The Finite Element Method Using MATLAB, Second Edition

The Finite Element Method Using MATLAB, Second Edition

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ISBN 9780849300967
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Features

  • Presents detailed, step-by-step procedures for understanding and programming of the finite element technique
  • Incorporates numerous examples of computer programs for boundary value, initial value, eigenvalue problems, and structural controls, including plate/shell analysis
  • Contains a new chapter of special topics for finite element applications
  • Includes access to webpages with numerous illustrative MATLAB functions and example problems
  • Solution manual available with qualifying course adoption
  • Summary

    Expanded to include a broader range of problems than the bestselling first edition, Finite Element Method Using MATLAB: Second Edition presents finite element approximation concepts, formulation, and programming in a format that effectively streamlines the learning process. It is written from a general engineering and mathematical perspective rather than that of a solid/structural mechanics basis.

    What's new in the Second Edition?

    Each chapter in the Second Edition now includes an overview that outlines the contents and purpose of each chapter. The authors have also added a new chapter of special topics in applications, including cracks, semi-infinite and infinite domains, buckling, and thermal stress. They discuss three different linearization techniques to solve nonlinear differential equations. Also included are new sections on shell formulations and MATLAB programs. These enhancements increase the book's already significant value both as a self-study text and a reference for practicing engineers and scientists.

    Table of Contents

    INTRODUCTION TO MATLAB
    Finite Element Method
    Overview of the Book
    About MATLAB
    Vector and Matrix Manipulations
    Matrix Functions
    Data Analysis Functions
    Tools for Polynomials
    Making Complex Numbers
    Nonlinear Algebraic Equations
    Solving Differential Equations
    Loop and Logical Statement
    Writing Function Subroutines
    File Manipulation
    Basic Input-Output Functions
    Plotting Tools
    APPROXIMATION TECHNIQUES
    Methods of Weighted Residual
    Weak Formulation
    Piecewise Continuous Trial Function
    Galerkin's Finite Element Formulation
    Variational Method
    Rayleigh-Ritz Method
    Rayleigh-Ritz Finite Element Method
    FINITE ELEMENT PROGRAMMING
    Overall Program Structure
    Input Data
    Assembly of Element Matrices and Vectors
    Application of Constraints
    Example Programs
    DIRECT APPROACH WITH SPRING SYSTEM
    Linear Spring
    Axial Member
    Torsional Member
    Other Systems
    LAPLACE'S AND POISSON'S EQUATIONS
    Governing Equation
    Linear Triangular Element
    Bilinear Rectangular Element
    Boundary Integral
    Transient Analysis
    Time Integration Technique
    Axisymmetric Analysis
    Three-Dimensional Analysis
    MATLAB Application to 2-D Steady State Analysis
    MATLAB Application to Axisymmetric Analysis
    MATLAB Application to Transient Analysis
    MATLAB Application to 3-D Steady State Analysis
    ISOPARAMETRIC ELEMENTS
    One-Dimensional Elements
    Quadrilateral Elements
    Triangular Elements
    Gauss Quadrature
    MATLAB Application to Gauss Quadrature
    MATLAB Application to Laplace Equation
    TRUSS STRUCTURES
    One-Dimensional Truss
    Plane Truss
    Space Truss
    MATLAB Application to Static Analysis
    MATLAB Application to Eigenvalue Analysis
    MATLAB Application to Transient Analysis
    BEAM AND FRAME STRUCTURES
    Euler-Bernoulli Beam
    Timoshenko Beam
    Beam Elements with Only Displacement Degrees of Freedom
    Mixed Beam Element
    Hybrid Beam Element
    Composite Beams
    Two-Dimensional Frame Element
    Three-Dimensional Frame Element
    MATLAB Application to Static Analysis
    MATLAB Application to Eigenvalue Analysis
    MATLAB Application to Transient Analysis
    MATLAB Application to Modal Analysis of Undamped Systems
    MATLAB Applications to Modal Analysis of Damped Systems
    MATLAB Applications to Frequency Response Analysis
    ELASTICITY PROBLEM
    Plane Stress and Plane Strain
    Force Vector
    Energy Method
    Three-Dimensional Solid
    Axisymmetric Solid
    Dynamic Analysis
    Thermal Stress
    MATLAB Application to 2-D Stress Analysis
    MATLAB Application to Axisymmetric Analysis
    MATLAB Application to 3-D Stress Analysis
    PLATE AND SHELL STRUCTURES
    Classical Plate Theory
    Classical Plate Bending Element
    Shear Deformable Plate Element
    Plate Element with Displacement Degrees of Freedom
    Mixed Plate Element
    Hybrid Plate Element
    Shell Made of Inplane and Bending Elements
    Shell Degenerated from 3-D Solid
    MATLAB Application to Plates
    MATLAB Application to Shells
    CONTROL OF FLEXIBLE STRUCTURES
    Introduction
    Stability Theory
    Stability of Multiple Degrees of Freedom Systems
    Analysis of a Second Order System
    State Space Form Description
    Transfer Function Analysis
    Control Law Design for State Space Systems
    Linear Quadratic Regulator
    Modal Control for Second Order Systems
    Dynamic Observer
    Compensator Design
    Output Feedback Design by Using Collocated Sensor/Actuator
    SPECIAL TOPICS
    Chapter Overview
    Stationary Singular Elements
    Quarter-Point Singular Elements
    Moving Singular Elements
    Semi-Infinite Element
    Thermal Stress in Layered Beams
    Buckling Analysis
    Nonlinear Analysis
    MATLAB Application to Buckling Problem
    MATLAB Application to Nonlinear Problem
    REFERENCES
    APPENDIX A: FEA MATLAB Function Files
    APPENDIX B: Examples of Pre- and Post-Processor
    INDEX
    Note: Each chapter also includes a Chapter Overview and Problems

    Downloads / Updates

    Resource OS Platform Updated Description Instructions
    0640.zip Platform type January 09, 2008

     
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