# The Finite Element Method Using Matlab 2Edition

₹995.00

- Publisher: Taylor & Francis
- ISBN-13: 9780849300967
- Pages: 624
- Binding: Hardcover
- Year of Pub / Reprint Year: 2000

## Description

**About The Book**

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