Showing papers on "Smoothed finite element method published in 1994"
Book•
01 Jan 1994TL;DR: In this paper, the authors present a study on the effect of differential expressions on the performance of a computations of a continuous-time transfer of heat transfer and fluid flow.
Abstract: EQUATIONS OF HEAT TRANSFER AND FLUID MECHANICS Present Study Governing Equations of a Continuum Governing Equations in Terms of Primitive Variables Porous Flow Equations Auxiliary Transport Equations sChemically Reacting Systems Boundary Conditions sChange of Phase Enclosure Radiation Summary of Equations THE FINITE ELEMENT METHOD: AN OVERVIEW Model Differential Equation Finite Element Approximation Weighted-Integral Statements and Weak Forms Finite Element Model Interpolation Functions Assembly of Elements Time-Dependent Problems Axisymmetric Problems Convective Boundary Conditions Library of Finite Elements Numerical Integration Modeling Considerations Illustrative Examples 3D CONDUCTION HEAT TRANSFER Semidiscrete Finite Element Model Interpolation Functions Numerical Integration Computation of Surface Fluxes Semidiscrete Finite Element Model Solution of Nonlinear Equations Radiation Solution Algorithms Variable Properties sPost-Processing Operations sAdvanced Topics in Conduction sExamples of Diffusion Problems VISCOUS INCOMPRESSIBLE FLOWS Mixed Finite Element Model Penalty Finite Element Models Finite Element Models of Porous Flow Computational Considerations Solution of Nonlinear Equations Time-Approximation Schemes sStabilized Methods Post-Processing sAdvanced Topics Advanced Topics - Turbulence Numerical Examples CONVECTIVE HEAT TRANSFER Mixed Finite Element Model Penalty Finite Element Model Finite Element Models of Porous Flow Solution Methods Convection with Change of Phase Convection with Enclosure Radiation Post-Computation of Heat Flux Advanced Topics - Turbulent Heat Transfer Advanced Topics - Chemically Reacting Systems Numerical Examples sNON-NEWTONIAN FLUIDS Governing Equations of Inelastic Fluids Finite Element Models of Inelastic Fluids Solution Methods for Inelastic Fluids Governing Equations of Viscoelastic Fluids Finite Element Model of Differential Form Finite Element Model of Integral Form Unresolved Problems Numerical Examples sCOUPLED PROBLEMS Coupled Boundary Value Problems Fluid Mechanics and Heat Transfer Solid Mechanics Electromagnetics Coupled Problems in Mechanics Implementation of Coupled Algorithms Numerical Examples sADVANCED TOPICS Parallel Processing Other Topics Note: Chapters also include an Introduction, Exercises, and References APPENDIX A: COMPUTER PROGRAM--HEATFLOW Heat Transfer and Related Problems Flows of Viscous Incompressible Fluids Description of the Input Data A Source Listings of Selective Subroutines Reference sAPPENDIX B: SOLUTION OF LINEAR EQUATIONS Introduction Direct Methods Iterative Methods References for Additional Reading sAPPENDIX C: FIXED POINT METHODS AND CONTRACTION MAPPINGS Fixed Point Theorem Chord Method Newton's Method The Newton-Raphson Method Descent Methods References for Additional Reading
876 citations
Book•
01 Jan 1994
512 citations
297 citations
01 Jan 1994
250 citations
TL;DR: In this article, the accuracy of the Darcy velocity, flux, and stream function computed from lowest-order, triangle-based, control volume and mixed finite element approximations to the two-dimensional pressure equation is considered.
Abstract: The accuracy of the Darcy velocity, flux, and stream function computed from lowest-order, triangle-based, control volume and mixed finite element approximations to the two-dimensional pressure equation is considered. The control volume finite element method, similar to integrated finite difference methods and analogous to the interpolation of Galerkin finite element results over “control volumes,” is shown to yield a conservative velocity field and smooth streamlines. The streamlines and fluxes through the system computed with the control volume finite element approach are compared to those computed from the mixed finite element method, which approximates the pressure and velocity variables separately. It is shown that for systems with only moderate degrees of heterogeneity, the control volume finite element method is the more computationally efficient alternative; i.e., it provides more accurate flow results for a given number of unknowns. For more variable or discontinuous permeability fields, by contrast, such as sand/shale systems, the mixed finite element method is shown to approximate flow variables more accurately and more realistically than the control volume method with the same number of unknowns.
