| Contents
Chapter 1 Introduction 1-34
1.1 Design and Analysis of a Component;
1.2 Approximate Method vs. Exact Method
1.3 Weighted Residual Methods
1.4 Variational Method or Rayleigh - Ritz Method
1.5 Principle of Minimum Potential Energy
1.6 Origin ofFEM
1.7 Principle ofFEM
1.8, Classification of FEM
1.9 Types of Analyses
1.10 Summary
Chapter 2 Matrix Operations 35-60
2.1 Types of Matrices
2.2 MatrixAlgebra
2.3 Detenninant
2.4 Inversion of a Matrix
2.5 Methods of Solution of Simultaneous Equations
2.5.1 By Inversion of the Coefficient Matrix
2.5.2 Direct Methods
2.5.3 Iterative Methods
2.6 Eigen Values and Eigen Vectors
2.7 Matrix Inversion Through Characteristic Equation
2.8 Summary
Chapter 3 Theory of Elasticity 61-84
3.1 Degrees of Freedom
3.2 Rigid Body Motion
3.3 Discrete Structures
3.4 Continuum Structures
3.5 Material Properties
3.6 Linear Analysis
3.7 Non-linear Analysis
3.8 Stiffness and Flexibility
3.9 Principle of Minimum Potential Energy
3.10 Stress and Strain at a Point
3.11 Principal Stresses
3.12 Mohr's Circle for Representation of 2-D Stresses
3.13 VonMises Stress
3.14 Theory of Elasticity
3.15 Summary
Chapter 4 Discrete (1-D) Elements
4.1 Degrees of Freedom of Different Elements
4.2 Calculation of Stiffness Matrix by Direct Method
4.3 Calculation of Stiffness Matrix by Variational Principle
4.4 Transformation Matrix
4.5 Assembling Element Stiffness Matrices
4.6 Boundary Conditions
4.7 Beam Element Stiffness Matrix by Variational Approach
4.8 General Beam Element
4.9 Pipe Element
4.10 Summary
Chapter 5 Continuum (2-D & 3-D) Elements
5.1 2-D Elements Subjected to In-plane Loads
5.2 Simplex, Complex and Multiplex Elements
53 Stiffness Matrix of a CST Element
5.3.1 Stiffness Matrix of a Right Angled Triangle
5.4 Convergence Conditions
5.5 Geometric Isotropy
5.6 Aspect Ratio
5.7 Inter-Element Compatibility
5.8 2-D Elements Subjected to Bending Loads
5.9 3-D Elements
5.10 Axi-symmetric Elements
5.11 Summary
Chapter 6 Higher Order and Iso-Parametric Elements
6.1 Higher Order Elements
6.2 Isoparametric Elements
6.3 Stiffness Matrices of Some Iso-parametric Elements
6.4 Jacobian
6.5 Strain-displacement Relations
6.6 Summary
Chapter 7
Factors Influencing Solution
7.1 Distributed Loads
7.2 Statically Equivalent Loads vs. Consistent Loads
7.3 Consistent Loads for a Few Common Cases
7.4 Assembling Element Stiffness Matrices
7.5 Automatic Mesh Generation
7.6 Optimum Mesh Model
7.7 Gaussian Points & Numerical Integration
7.8 Modelling Techniques
7.9 Boundary Conditions for Continuum Analysis
7.10 Transition Element
7.11 Substructuring or Super Element Approach
7.12 Deformed and Undeformed Plots
7.13 Summary
Chapter 8 Dynamic Analysis (undamped free vibrations)
8.1 Normalising Eigenvectors
8.2 Modelling for Dynamic Analysis
8.3 Mass Matrix
8.4 Summary
Chapter 9 Steady State Heat Conduction
9.1 Governing Equations
9.2 1-0 Heat Conduction
9.2.1 Heat Conduction Through a Wall
9.2.2 Heat Transfer Through a Fin
9.3 2-D heat Conduction in a Plate
9.4 Summary
Chapter 10 Design Validation and Other Types of Analysis
10.1 Compliance with Design Codes
10.2 Transient Heat Condition
10.3 Buckling of Columns
10.4 FatigueAnalysis;
10.5 Creep Analysis;
10.6 Damped Free Vibration;
10.7 Forced Vibration;
10.8 Torsion of a Non-circular Rod;
Chapter 11 Computational Fluid Dynamics
11.1 Introduction;
11.2 Governing Equation;
11.3 Finite Difference Method (FDM)
11.4 Elliptic Equations (or boundary value problems)
11.5 Finite Volume Method (FVM)
11.6 FDM vs. FEM
Chapter 12 Practical Analysis Using a Software
12.1 Using a General Purpose Software
12.2 Some Examples with ANSYS O |
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