the element internal forces between the space points are derived from the flexible truss structure. Finally, the motion equations of space points are solved by the central difference method with reasonable time integration step. The tangential tension of the bearing rope in a test ropeway with the moving concentrated loads is calculated and compared with the experimental data. The results show that the tangential tension of suspension cable with moving loads is consistent with the experimental data. This method has high calculated precision and meets the requirements of engineering application.
Practical Aspects of Finite Element Method Applications in Dentistry
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Grbović Aleksandar
2017-07-01
Full Text Available The use of numerical methods, such as finite element method (FEM, has been widely adopted in solving structural problems with complex geometry under external loads when analytical solutions are unachievable. Basic idea behind FEM is to divide the complex body geometry into smaller and simpler domains, called finite elements, and then to formulate solution for each element instead of seeking a solution for the entire domain. After finding the solutions for all elements they can be combined to obtain a solution for the whole domain. This numerical method is mostly used in engineering, but it is also useful for studying the biomechanical properties of materials used in medicine and the influence of mechanical forces on the biological systems. Since its introduction in dentistry four decades ago, FEM became powerful tool for the predictions of stress and strain distribution on teeth, dentures, implants and surrounding bone. FEM can indicate aspects of biomaterials and human tissues that can hardly be measured in vivo and can predict the stress distribution in the contact areas which are not accessible, such as areas between the implant and cortical bone, denture and gingiva, or around the apex of the implant in trabecular bone. Aim of this paper is to present - using results of several successful FEM studies - the usefulness of this method in solving dentistry problems, as well as discussing practical aspects of FEM applications in dentistry. Some of the method limitations, such as impossibility of complete replication of clinical conditions and need for simplified assumptions regarding loads and materials modeling, are also presented. However, the emphasis is on FE modelling of teeth, bone, dentures and implants and their modifications according to the requirements. All presented studies have been carried out in commercial software for FE analysis ANSYS Workbench.
Automating the generation of finite element dynamical cores with Firedrake
Ham, David; Mitchell, Lawrence; Homolya, Miklós; Luporini, Fabio; Gibson, Thomas; Kelly, Paul; Cotter, Colin; Lange, Michael; Kramer, Stephan; Shipton, Jemma; Yamazaki, Hiroe; Paganini, Alberto; Kärnä, Tuomas
2017-04-01
The development of a dynamical core is an increasingly complex software engineering undertaking. As the equations become more complete, the discretisations more sophisticated and the hardware acquires ever more fine-grained parallelism and deeper memory hierarchies, the problem of building, testing and modifying dynamical cores becomes increasingly complex. Here we present Firedrake, a code generation system for the finite element method with specialist features designed to support the creation of geoscientific models. Using Firedrake, the dynamical core developer writes the partial differential equations in weak form in a high level mathematical notation. Appropriate function spaces are chosen and time stepping loops written at the same high level. When the programme is run, Firedrake generates high performance C code for the resulting numerics which are executed in parallel. Models in Firedrake typically take a tiny fraction of the lines of code required by traditional hand-coding techniques. They support more sophisticated numerics than are easily achieved by hand, and the resulting code is frequently higher performance. Critically, debugging, modifying and extending a model written in Firedrake is vastly easier than by traditional methods due to the small, highly mathematical code base. Firedrake supports a wide range of key features for dynamical core creation: A vast range of discretisations, including both continuous and discontinuous spaces and mimetic (C-grid-like) elements which optimally represent force balances in geophysical flows. High aspect ratio layered meshes suitable for ocean and atmosphere domains. Curved elements for high accuracy representations of the sphere. Support for non-finite element operators, such as parametrisations. Access to PETSc, a world-leading library of programmable linear and nonlinear solvers. High performance adjoint models generated automatically by symbolically reasoning about the forward model. This poster will present
Finite element modeling of electrically rectified piezoelectric energy harvesters
International Nuclear Information System (INIS)
Wu, P H; Shu, Y C
2015-01-01
Finite element models are developed for designing electrically rectified piezoelectric energy harvesters. They account for the consideration of common interface circuits such as the standard and parallel-/series-SSHI (synchronized switch harvesting on inductor) circuits, as well as complicated structural configurations such as arrays of piezoelectric oscillators. The idea is to replace the energy harvesting circuit by the proposed equivalent load impedance together with the capacitance of negative value. As a result, the proposed framework is capable of being implemented into conventional finite element solvers for direct system-level design without resorting to circuit simulators. The validation based on COMSOL simulations carried out for various interface circuits by the comparison with the standard modal analysis model. The framework is then applied to the investigation on how harvested power is reduced due to fabrication deviations in geometric and material properties of oscillators in an array system. Remarkably, it is found that for a standard array system with strong electromechanical coupling, the drop in peak power turns out to be insignificant if the optimal load is carefully chosen. The second application is to design broadband energy harvesting by developing array systems with suitable interface circuits. The result shows that significant broadband is observed for the parallel (series) connection of oscillators endowed with the parallel-SSHI (series-SSHI) circuit technique. (paper)
Finite element modeling of electrically rectified piezoelectric energy harvesters
Wu, P. H.; Shu, Y. C.
