Cover -- Preface -- Acknowledgement -- Contents -- Chapter 1 Introduction -- 1.1 General -- 1.2 General Description of the Method -- 1.3 A Brief Explanation of FEA for a Stress Analysis Problem -- 1.4 Finite Element Method vs Classical Methods -- 1.5 FEM vs FDM -- 1.6 A Brief History of FEM -- 1.7 Need for Studying FEM -- 1.8 Warning to FEA Package Users -- Questions -- References -- Chapter 2 Basic Equations in Elasticity -- 2.1 Introduction -- 2.2 Stresses in a Typical Element -- 2.3 Equations of Equilibrium -- 2.4 Strains -- 2.5 Strain Displacement Equations -- 2.6 Linear Constitutive Law -- Questions -- Chapter 3 Matrix Displacement Formulation -- 3.1 Introduction -- 3.2 Matrix Displacement Equations -- 3.3 Solution of Matrix Displacement Equations -- 3.4 Techniques of Saving Computer Memory Requirements -- Questions -- Chapter 4 Element Shapes, Nodes, Nodal Unknowns and Coordinate Systems -- 4.1 Introduction -- 4.2 Element Shapes -- 4.3 Nodes -- 4.4 Nodal Unknowns -- 4.5 Coordinate Systems -- Questions -- Chapter 5 Shape Functions -- 5.1 Introduction -- 5.2 Polynomial Shape Functions -- 5.3 Convergence Requirements of Shape Functions -- 5.4 Derivation of Shape Functions Using Polynomials -- 5.5 Finding Shape Functions Using Lagrange Polynomials -- 5.6 Shape Functions for Serendipity Family Elements -- 5.7 Hermite Polynomials as Shape Functions -- 5.8 Construction of Shape Functions by Degrading Technique -- Questions -- Chapter 6 Strain Displacement Matrix -- 6.1 Introduction -- 6.2 Strain-Displacement Matrix for Bar Elements -- 6.3 Strain Displacement Matrix for CST Element -- 6.4 Strain Displacement Matrix for a Beam Element -- Questions -- Chapter 7 Assembling Stiffness Equations-Direct Approach -- 7.1 Introduction -- 7.2 Element Stiffness Matrix for CST Element by Direct Approach -- 7.3 Nodal Loads by Direct Approach -- Questions.

Chapter 8 Assembling Stiffness Equations-Galerkin's Method, Virtual Work Method -- 8.1 Introduction -- 8.2 Galerkin's Method -- 8.3 Galerkin's Method Applied to Elasticity Problems -- Questions -- Chapter 9 Assembling Stiffness Equations-Variational Method -- 9.1 Introduction -- 9.2 General Variational Method in Elasticity Problems -- 9.3 Potential Energy in Elastic Bodies -- 9.4 Principle of Minimum Potential Energy -- 9.5 The Rayleigh-Ritz Method -- 9.6 Variational Formulation in Finite Element Analysis -- Questions -- Chapter 10 Discretization of Structures -- 10.1 Introduction -- 10.2 Nodes at Discontinuities -- 10.3 Refining Mesh -- 10.4 Use of Symmetry -- 10.5 Finite Representation of Infinite Bodies -- 10.6 Element Aspect Ratio -- 10.7 Higher Order Elements vs Refined Mesh -- 10.8 Numbering System to Reduce Band Width -- Questions -- Chapter 11 Finite Element Analysis-Bars and Trusses -- 11.1 Introduction -- 11.2 Tension Bars/Columns -- 11.3 Two Dimensional Trusses (Plane Trusses) -- 11.4 Three Dimensional Trusses (Space Trusses) -- Questions -- Chapter 12 Finite Element Analysis-Plane Stress and Plane Strain Problems -- 12.1 Introduction -- 12.2 General Procedure when CST Elements are Used -- 12.3 Use of Higher Order Elements -- Questions -- Chapter 13 Isoparametric Formulation -- 13.1 Introduction -- 13.2 Coordinate Transformation -- 13.3 Basic Theorems of Isoparametric Concept -- 13.4 Uniqueness of Mapping -- 13.5 Isoparametric, Superparametric and Subparametric Elements -- 13.6 Assembling Stiffness Matrix -- 13.7 Numerical Integration -- 13.8 Numerical Examples -- Questions -- References -- Chapter 14 Analysis of Beams and Rigid Frames -- 14.1 Introduction -- 14.2 Beam Analysis Using Two Noded Elements -- 14.3 Analysis of Rigid Plane Frames Using 2 Noded Beam Elements -- 14.4 A Three Dimensional Rigid Frame Element.

14.5 Timoshenko Beam Element -- Questions -- References -- Chapter 15 Bending of Thin Plates -- 15.1 Introduction -- 15.2 Basic Relations in Thin Plate Theory -- 15.3 Displacement Models for Plate Analysis -- 15.4 Rectangular Plate Element with 12 Degrees of Freedom -- 15.5 Rectangular Plate Element with 16 Degrees of Freedom -- 15.6 Mindlin's Plate Element -- Questions -- References -- Chapter 16 Analysis of Shells -- 16.1 Introduction -- 16.2 Forces on Shell Element -- 16.3 Finite Elements of Shell Analysis -- 16.4 Finite Element Formulation Using Four Noded Degenerated Quadrilateral Shell Element -- Questions -- References -- Chapter 17 Non Linear Analysis -- 17.1 Introduction -- 17.2 Non-Linear Problems -- 17.3 Analysis of Material Non-Linear Problems -- 17.4 Analysis of Geometric Non-Linear Problems -- 17.5 Analysis of Both Material and Geometric Non-Linear Problems -- Questions -- References -- Chapter 18 Standard Packages and Their Features -- 18.1 Introduction -- 18.2 Commercially Available Standard Packages -- 18.3 Structure of a Finite Element Analysis Program -- 18.4 Pre and Post Processors -- 18.5 Desirable Features of FEA Packages -- Questions.

With the authors experience of teaching the courses on Finite Element Analysis to undergraduate and postgraduate students for several years, the author felt need for writing this book. The concept of finite element analysis, finding properties of various elements and assembling stiffness equation is developed systematically by splitting the subject into various chapters.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.