The Finite Element Method using MATLAB

The Finite Element Method using MATLAB
اسم المؤلف
Young W. Kwon, Hyochoong Bang
التاريخ
2 فبراير 2019
المشاهدات
التقييم
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The Finite Element Method using MATLAB
Young W. Kwon
Hyochoong Bang
TABLE OF CONTENTS
CHAPTER 1. INTRODUCTION TO MATLAB 1
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 31
2.1 Methods of Weighted Residual
2.2 Weak Formulation
2.3 Piecewise Continuous Trial Function
2.4 Galerkin’s Finite Element Formulation
2.5 Variational Method
2.6 Rayleigh-Ritz Method
2.7 Rayleigh-Ritz Finite Element Method
Problems
CHAPTER 3. FINITE ELEMENT PROGRAMMING 51
3.1 Overall Program Structure
3.2 Input Data
3.3 Assembly of Element Matrices and Vectors
3.4 Application of Constraints
3.5 Example Programs
Problems
CHAPTER 4. DIRECT APPROACH WITH SPRING SYSTEM 71
4.1 Linear Spring
4.2 Axial Member
4.3 Torsional Member
774.4 Other Systems
Problems
CHAPTER 5. LAPLACE’S AND POISSON’S EQUATIONS 83
5.1 Governing Equation
5.2 Linear Triangular Element
5.3 Bilinear Rectangular Element
5.4 Boundary Integral
5.5 Transient Analysis
5.6 Time Integration Technique
5.7 Axisymmetric Analysis
5.8 Three-Dimensional Analysis
5.9 MATLAB Application to 2-D Steady State Analysis
5.10 MATLAB Application to Axisymmetric Analysis
5.11 MATLAB Application to Transient Analysis
5.12 MATLAB Application to 3-D Steady State Analysis
Problems
CHAPTER 6. ISOPARAMETRIC ELEMENTS 157
6.1 One-Dimensional Elements
6.2 Quadrilateral Elements
6.3 Triangular Elements
6.4 Gauss Quadrature
6.5 MATLAB Application to Gauss Quadrature
6.6 MATLAB Application to Laplace Equation
Problems
CHAPTER 7. TRUSS STRUCTURES 197
One-Dimensional Truss
7.2 Plane Truss
7.3 Space Truss
7.4 MATLAB Application to Static Analysis
7.5 MATLAB Application to Eigenvalue Analysis
7.6 MATLAB Application to Transient Analysis
Problems
CHAPTER 8. BEAM AND FRAME STRUCTURES 235
8.1 Euler-Bernoulli Beam
8.2 Timoshenko Beam
8.3 Beam Elements With Only Displacement Degrees of Freedom
8.4 Mixed Beam Element
8.5 Hybrid Beam Element
2538.6 Composite Beams
8.7 Two-Dimensional Frame Element
8.8 Three-Dimensional Frame Element
8.9 MATLAB Application to Static Analysis
8.10 MATLAB Application to Eigenvalue Analysis
8.11 MATLAB Application to Transient Analysis
8.12 MATLAB Application to Modal Analysis of Undamped System 288
8.13 MATLAB Application to Modal Analysis of Damped System 296
8.14 MATLAB Application to Frequency Response Analysis
Problems
CHAPTER 9. ELASTICITY PROBLEM 307
Plane Stress and Plane Strain
9.2 Force Vector
9.3 Energy Method
9.4 Three-Dimensional Solid
9.5 Axisymmetric Solid
9.6 Dynamic Analysis
9.7 MATLAB Application to 2-D Stress Analysis
9.8 MATLAB Application to Axisymmetric Analysis
9.9 MATLAB Application to 3-D Stress Analysis
Problems
CHAPTER 10. PLATE STRUCTURES 361
10.1 Classical Plate Theory
10.2 Classical Plate Bending Element
10.3 Shear Deformable Plate Element
10.4 Plate Element With Displacement Degrees of Freedom
10.5 Mixed Plate Element
10.6 Hybrid Plate Element
10.7 MATLAB Application
Problems
CHAPTER 11. CONTROL OF FLEXIBLE STRUCTURES 393
11.1 Introduction
11.2 Stability Theory
11.3 Stability of Multiple Degrees of Freedom Systems
11.4 Analysis of a Second Order System
11.5 State Space Form Description
11.6 Transfer Function Analysis
11.7 Control Law Design for State Space Systems
11.8 Linear Quadratic Regulator
11.9 Modal Control for Second Order Systems
11.10 Dynamic Observer
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