Introduction to Finite Element Analysis Using MATLAB® and Abaqus

This book introduces the theory of the finite element method using a balanced approach between its mathematical formulations and programming implementation. The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. All of the key steps are presented in great detail. MATLAB will allow the reader to focus on the finite element method by alleviating the programming burden. Detailed step-by-step procedures for solving sample problems with Abaqus interactive and keyword editions are provided at the end of each chapter.

There are some books that target the theory of the finite element, while others focus on the programming side of things. Introduction to Finite Element Analysis Using MATLAB® and Abaqus accomplishes both. This book teaches the first principles of the finite element method. It presents the theory of the finite element method while maintaining a balance between its mathematical formulation, programming implementation, and application using commercial software. The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. MATLAB is a high-level language specially designed for dealing with matrices, making it particularly suited for programming the finite element method, while Abaqus is a suite of commercial finite element software. Includes more than 100 tables, photographs, and figures Provides MATLAB codes to generate contour plots for sample results Introduction to Finite Element Analysis Using MATLAB and Abaqus introduces and explains theory in each chapter, and provides corresponding examples. It offers introductory notes and provides matrix structural analysis for trusses, beams, and frames. The book examines the theories of stress and strain and the relationships between them. The author then covers weighted residual methods and finite element approximation and numerical integration. He presents the finite element formulation for plane stress/strain problems, introduces axisymmetric problems, and highlights the theory of plates. The text supplies step-by-step procedures for solving problems with Abaqus interactive and keyword editions. The described procedures are implemented as MATLAB codes and Abaqus files can be found on the CRC Press website.

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 Solved 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 Solved Problems Plane Problems Introduction Finite Element Formulation for Plane Problems Spatial Discretization Constant Strain Triangle Linear Strain Triangle The Bilinear 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 Appendix A: List of MATLAB Modules and Functions Appendix B: Statically Equivalent Nodal Forces Appendix C: Index Notation and Transformation Laws for Tensors References and Bibliography Index

Dr. Amar Khennane is a senior lecturer in the School of Engineering and Information Technology at the University of New South Wales, Canberra, Australian Capital Territory, Australia. He earned his PhD in civil engineering from the University of Queensland, Australia; a Master of Science in structural engineering from Heriot-Watt University, United Kingdom; and a bachelor’s degree in civil engineering from the University of Tizi-Ouzou, Algeria. His teaching experience spans 20 years, and two continents. He has taught structural analysis, structural mechanics, and the finite element method at various universities.