2015-09-01
Finite element models are developed for designing electrically rectified piezoelectric energy harvesters. They account for the consideration of common interface circuits such as the standard and parallel-/series-SSHI (synchronized switch harvesting on inductor) circuits, as well as complicated structural configurations such as arrays of piezoelectric oscillators. The idea is to replace the energy harvesting circuit by the proposed equivalent load impedance together with the capacitance of negative value. As a result, the proposed framework is capable of being implemented into conventional finite element solvers for direct system-level design without resorting to circuit simulators. The validation based on COMSOL simulations carried out for various interface circuits by the comparison with the standard modal analysis model. The framework is then applied to the investigation on how harvested power is reduced due to fabrication deviations in geometric and material properties of oscillators in an array system. Remarkably, it is found that for a standard array system with strong electromechanical coupling, the drop in peak power turns out to be insignificant if the optimal load is carefully chosen. The second application is to design broadband energy harvesting by developing array systems with suitable interface circuits. The result shows that significant broadband is observed for the parallel (series) connection of oscillators endowed with the parallel-SSHI (series-SSHI) circuit technique.
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.
Distributed Finite Element Analysis Using a Transputer Network
Watson, James; Favenesi, James; Danial, Albert; Tombrello, Joseph; Yang, Dabby; Reynolds, Brian; Turrentine, Ronald; Shephard, Mark; Baehmann, Peggy
1989-01-01
The principal objective of this research effort was to demonstrate the extraordinarily cost effective acceleration of finite element structural analysis problems using a transputer-based parallel processing network. This objective was accomplished in the form of a commercially viable parallel processing workstation. The workstation is a desktop size, low-maintenance computing unit capable of supercomputer performance yet costs two orders of magnitude less. To achieve the principal research objective, a transputer based structural analysis workstation termed XPFEM was implemented with linear static structural analysis capabilities resembling commercially available NASTRAN. Finite element model files, generated using the on-line preprocessing module or external preprocessing packages, are downloaded to a network of 32 transputers for accelerated solution. The system currently executes at about one third Cray X-MP24 speed but additional acceleration appears likely. For the NASA selected demonstration problem of a Space Shuttle main engine turbine blade model with about 1500 nodes and 4500 independent degrees of freedom, the Cray X-MP24 required 23.9 seconds to obtain a solution while the transputer network, operated from an IBM PC-AT compatible host computer, required 71.7 seconds. Consequently, the $80,000 transputer network demonstrated a cost-performance ratio about 60 times better than the $15,000,000 Cray X-MP24 system.
Finite Element Modeling of the Posterior Eye in Microgravity
Feola, Andrew; Raykin, Julia; Mulugeta, Lealem; Gleason, Rudolph; Myers, Jerry G.; Nelson, Emily S.; Samuels, Brian; Ethier, C. Ross
2015-01-01
Microgravity experienced during spaceflight affects astronauts in various ways, including weakened muscles and loss of bone density. Recently, visual impairment and intracranial pressure (VIIP) syndrome has become a major concern for space missions lasting longer than 30 days. Astronauts suffering from VIIP syndrome have changes in ocular anatomical and visual impairment that persist after returning to earth. It is hypothesized that a cephalad fluid shift in microgravity may increase the intracranial pressure (ICP), which leads to an altered biomechanical environment of the posterior globe and optic nerve sheath (ONS).Currently, there is a lack of knowledge of how elevated ICP may lead to vision impairment and connective tissue changes in VIIP. Our goal was to develop a finite element model to simulate the acute effects of elevated ICP on the posterior eye and optic nerve sheath. We used a finite element (FE) analysis approach to understand the response of the lamina cribrosa and optic nerve to the elevations in ICP thought to occur in microgravity and to identify which tissue components have the greatest impact on strain experienced by optic nerve head tissues.
