Introduction to Finite Element Analysis Using MATLAB® and Abaqus

Introduction Prologue Finite Element Analysis and the User Aim of the Book Book Organization Bar Element Introduction One-Dimensional Truss Element Global Stiffness Matrix Assembly Boundary Conditions Solution of the System of Equations Support Reactions Members' Forces Computer Code: truss.m Problems Analysis of a Simple Truss with Abaqus Beam Element Introduction Stiffness Matrix Uniformly Distributed Loading Internal Hinge Computer Code: beam.m Problems Analysis of a Simple Beam with Abaqus Rigid Jointed Frames Introduction Stiffness Matrix of a Beam-Column Element Stiffness Matrix of a Beam-Column Element In The Presence Of Hinged End Global and Local Coordinate Systems Global Stiffness Matrix Assembly and Solution for Unknown Displacements Computer Code: frame.m Analysis of a Simple Frame with Abaqus Stress And Strain Analysis Introduction Stress Tensor Deformation and Strain Stress Strain Constitutive Relations Problems Weighted Residual Methods Introduction General Formulation Galerkin Method Weak Form Integrating By Part over Two and Three Dimensions (Green Theorem) Rayleigh Ritz Method Finite Element Approximation Introduction General and Nodal Approximations Finite Element Approximation Basic Principles for the Construction of Trial Functions Two-Dimensional Finite Element Approximation Shape Functions of Some Classical Elements for C0 Problems Numerical Integration Introduction Gauss Quadrature Integration over a Reference Element Integration over a Triangular Element Worked Examples Plane Problems Introduction Finite Element Formulation for Plane Problems Spatial Discretization Constant Strain Triangle Linear Strain Triangle The Bi-Linear Quadrilateral The 8 Node Quadrilateral Solved Problem with Matlab Axisymmetric Problems Definition Strain Displacement Relationship Stress Strain Relations Finite Element Formulation Programming Analysis with Abaqus Using the 8-Node Quadrilateral Thin and Thick Plates Introduction Thin Plates Thick Plate Theory or Mindlin Plate Theory Linear Elastic Finite Element Analysis of Plates Boundary Conditions Computer Program for Thick Plates Using the 8-Node Quadrilateral Analysis with Abaqus Bibliography Appendix A: List of MATLAB function Appendix B: Statically equivalent nodal forces Appendix C: Index notation and transformation laws for tensors