The Finite Element Method Using MATLAB
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Book Description
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