Finite element and analytical models for twisted and coiled actuator
Tang, Xintian; Liu, Yingxiang; Li, Kai; Chen, Weishan; Zhao, Jianguo
2018-01-01
Twisted and coiled actuator (TCA) is a class of recently discovered artificial muscle, which is usually made by twisting and coiling polymer fibers into spring-like structures. It has been widely studied since discovery due to its impressive output characteristics and bright prospects. However, its mathematical models describing the actuation in response to the temperature are still not fully developed. It is known that the large tensile stroke is resulted from the untwisting of the twisted fiber when heated. Thus, the recovered torque during untwisting is a key parameter in the mathematical model. This paper presents a simplified model for the recovered torque of TCA. Finite element method is used for evaluating the thermal stress of the twisted fiber. Based on the results of the finite element analyses, the constitutive equations of twisted fibers are simplified to develop an analytic model of the recovered torque. Finally, the model of the recovered torque is used to predict the deformation of TCA under varying temperatures and validated against experimental results. This work will enhance our understanding of the deformation mechanism of TCAs, which will pave the way for the closed-loop position control.
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.
Modelling of Shaft Orbiting with 3-D Solid Finite Elements
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J. Yu
1999-01-01
Full Text Available A 3-D solid finite element model which can include bending, torsional, axial and other motions is proposed to analyse dynamic responses of shafts. For uniform shafts, this model shows consistency with beam theories when bending vibration is examined. For non-uniform shafts such as tapered ones, however, this model gives much more reliable and accurate results than beam theories which use an assumption that plane sections remain plane. Reduction procedures can be applied which involve only small matrix operations for such a system with a large number of degrees of freedom. The equations of motion have been consistently derived in a rotating frame. Shaft orbiting motion is then defined in this frame, giving a clear view of its trajectories. Forced responses due to excitation in the rotating frame have been examined to find some characteristics of the orbiting shaft. Resonant orbiting frequencies, i.e., natural frequencies of rotating shafts, can be determined in terms of the rotating or fixed frame. Trajectories of transverse displacements have been found to be varying with the forcing frequencies. At resonance, a uniform shaft will only have forward or backward orbiting motion with circular orbits. For other forcing frequencies, however, even a uniform shaft could present both forward and backward orbiting motions with non-circular orbits at different locations along its length. It is anticipated that modelling of shaft orbiting in the rotating frame with the proposed 3-D solid finite elements will lead to accurate dynamic stress evaluation.
Investigation of Apple Vibration Characteristics Using Finite Element Modal Analysis
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R Mirzaei
2013-02-01
Full Text Available The most important quality indicator of fruits is the flesh firmness which is well correlated to their young’s modulus. In this research variation of vibration characteristics (shape modes, natural frequency of apple due to change of material characteristics (density, young's models, Poisson ratio and apple volume was investigated using Finite Element simulation. An image processing technique was used to obtain an unsymmetrical and non-spherical geometric model of apple. The exact three-dimensional shape of the fruit was created by determining the coordinates of apple surface and forming uneven rotational curvatures. Modal analysis with no boundary constraints has been applied. The first 20 Eigen frequencies and the corresponding mode shape were determined. Six rigid body modes possess zero resonant frequency which is related to the degree of freedom of a rigid body in space indicated the validity of finite element model. The modal analysis results showed that resonant frequency increased by increasing young's modulus of the fruit, while it decreased by increasing apple density. First mode torsion has a mean resonant frequency of 584 Hz. Variations of natural frequency due to change in young's modulus, density, and Poisson ratio were 80%, 11% and 4%, respectively. Coefficient of variation of resonant frequency in response to changing young's modulus was 2-3 times of that of density which shows the greatest effect of young modulus changes on natural frequency of fruits. Consequently with determination of fruits' natural frequency, their young modulus and firmness can be estimated.
Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
Bonito, Andrea
2013-01-01
Elliptic PDEs with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electromagnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the L∞ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an Lq norm with q < ∞ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis. © 2013 Societ y for Industrial and Applied Mathematics.