Showing papers on "Smoothed finite element method published in 1982"
Book•
01 Jan 1982
TL;DR: In this paper, the Finite Element Method is used to derive a system equation from a set of finite element vectors and matrices and then to solve the problem of finding the solution.
Abstract: 1. Overview of the Finite Element Method, 2. Discretization of the Domain, 3. Interpolation Models, 4. Higher Order and Isoparametric Elements, 5. Derivation of Element Matrices and Vectors, 6. Assembly of Element Matrices and Vectors and Derivation of System Equations, 7. Numerical Solution of Finite Element Equations, 8. Basic Equations and Solution Procedure, 9. Analysis of Trusses, Beams and Frames, 10. Analysis of Plates, 11. Analysis of Three-Dimensional Problems, 12. Dynamic Analysis, 13. Formulation and Solution Procedure, 14. One-Dimensional Problems, 15. Two-Dimensional Problems, 16. Three-Dimensional Problems, 17. Basic Equations of Fluid Mechanics, 18. Inviscid and Incompressible Flows, 19. Viscous and Non-Newtonian Flows, 20. Solution of Quasi-Harmonic Equations, 21. Solution of Helmhotz Equation, 22. Solution of Reynolds Equation, Appendix-A Green Greass Theorem.
1,247 citations
TL;DR: Finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form $cu_t + bu_x - (au_x )_x = f as mentioned in this paper.
Abstract: Finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form $cu_t + bu_x - (au_x )_x = f$. Optimal order error estimates in $L^2 $ and $W^{1,2} $ are derived for the finite element procedure. Various error estimates are presented for a variety of finite difference methods. The estimates show that, for convection-dominated problems $(b \gg a)$, these schemes have much smaller time-truncation errors than those of standard methods. Extensions to n-space variables and time-dependent or nonlinear coefficients are indicated, along with applications of the concepts to certain problems described by systems of differential equations.
1,018 citations
369 citations
TL;DR: In this article, a method of discretizing the die boundary conditions is considered for the analysis of metal forming processes by the rigid viscoplastic finite element method, and solutions of the spike forging process are obtained by using the method.
179 citations
TL;DR: In this article, the authors proposed two new methods, called the "finite element method taking account of external power source" and the "fine element method with shape modification" to calculate the magnetic flux distribution of a magnetic circuit by using the conventional finite element method.
Abstract: When the flux distribution of a magnetic circuit is analyzed by using the conventional finite element method, the magnetizing currents must be given. Therefore, if the flux distribution is specified, it is difficult to obtain the distributions of magnetomotive forces or configuration of magnets producing the specified field distribution by the conventional finite element method. New methods which are called the "finite element method taking account of external power source" and the "finite element method with shape modification" have been developed. The processes of calculation in these methods are contrary to the conventional technique. These new methods have the following advantages: (a) If there are many unknown independent magnetizing currents, these currents are directly calculated by the new method. (b) When a flux distribution is specified, the optimum shapes of the magnets can be directly calculated. (c) As these new methods need no repetition, computing time can be considerably reduced. The principles and the finite element formulations of these new methods are described, and a few examples of application of these methods are shown. These new methods make it possible to design the optimum magnetic circuits by using the finite element method.
127 citations
TL;DR: The first textbook specifically designed for university courses in groundwater modeling is as discussed by the authors, which leads the student from elementary concepts through the mathematics and modeling procedures and to the solution of problems, and is aimed at the student whose preparation is limited to elementary calculus.
Abstract: This is the first textbook specifically designed for university courses in groundwater modeling. There are books devoted to the exposition of the mechanics of groundwater, to the mathematics of finite differences and finite elements, and to overviews of modeling technology. However, this book leads the student from elementary concepts through the mathematics and modeling procedures and to the solution of problems.
The book is very readable and is aimed at the student whose preparation is limited to elementary calculus. More difficult and peripheral topics such as Anisotropy and Tensors, the Variational Method, Isoparametric Quadrilateral Elements, and Analogies are reserved for appendices.
126 citations
TL;DR: In this article, the authors prove error estimates for two mixed finite element methods related to reduced integration: a method for Stokes' problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure.
Abstract: We prove error estimates for the following two mixed finite element methods related to reduced integration: A method for Stokes' problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure, and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants for the shear stress. The main idea of the proof in the case of Stokes' problem is to combine a weak Babuska-Brezzi type stability estimate for the pressure with a superapproximability property for the velocities. A similar technique is used in the case of the plate problem.