206 citations
01 Dec 1994
TL;DR: In this article, the authors discuss the advantages and disadvantages of finite element method and compare and contrast the Rayleigh comment on both the methods and explain the various teps involved in finite Element method and explain them through an Example.
Abstract: 1. If a displacement field is described as follows, u = (−x+2y+6xy)10 and v = (3x + 6y Determine the strain components v xx , v yy , and v xy at the point x = 1; y = 0. 2. Explain briefly about the following: (a) Variational method. (b) Importance of Boundary cond itions. 3. Discuss the following basic principles of finite element method. (a) Derivation of element stiffness matrix. (b) Assembly of Global stiffness Matrix. 4.What are the various teps involved in finite Element method and explain them through an Example 5. Compare and contrast the “Rayleigh comment on both the methods. 6. What are the various approximate methods of anal ysis and exp 7. (a) Explain the advantages and disadvantages of Finite Element Method. (b) What is meant by total potential of elastic str uc ure? Write the expression for total potential of a cantilever beam with uniformly dist ributed 8. In a plane strain problem, we have σx = 137.90*10 6 Pa σy= -68.95*10 Determine the value of the stress
200 citations
TL;DR: In this article, a comparison between the mixed hybrid finite element and the standard finite element method is performed in the bidimensional case with a triangular space discretization, and the results of the simulations are presented in the form of streamlines.
Abstract: Selected groundwater flow scenarios are used in a two-way comparison between the mixed hybrid finite element method and the standard finite element method (also called the conforming finite element method). The simulations presented are performed in the bidimensional case with a triangular space discretization because of its practical interest for hydrogeologists. The basic idea of the mixed procedure is to approximate both the hydraulic potential and the velocity simultaneously and to satisfy an exact water balance for each element. By contrast, the conforming finite element method calculates the potential field everywhere and then calculates the velocity by differentiation of the potential. The conventional approach results in an elementwise constant velocity which can be subject to significant problems because of the normal component discontinuity of the velocity. The mixed hybrid finite element method provides velocities everywhere in the field, as well as potentials at the center of each element and each edge. Moreover, the normal component of the velocity field is continuous between adjacent elements. The results of the simulations are presented in the form of streamlines. To avoid the problem of velocity discontinuity, the method of Cordes and Kinzelbach (1992) is used; it allows the construction of a continuous velocity field from potentials obtained by the conforming finite element method. The comparison studies show that the mixed hybrid finite element is superior to the conforming method in terms of accuracy. It is also superior to the conforming method in terms of computational effort. The potential fields obtained by the mixed hybrid and the conforming finite element methods are the same.
177 citations
161 citations
TL;DR: In this article, the authors present a method for the numerical computation of the wavenumbers and associated modes of the cross-section of thin-walled waveguides based on finite element techniques, and compare results obtained by the finite element method, by Donnell's shell theory and by simple Euler-Bernoulli beam theory.
Book•
01 Jan 1994
TL;DR: In this article, the authors proposed a Compact Combination of the Finite Element, Linear Iteration and Finite Difference Methods for solving the one-dimensional Bar Model Problem (Principle of Virtual Work).
Abstract: Introduction. 1. One-Dimensional Bar Model Problem (Principle of Virtual Work). 2. Spatial Discretisation by the Finite Element Method. 3. Solution of Nonlinearities by the Linear Iteration Method. 4. Time Integration by the Finite Difference Method. 5. Compact Combination of the Finite Element, Linear Iteration and Finite Difference Methods. 6. Two and Three-Dimensional Deformable Solids. Conclusion. Bibliography. Appendix A: List of Symbols. Appendix B: Exercises. Index.
TL;DR: In this article, the authors present a new space-time finite element method for the wave equation, which is explicit in the sense that, with an appropriate mesh, the finite element approximation can be developed one element at a time.
01 Jan 1994
TL;DR: It is concluded that finite-element methods can be used to the same degree of accuracy or better than spring-network models for elastic deformation and fracture of brittle, disordered materials.
