MATLAB Codes for Finite Element Analysis: Solids and Structures (Solid Mechanics and Its Applications (157), Band 157)

✍ Scribed by Antonio J. M. Ferreira, Nicholas Fantuzzi

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 354
• Edition: 2
• Category: Library

✦ Synopsis

This book illustrates how MATLAB compact and powerful programming framework can be very useful in the finite element analysis of solids and structures. The book shortly introduces finite element concepts and an extensive list of MATLAB codes for readers to use and modify. The book areas range from very simple springs and bars to more complex beams and plates in static bending, free vibrations, buckling and time transient problems. Moreover, laminated and functionally graded material structures are introduced and solved.

✦ Table of Contents

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