116 citations
TL;DR: In this article, a quasi-Eulerian finite element formulation for the analysis of transients in a fluid with a pressurized bubble is developed in both two and three dimensions, which can be programmed to move independent of the material, so that the method lends itself well to the treatment of fluid-structure problems.
93 citations
TL;DR: In this paper, it is shown that most of the necessary quantities for this subsidiary computation are available as computed by-products in the preceding finite element solution procedure, which is shown to be a particular form of a procedure for which superconvergent theoretical error estimates have been proven elsewhere.
80 citations
TL;DR: The computer implementation aspects for fluid-structure interaction problems are presented and special attention is placed on finite element fluid modelling, implicit-explicit transient algorithms and finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis.
TL;DR: In this article, a method of providing bounded solutions to a wide range of magnetostatic field problems is outlined, which extends complementary and dual energy variational principles to encompass the T-Ω formulation of electromagnetic field problems.
Abstract: A method of providing bounded solutions to a wide range of magnetostatic field problems is outlined. The method extends complementary and dual energy variational principles to encompass the T-Ω formulation of electromagnetic field problems and shows how this leads to efficient finite element implementation of the technique. Examples are given that show clearly the bounded nature of the procedure, and indicate how it may be used to reduce the computational requirements necessary for a specific accuracy of solution.
TL;DR: In this article, a mixed formulation of the Signorini problem with normal forces on the contact surface is derived, making use of the duality approach, which allows us to approximate independently the displacement field in the body and the normal and 99 0022-247x/82/030099-24eo2.
Dissertation•
01 Jan 1982
TL;DR: In this article, the authors describe new techniques for analyzing linear, steady-state, skin effect phenomena in multi-conductor systems by the finite element method, which are applied to single phase sheet-wound transformer problems in which the current windings are modeled by thin axisymmetric sheets.
Abstract: This paper describes fwo new techniques for analyzing linear, steady-state, skin effect phenomena in multi-conductor systems by the finite element method. The first of these is based on a linear superposition principle for the field solution, while the second one is based on an integrodifferential equation field formulation. The techniques are applied to single phase sheet-wound transformer problems in which the current windings are modeled by thin axisymmetric sheets.
TL;DR: In this article, a review of the application of the finite element method to metal forming process modeling is presented, including elastoplastic, rigid-plastic, and viscoplastic analyses.
Abstract: Recent developments in the application of the finite element method to metal forming process modeling are reviewed. Various finite element approaches, namely, elastoplastic, rigid-plastic, and viscoplastic analyses are presented, including the coupled analysis of heat transfer and metal flow. In concluding the role of finite element analysis in future metalworking technology is indicated.
TL;DR: In this article, a theoretical accuracy study of finite element models for thin arches is presented, where the perturbation theory of mixed models and the technique of asymptotic expansion are used to obtain order estimates of errors.
01 Jan 1982
01 Jan 1982
TL;DR: Numerical results are given that show that the method can simulate adverse mobility ratio displacements accurately without suffering from grid orientation, numerical dispersion, or overshoot.
Abstract: An efficient method for modeling convection-dominated flows is presented and applied to miscible displacement in a porous medium. The method uses characteristics to model convection and finite elements for diffusion and dispersion, thereby treating each physical process with a well-suited numerical scheme. A finite difference analogue can also be formulated. Numerical results are given that show that the method can simulate adverse mobility ratio displacements accurately without suffering from grid orientation, numerical dispersion, or overshoot. 14 refs.
TL;DR: In this article, finite difference and finite element methods are investigated as applied to Laplace and Poisson linear equations in two dimensions, and the results are found to be independent of the method used to establish the matrix equations but dependent upon the choice of grid systems employed to discretize the problem.
Abstract: Finite difference and finite element methods are investigated as applied to Laplace and Poisson linear equations in two dimensions. The comparative analysis concentrates on first-order square, rectangular, triangular and polar algorithms which are characteristic to each method. The results are found to be independent of the method used to establish the matrix equations but dependent upon the choice of grid systems employed to discretize the problem. It is found that for special cases the solutions are also independent of the type and structure of the grid systems used.
TL;DR: This technique models the differentiation and product-embedding operators as rectangular matrices, and produces finite element matrices by replacing all required analytic operations by their finite matrix analogues.
Abstract: Methods are described for forming finite element matrices for a wide variety of operators on tetrahedral finite elements, in a manner similar to that previously employed for line segments and triangles. This technique models the differentiation and product-embedding operators as rectangular matrices, and produces finite element matrices by replacing all required analytic operations by their finite matrix analogues. The method is illustrated by deriving the conventional matrix representation for Laplace's equation. Brief computer programs are given, which generate universal finite element matrices for use in various applications