Abstract: This paper discusses computational models for elastic deformation and fracture of brittle, disordered materials In particular, we compare models based on networks of springs and finite-element discretizations When the length scale of elements in the numerical model corresponds to discrete material elements, spring-network approaches are valid Their validity as models for a continuous medium is examined by comparing to a finite-volume discretization and by studying (a) the ability to capture uniform strain, and (b) the ability to model crack propagation in an isotropic, homogeneous, brittle material As models of continuous media, spring-networks exhibit several numerical artifacts For such problems, we conclude that finite-element methods can be used to the same degree of accuracy or better than spring-network models
TL;DR: The finite difference method for dealing with contaminant transport problems in porous media is briefly outlined and a numerical example has been given to show how the finite element method is applied to solve contaminant Transport problems in engineering practice.
TL;DR: In this paper, a variational method for obtaining smoothed stresses from a finite element derived non-smooth stress field is presented, based on minimizing a functional involving discrete least-squares error plus a penalty constraint that ensures smoothness of the stress field.
TL;DR: In this paper, a triangular flat facet finite element for the analysis of general thin shells is presented, which is constructed from simple cubic polynomial displacement fields using a complete set of six degrees of freedom at the element vertices.
Abstract: A triangular flat facet finite element for the analysis of general thin shells is presented. It is constructed from simple cubic polynomial displacement fields using a complete set of six degrees of freedom at the element vertices, thereby easily meeting the requirements of standard commercial computer programs. The theoretical development is based on a variational principle which allows a direct formulation of the element stiffness matrix, without inversion, and which permits considerable simplification of the mathematical formulation. The new flat facet element generally produces more accurate numerical results than those obtained in earlier related work. It also offers a possible basis for constructing an improved curved approximation to a shell surface and for further developments in connection with applications involving geometric non-linearity.
TL;DR: The finite element method is discussed and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions and artificial absorbers for terminating the mesh is discussed.
Abstract: Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the finite element method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid finite element methods for simulating composite scatterers, conformal microstrip antennas, and finite periodic arrays. Specifically, we discuss the finite element method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions, and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods, and solvers for achieving low memory requirements and code performance on parallel computing architectures.
TL;DR: The article reviews what has been achieved in areas where the C-concepts can be applied fruitfully in the study of the displacement type finite element method and provides a more complete paradigmatic understanding of the issues involved.
10 Aug 1994
TL;DR: In this article, the authors present an iterative method for solving 3D Harmonic Maxwell Equations with Finite Elements, Lagrange Multipliers, and Iterative Methods for Compressible Flow Computations Parallel Finite Volume Algorithms for Solving the Time Domain Maxwell Equation on Nonstructured Meshes Coupling Between Nonlinear Maxwell and Heat Equations for an Induction Heating Problem.
Abstract: Coupling Mortar Finite Element and Boundary Element Methods for 2D Navier-Stokes Equations Courant Element: Before and After Iterative Methods for Solving Stiff Elliptic Problems Straight and Curved Finite Elements of Class C1 and Some Applications to Thin Shell Problems Exact Controllability to Solve the Helmholtz Equation with Absorbing Boundary Conditions Cubic Version of FEM in Elliptic Problems with Interfaces and Singularities Least Squares Mixed Finite Elements Turbulence Modelling in Finite Element Industrial Applications Necessary and Sufficient Conditions for the Numerical Approximation of a Partial Differential Equation Depending on a Small Parameter Efficient Solution Methods for Compressible Flow Computations Parallel Finite Volume Algorithms for Solving the Time-Domain Maxwell Equations on Nonstructured Meshes Coupling Between Nonlinear Maxwell and Heat Equations for an Induction Heating Problem: Modelling and Numerical Methods Solving the 3D Harmonic Maxwell Equations with Finite Elements, Lagrange Multipliers, and Iterative Methods Some Applications of the Hierarchic High Order MITC Finite Elements for Reissner-Mindlin Plates Domain Decomposition for Immiscible Displacement in Single Porosity Systems An Error Estimator for Nonconforming Approximations of a Nonlinear Problem Some Observations on Raviart-Thomas Mixed Finite Elements in p Extension for Parabolic Problems Mixed Finite Element Methods in Fluid Structure Systems A Black-Box Solver for the Solution of General Nonlinear Functional Equations by Mixed FEM A Remark on the Asymptotic Behaviour of Parabolic Variational Inequalities and Their Finite Element Approximation by the Courant Element Domain Decomposition vs. Adaptivity Material Optimization of Composites. Part Contents.
TL;DR: In this article, a finite element formulation for structural sensitivity analysis of non-linear systems with fixed overall shape is discussed, where both the direct differentiation and adjoint variable methods are employed.
