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.
Aus dem Inhalt CONTENTS OF THE BOOK WEB SITE.
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.
