Introduction to Finite Element Analysis Using MATLAB® and Abaqus

Introduction

Prologue

Finite Element Analysis and the User

Aim of the Book

Book Organization

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

Introduction

Stiffness Matrix

Uniformly Distributed Loading

Internal Hinge

Computer Code: beam.m

Problems

Analysis of a Simple Beam with Abaqus

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

Introduction

Stress Tensor

Deformation and Strain

Stress-Strain Constitutive Relations

Solved Problems

Introduction

General Formulation

Galerkin Method

Weak Form

Integrating by Part over Two and Three Dimensions (Green Theorem)

Rayleigh Ritz Method

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

Gauss Quadrature

Integration over a Reference Element

Integration over a Triangular Element

Solved 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

Definition

Strain–Displacement Relationship

Stress–Strain Relations

Finite Element Formulation

Programming

Analysis with Abaqus Using the 8-Node Quadrilateral

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

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