Book•
Concepts and Applications of Finite Element Analysis
01 Jan 1974-
TL;DR: In this article, the authors present a formal notation for one-dimensional elements in structural dynamics and vibrational properties of a structural system, including the following: 1. Isoparametric Elements.
Abstract: Notation. Introduction. One-Dimensional Elements, Computational Procedures. Basic Elements. Formulation Techniques: Variational Methods. Formulation Techniques: Galerkin and Other Weighted Residual Methods. Isoparametric Elements. Isoparametric Triangles and Tetrahedra. Coordinate Transformation and Selected Analysis Options. Error, Error Estimation, and Convergence. Modeling Considerations and Software Use. Finite Elements in Structural Dynamics and Vibrations. Heat Transfer and Selected Fluid Problems. Constaints: Penalty Forms, Locking, and Constraint Counting. Solid of Revolution. Plate Bending. Shells. Nonlinearity: An Introduction. Stress Stiffness and Buckling. Appendix A: Matrices: Selected Definition and Manipulations. Appendix B: Simultaneous Algebraic Equations. Appendix C: Eigenvalues and Eigenvectors. References. Index.
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01 Jan 1984
TL;DR: Second-order Differential Equations in One Dimension: Finite Element Models (FEM) as discussed by the authors is a generalization of the second-order differential equation in two dimensions.
Abstract: 1 Introduction 2 Mathematical Preliminaries, Integral Formulations, and Variational Methods 3 Second-order Differential Equations in One Dimension: Finite Element Models 4 Second-order Differential Equations in One Dimension: Applications 5 Beams and Frames 6 Eigenvalue and Time-Dependent Problems 7 Computer Implementation 8 Single-Variable Problems in Two Dimensions 9 Interpolation Functions, Numerical Integration, and Modeling Considerations 10 Flows of Viscous Incompressible Fluids 11 Plane Elasticity 12 Bending of Elastic Plates 13 Computer Implementation of Two-Dimensional Problems 14 Prelude to Advanced Topics
3,043 citations
Book•
01 Jan 1989TL;DR: In this article, the authors propose a floating frame of reference formulation for large deformation problems in linear algebra, based on reference kinematics and finite element formulation for deformable bodies.
Abstract: 1. Introduction 2. Reference kinematics 3. Analytical techniques 4. Mechanics of deformable bodies 5. Floating frame of reference formulation 6. Finite element formulation 7. Large deformation problem Appendix: Linear algebra References Index.
2,125 citations
TL;DR: The finite element method (FEM) is a numerical technique used to perform finite element analysis of any given physical phenomenon as discussed by the authors, such as structural or fluid behavior, thermal transport, wave propagation, and the growth of biological cells.
Abstract: Introduction to finite element analysis: 1.1 What is ... The finite element method (FEM) is a numerical technique used to perform finite element analysis of any given physical phenomenon. It is necessary to use mathematics to comprehensively understand and quantify any physical phenomena, such as structural or fluid behavior, thermal transport, wave propagation, and the growth of biological cells.
1,811 citations
TL;DR: The basic explicit finite element and finite difference methods that are currently used to solve transient, large deformation problems in solid mechanics are reviewed.
Abstract: Explicit finite element and finite difference methods are used to solve a wide variety of transient problems in industry and academia. Unfortunately, explicit methods are rarely discussed in detail in finite element text books. This paper reviews the basic explicit finite element and finite difference methods that are currently used to solve transient, large deformation problems in solid mechanics. A special emphasis has been placed on documenting methods that have not been previously published in journals.
1,218 citations
TL;DR: The equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established, which enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the Mixed method.
919 citations