MATLAB Codes for Finite Element Analysis: Solids and Structures

Preface to the Second Edition
Preface to the First Edition
Contents
1 Short Introduction to MATLAB
	1.1 Introduction
	1.2 Getting Started
	1.3 Matrices
		1.3.1 Operating with Matrices
		1.3.2 Statements
		1.3.3 Matrix Functions
		1.3.4 Inverse
		1.3.5 Component Operations
		1.3.6 Colon Notation and Submatrices
	1.4 Loops and Repetitive Actions
		1.4.1 Conditionals, if and Switch
		1.4.2 Loops: For and While
		1.4.3 Relations and Logical Operators
		1.4.4 Logical Indexing
	1.5 Library and User Defined Functions
		1.5.1 Standard Library
		1.5.2 Vector Functions
		1.5.3 Matrix Functions
		1.5.4 Scripting and User\'s Defined Functions
		1.5.5 Debug Mode
	1.6 Linear Algebra
	1.7 Graphics
		1.7.1 2D Linear Plots
		1.7.2 3D Linear Plots
		1.7.3 3D Surface Plots
		1.7.4 Patch Plots
	References
2 Discrete Systems
	2.1 Introduction
	2.2 Springs and Bars
	2.3 Equilibrium at Nodes
	2.4 Some Basic Steps
	2.5 First Problem and First MATLAB Code
	References
3 Bars or Trusses
	3.1 Introduction
	3.2 A Bar Element
	3.3 Post-computation of Stress
	3.4 Numerical Integration
	3.5 Isoparametric Bar Under Uniform Load
	3.6 Fixed Bar with Spring Support
	3.7 Bar in Free Vibrations
	References
4 Trusses in 2D Space
	4.1 Introduction
	4.2 2D Trusses
	4.3 Stiffness Matrix
	4.4 Mass Matrix
	4.5 Post-computation of Stress
	4.6 First 2D Truss Problem
	4.7 Second 2D Truss Problem
	4.8 2D Truss with Spring
	4.9 2D Truss in Free Vibrations
	Reference
5 Trusses in 3D Space
	5.1 Introduction
	5.2 Basic Formulation
	5.3 First 3D Truss Problem
	5.4 Second 3D Truss Example
	5.5 3D Truss Problem in Free Vibrations
	Reference
6 Bernoulli Beams
	6.1 Introduction
	6.2 Bernoulli Beam
	6.3 Bernoulli Beam Problem
	6.4 Bernoulli Beam with Spring
	6.5 Bernoulli Beam Free Vibrations
	6.6 Stability of Bernoulli Beam
	References
7 Bernoulli 2D Frames
	7.1 Introduction
	7.2 2D Frame Element
	7.3 First 2D Frame Problem
	7.4 Second 2D Frame Problem
	7.5 2D Frame in Free Vibrations
8 Bernoulli 3D Frames
	8.1 Introduction
	8.2 Matrix Transformation in 3D Space
	8.3 Stiffness Matrix and Vector of Equivalent Nodal Forces
	8.4 Mass Matrix
	8.5 First 3D Frame Problem
	8.6 Second 3D Frame Problem
	8.7 3D Frame in Free Vibrations
9 Grids
	9.1 Introduction
	9.2 First Grid Problem
	9.3 Second Grid Problem
10 Timoshenko Beams
	10.1 Introduction
	10.2 Static Analysis
	10.3 Free Vibrations
	10.4 Buckling Analysis
	References
11 Plane Stress
	11.1 Introduction
	11.2 Displacements, Strains and Stresses
	11.3 Boundary Conditions
	11.4 Hamilton Principle
	11.5 Finite Element Discretization
	11.6 Interpolation of Displacements
	11.7 Element Energy
		11.7.1 Quadrilateral Element Q4
		11.7.2 Quadrilateral Elements Q8 and Q9
	11.8 Post-processing
		11.8.1 Stress Extrapolation
		11.8.2 Inter-element Averaging
	11.9 Plate in Traction
	11.10 2D Beam in Bending
	11.11 2D Beam in Free Vibrations
	Reference
12 Kirchhoff Plates
	12.1 Introduction
	12.2 Mathematical Background
	12.3 Finite Element Approximation
		12.3.1 Interpolation Functions
		12.3.2 Stiffness Matrix
	12.4 Isotropic Square Plate in Bending
	12.5 Orthotropic Square Plate in Bending
	References
13 Mindlin Plates
	13.1 Introduction
	13.2 The Mindlin Plate Theory
		13.2.1 Displacement Field
		13.2.2 Strains
		13.2.3 Stresses
		13.2.4 Hamilton\'s Principle
	13.3 Finite Element Discretization
	13.4 Stress Recovery
	13.5 Square Mindlin Plate in Bending
	13.6 Free Vibrations of Mindlin Plates
	13.7 Stability of Mindlin Plates
	References
14 Laminated Plates
	14.1 Introduction
	14.2 Displacement Field
	14.3 Strains
	14.4 Stresses
	14.5 Hamilton\'s Principle
	14.6 Finite Element Approximation
		14.6.1 Strain-Displacement Matrices
		14.6.2 Stiffness Matrix
		14.6.3 Load Vector
		14.6.4 Mass Matrix
	14.7 Stress Recovery
	14.8 Static Analysis
	14.9 Free Vibrations
	14.10 Buckling Analysis
		14.10.1 Buckling of Cross- and Angle-Ply Laminates
	References
15 Functionally Graded Structures
	15.1 Introduction
	15.2 Functionally Graded Materials
	15.3 Timoshenko Beam
		15.3.1 Finite Element Approximation
		15.3.2 Bending of Micro-Beams
		15.3.3 Free Vibrations of Micro-Beams
	15.4 Mindlin Plate
		15.4.1 Bending of Micro-Plates
		15.4.2 Free Vibrations of Micro-Plates
	References
16 Time Transient Analysis
	16.1 Introduction
	16.2 Numerical Time Integration
	16.3 Clamped Timoshenko Beam
	16.4 Simply-Supported Laminated Plate
	References
Index