1st Edition

Introduction to Finite Element Analysis Using MATLAB® and Abaqus

By Amar Khennane Copyright 2013
    488 Pages 360 B/W Illustrations
    by CRC Press

    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

    Biography

    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.

    "A very good introduction to the Finite Element Method with a balanced treatment of theory and implementation."
    —F. Albermani, Reader in Structural Engineering, The University of Queensland, Australia