Cover13; -- Copyright -- Preface -- Acknowledgement -- Contents -- Chapter 1 Introduction -- 1.1 General13; -- 1.2 General Description of the Method13; -- 1.3 A Brief Explanation of FEA for a Stress Analysis Problem13; -- 1.4 Finite Element Method vs Classical Methods13; -- 1.5 FEM vs FDM13; -- 1.6 A Brief History of FEM13; -- 1.7 Need for Studying FEM13; -- 1.8 Warning to FEA Package Users13; -- Questions13; -- References13; -- Chapter 2 Basic Equations in Elasticity -- 2.1 Introduction13; -- 2.2 Stresses in a Typical Element 13; -- 2.3 Equations of Equilibrium13; -- 2.4 Strains13; -- 2.5 Strain Displacement Equations13; -- 2.6 Linear Constitutive Law -- Questions13; -- Chapter 3 Matrix Displacement Formulation -- 3.1 Introduction13; -- 3.2 Matrix Displacement Equations13; -- 3.3 Solution of Matrix Displacement Equations13; -- 3.4 Techniques of Saving Computer Memory Requirements13; -- Questions13; -- Chapter 4 Element Shapes, Nodes, Nodal Unknowns and Coordinate Systems -- 4.1 Introduction13; -- 4.2 Element Shapes13; -- 4.3 Nodes13; -- 4.4 Nodal Unknowns13; -- 4.5 Coordinate Systems13; -- Questions13; -- Chapter 5 Shape Functions -- 5.1 Introduction13; -- 5.2 Polynomial Shape Functions13; -- 5.3 Convergence Requirements of Shape Functions13; -- 5.4 Derivation of Shape Functions Using Polynomials13; -- 5.5 Finding Shape Functions Using Lagrange Polynomials13; -- 5.6 Shape Functions for Serendipity Family Elements13; -- 5.7 Hermite Polynomials as Shape Functions 13; -- 5.8 Construction of Shape Functions by Degrading Technique13; -- Questions13; -- Chapter 6 Strain Displacement Matrix -- 6.1 Introduction13; -- 6.2 Strain-Displacement Matrix for Bar Elements13; -- 6.3 Strain Displacement Matrix for CST Element13; -- 6.4 Strain Displacement Matrix for a Beam Element13; -- Questions13; -- Chapter 7 Assembling Stiffness Equations-Direct Approach -- 7.1 Introduction13; -- 7.2 Element Stiffness Matrix for CST Element by Direct Approach13; -- 7.3 Nodal Loads by Direct Approach13; -- Questions13; -- Chapter 8 Assembling Stiffness Equations-Galerkin's Method, Virtual Work Method -- 8.1 Introduction13; -- 8.2 Galerkin's Method13; -- 8.3 Galerkin's Method Applied to Elasticity Problems13; -- Questions13; -- Chapter 9 Assembling Stiffness Equations-Variational Method -- 9.1 Introduction13; -- 9.2 General Variational Method in Elasticity Problems13; -- 9.3 Potential Energy in Elastic Bodies13; -- 9.4 Principle of Minimum Potential Energy13; -- 9.5 The Rayleigh-Ritz Method13; -- 9.6 Variational Formulation in Finite Element Analysis13; -- Questions13; -- Chapter 10 Discretization of Structures -- 10.1 Introduction13; -- 10.2 Nodes at Discontinuities13; -- 10.3 Refining Mesh13; -- 10.4 Use of Symmetry13; -- 10.5 Finite Representation of Infinite Bodies 13; -- 10.6 Element Aspect Ratio13; -- 10.7 Higher Order Elements vs Refined Mesh13; -- 10.8 Numbering System to Reduce Band Width13; -- Questions13; -- Chapter 11 Finite Element Analysis-Bars and Trusses -- 11.1 Introduction13; -- 11.2 Tension Bars/Columns13; -- 11.3 Two Dimensional Trusses (Plane Trusses)13; -- 11.4 Three Dimensional Truss.