Abstract: Finite element formulations for structural sensitivity analysis of non-linear systems with fixed overall shape are discussed. Both the direct differentiation and adjoint variable methods are employed. The resulting sensitivity algorithms are consistent with time integration scheme adopted for solving equilibrium problem. Effectiveness and computational aspects of the procedures are discussed and compared. Numerical algorithms are shown to be readily implemented in existing finite element codes. Large-scale examples illustrate the paper.
TL;DR: It is demonstrated that both approximate truncation schemes yield reasonably accurate results even when the mesh is extended only 0.3 wavelengths away from the array aperture, and it is shown that the FEM-BI method remains quite competitive with the F EM-artificial absorber method when the fast Fourier transform is used for computing the matrixvector products in the iterative solution algorithm.
Abstract: The type of mesh termination used in the context of finite element formulations plays a major role on the efficiency and accuracy of the field solution. In this work we evaluate the performance of an absorbing boundary condition and an artificial absorber (a new concept) for terminating the finite element mesh. This analysis is done in connection with the problem of scattering by a finite slot array in a thick ground plane. The two approximate mesh truncation schemes are compared with the exact finite element - boundary integral (FEM-BI) method in terms of accuracy and efficiency. It is demonstrated that both approximate truncation schemes yield reasonably accurate results even when the mesh is extended only 0.3 wavelengths away from the array aperture. However, the artificial absorber termination method leads to a substantially more efficient solution. Moreover, it is shown that the FEM-BI method remains quite competitive with the FEM-artificial absorber method when the fast Fourier transform is used for computing the matrixvector products in the iterative solution algorithm. These conclusions are indeed surprising and of major importance in electromagnetic simulations based on the finite element method.
TL;DR: This chapter outlines the physical basis, formulation, and principal features of finite element methods for developmental biology, and presents solutions to technical difficulties that arise when the methods are applied to developmental biology.
Abstract: Publisher Summary This chapter outlines the physical basis, formulation, and principal features of finite element methods for developmental biology, and presents solutions to technical difficulties that arise when the methods are applied to developmental biology The finite element method involves breaking a system or region of interest into finite-sized elements Equations describing the physical behavior of each element are then written Finally, systems of equations which describe the behavior of the system are constructed and solved to determine the behavior of the system The first step in a finite element analysis is to identify the quantities of interest Next, it is necessary to choose a set of independent quantities (primary quantities) in which all other relevant quantities can be written These quantities must be sufficient to completely describe the system In the finite element method, these primary quantities determine the state space available at each node One of the most important steps in the formulation of a finite element problem is the choice of shape functions These functions define quantities within a given element in terms of its nodal values
TL;DR: In this article, a continuum damage model based on the theory of materials of type N is proposed and its nonlinear finite element approximation and numerical simulation are carried out to solve the finite elastoplasticity problems.
Abstract: A continuum damage modeling based on the theory of materials of type N is proposed and its nonlinear finite element approximation and numerical simulation are carried out. To solve the finite elastoplasticity problems, the reasonable kinematical strain measure for large deformed solids are introduced and constitutive relations based on the theory of materials of type N are derived. These highly nonlinear equations are reduced to the incremental weak formulation and approximated by the theory of nonlinear finite element method. Two example problems, bending problem and billet forming problem, are simulated
01 Jan 1994
TL;DR: In this paper, the Navier-Stokes equations can be analytically solved, however, this, is possible only for the simplest type of problems and not for all problems.
Abstract: If the fluid flow domain and boundary conditions are well posed then the Navier-Stokes equations can be analytically solved, however this, is possible only for the simplest type of problems.
TL;DR: The Lesaint-Raviart finite element method is used to solve both the transport problem and the error equation and the use of a hierarchical finite element basis on triangles leads to a very efficient error estimation algorithm.
Abstract: SUMMARY This paper presents an adaptive finite element method for solving scalar hyperbolic transport problems. An equation for the evolution of the error is developed. The Lesaint-Raviart finite element method is used to solve both the transport problem and the error equation. The use of a hierarchical finite element basis on triangles leads to a very efficient error estimation algorithm. The adaptive strategy, based on remeshing, is dmonstrated on several non-trivial problems with known analytical solutions. Higher degree polynomials combined with adaptation produce a very efficient solution algorithm even for problems involving discontinuities.