1st Edition
Introduction to Finite Element Analysis Using MATLAB® and Abaqus
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