The Finite Element Method Using MATLAB

Chapter 1. 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
Chapter 2. 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
Problems
Chapter 3. Finite Element Programming
Overall Program Structure
Input Data
Assembly of Element Matrices and Vectors
Application of Constraints
Example Programs
Problems
Chapter 4. Direct Approach with Spring System
Linear Spring
Axial Member
Torsional Member
Other Systems
Problems
Chapter 5. 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
Problems
Chapter 6. Isoparametric Elements
One-Dimensional Elements
Quadrilateral Elements
Triangular Elements
Gauss Quadrature
MATLAB Application to Gauss Quadrature
MATLAB Application to Laplace Equation
Problems
Chapter 7. Truss Structures
One-Dimensional Truss
Plane Truss
Space Truss
MATLAB Application to Static Analysis
MATLAB Application to Eigenvalue Analysis
MATLAB Application to Transient Analysis
Problems
Chapter 8. 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 System
MATLAB Application to Modal Analysis of Damped System
MATLAB Application to Frequency Response Analysis
Problems
Chapter 9. Elasticity Problem
Plane Stress and Plane Strain
Force Vector
Energy Method
Three-Dimensional Solid
Axisymmetric Solid
Dynamic Analysis
MATLAB Application to 2-D Stress Analysis
MATLAB Application to Axisymmetric Analysis
MATLAB Application to 3-D Stress Analysis
Problems
Chapter 10. Plate 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
MATLAB Application
Problems
Chapter 11. 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
Problems
References
Appendix A: FEA MATLAB Function Files
Index