Advanced Topics in Finite Element Analysis of Structures
With Mathematica and MATLAB Computations
1. Auflage Januar 2006
608 Seiten, Hardcover
Wiley & Sons Ltd
Kurzbeschreibung
This new book, resulting from the author's 22 years of teaching finite element analysis to undergraduate and graduate students, intends to strike an appropriate balance between the theory and application of the FEM. Utilizing a unique combination of live MATHEMATICA(r) and MATLAB(r) implementations, the book enables students to see behind the equations, "inside the black box", to fully understand the methods being presented and the solutions produced.
A residual approach to advanced topics in finite element analysis of solids and structures
Starting from governing differential equations, a unique and consistently weighted residual approach is used to present advanced topics in finite element analysis of structures, such as mixed and hybrid formulations, material and geometric nonlinearities, and contact problems. This book features a hands-on approach to understanding advanced concepts of the finite element method (FEM) through integrated Mathematica(r) and MATLAB(r) exercises. In ten chapters, Advanced Topics in Finite Element Analysis of Structures: with Mathematica(r) and MATLAB(r) Computations covers:
* Essential background
* Analysis of elastic solids
* Solids of revolution
* Multifield formulations for beam elements
* Multifield formulations for analysis of elastic solids
* Plates and shells
* Introduction to nonlinear problems
* Material nonlinearity
* Geometric nonlinearity
* Contact problems
An associated Web site (wiley.com/go/bhatti) includes expanded computational details of some of the lengthy examples in the text. It also contains live MATLAB(r) files and Mathematica(r) notebooks to overcome the tedious nature of calculations associated with finite elements.
PREFACE.
1 ESSENTIAL BACKGROUND.
1.1 Steps in a Finite Element Solution.
1.2 Interpolation Functions.
1.3 Integration by Parts.
1.4 Numerical Integration Using Gauss Quadrature.
1.5 Mapped Elements.
Problems.
2 ANALYSIS OF ELASTIC SOLIDS.
2.1 Governing Equations.
2.2 General Form of Finite Element Equations.
2.3 Tetrahedral Element.
2.4 Mapped Solid Elements.
2.5 Stress Calculations.
2.6 Static Condensation.
2.7 Substructuring.
2.8 Patch Test and Incompatible Elements.
2.9 Computer Implementation: fe2Quad.
Problems.
3 SOLIDS OF REVOLUTION.
3.1 Equations of Elasticity in Cylindrical Coordinates.
3.2 Axisymmetric Analysis.
3.3 Unsymmetrical Loading.
Problems.
4 MULTIFIELD FORMULATIONS FOR BEAM ELEMENTS.
4.1 Euler-Bernoulli Beam Theory.
4.2 Mixed Beam Element Based on EBT.
4.3 Timoshenko Beam Theory.
4.4 Displacement-Based Beam Element for TBT.
4.5 Shear Locking in Displacement-Based Beam Elements for TBT.
4.6 Mixed Beam Element Based on TBT.
4.7 Four-Field Beam Element for TBT.
4.8 Linked Interpolation Beam Element for TBT.
4.9 Concluding Remarks.
Problems.
5 MULTIFIELD FORMULATIONS FOR ANALYSIS OF ELASTIC SOLIDS.
5.1 Governing Equations.
5.2 Displacement Formulation.
5.3 Stress Formulation.
5.4 Mixed Formulation.
5.5 Assumed Stress Field For Mixed Formulation.
5.6 Analysis of Nearly Incompressible Solids.
Problems.
6 PLATES AND SHELLS.
6.1 Kirchhoff Plate Theory.
6.2 Rectangular Kirchhoff Plate Elements.
6.3 Triangular Kirchhoff Plate Elements.
6.4 Mixed Formulation for Kirchhoff Plates.
6.5 Mindlin Plate Theory.
6.6 Displacement-Based Finite Elements for Mindlin Plates.
6.7 Multifield Elements for Mindlin Plates.
6.8 Analysis of Shell Structures.
Problems.
7 INTRODUCTION TO NONLINEAR PROBLEMS.
7.1 Nonlinear Differential Equation.
7.2 Solution Procedures for Nonlinear Problems.
7.3 Linearization and Directional Derivative.
Problems.
8 MATERIAL NONLINEARITY.
8.1 Analysis of Axially Loaded Bars.
8.2 Nonlinear Analysis of Trusses.
8.3 Material Nonlinearity in General Solids.
Problems.
9 GEOMETRIC NONLINEARITY.
9.1 Basic Continuum Mechanics Concepts.
9.2 Governing Differential Equations and Weak Forms.
9.3 Linearization of the Weak Form.
9.4 General Form of Element Tangent Matrices.
9.5 Constitutive Equations.
9.6 Computations For a Planar Analysis.
9.7 Deformation-Dependent Loading.
9.8 Linearized Buckling Analysis.
9.9 Appendix: Double Contraction of Tensors.
Problems.
10 CONTACT PROBLEMS.
10.1 Simple Normal Contact Example.
10.2 Contact Example Involving Friction.
10.3 General Contact Problems.
Problems.
BIBLIOGRAPHY.
INDEX.
