Finite Element Analysis

Bhavikati S. Finite Element Analysis (New Age International (P) Ltd., 2004)(ISBN 812241589X)(O)(347s) Preface......Page 6 Acknowledgement......Page 7 Contents......Page 8 1.2 General Description of the Method ......Page 14 1.3 A Brief Explanation of FEA for a Stress Analysis Problem ......Page 15 1.4 Finite Element Method vs Classical Methods ......Page 17 1.5 FEM vs FDM ......Page 18 1.7 Need for Studying FEM ......Page 19 References ......Page 20 2.2 Stresses in a Typical Element ......Page 22 2.3 Equations of Equilibrium ......Page 25 2.5 Strain Displacement Equations ......Page 26 2.6 Linear Constitutive Law......Page 27 Questions ......Page 32 3.2 Matrix Displacement Equations ......Page 34 3.3 Solution of Matrix Displacement Equations ......Page 41 3.4 Techniques of Saving Computer Memory Requirements ......Page 43 Questions ......Page 45 4.2 Element Shapes ......Page 46 4.3 Nodes ......Page 51 4.4 Nodal Unknowns ......Page 52 4.5 Coordinate Systems ......Page 53 Questions ......Page 66 5.1 Introduction ......Page 68 5.2 Polynomial Shape Functions ......Page 69 5.3 Convergence Requirements of Shape Functions ......Page 71 5.4 Derivation of Shape Functions Using Polynomials ......Page 74 5.5 Finding Shape Functions Using Lagrange Polynomials ......Page 95 5.6 Shape Functions for Serendipity Family Elements ......Page 102 5.7 Hermite Polynomials as Shape Functions ......Page 108 5.8 Construction of Shape Functions by Degrading Technique ......Page 111 Questions ......Page 115 6.2 Strain-Displacement Matrix for Bar Elements ......Page 117 6.3 Strain Displacement Matrix for CST Element ......Page 118 6.4 Strain Displacement Matrix for a Beam Element ......Page 120 Questions ......Page 121 7.2 Element Stiffness Matrix for CST Element by Direct Approach ......Page 123 7.3 Nodal Loads by Direct Approach ......Page 127 Questions ......Page 130 8.2 Galerkin's Method ......Page 131 8.3 Galerkin's Method Applied to Elasticity Problems ......Page 132 Questions ......Page 140 9.2 General Variational Method in Elasticity Problems ......Page 141 9.3 Potential Energy in Elastic Bodies ......Page 147 9.4 Principle of Minimum Potential Energy ......Page 149 9.5 The Rayleigh-Ritz Method ......Page 153 9.6 Variational Formulation in Finite Element Analysis ......Page 163 Questions ......Page 166 10.2 Nodes at Discontinuities ......Page 167 10.3 Refining Mesh ......Page 169 10.5 Finite Representation of Infinite Bodies ......Page 170 10.6 Element Aspect Ratio ......Page 171 10.8 Numbering System to Reduce Band Width ......Page 172 Questions ......Page 173 11.2 Tension Bars/Columns ......Page 174 11.3 Two Dimensional Trusses (Plane Trusses) ......Page 193 11.4 Three Dimensional Trusses (Space Trusses) ......Page 210 Questions ......Page 214 12.2 General Procedure when CST Elements are Used ......Page 217 12.3 Use of Higher Order Elements ......Page 229 Questions ......Page 230 13.1 Introduction ......Page 232 13.2 Coordinate Transformation ......Page 234 13.3 Basic Theorems of Isoparametric Concept ......Page 235 13.4 Uniqueness of Mapping ......Page 236 13.5 Isoparametric, Superparametric and Subparametric Elements ......Page 237 13.6 Assembling Stiffness Matrix ......Page 238 13.7 Numerical Integration ......Page 243 13.8 Numerical Examples ......Page 245 Questions ......Page 253 References ......Page 254 14.2 Beam Analysis Using Two Noded Elements ......Page 255 14.3 Analysis of Rigid Plane Frames Using 2 Noded Beam Elements ......Page 272 14.4 A Three Dimensional Rigid Frame Element ......Page 279 14.5 Timoshenko Beam Element ......Page 282 Questions ......Page 291 References ......Page 292 15.1 Introduction ......Page 293 15.2 Basic Relations in Thin Plate Theory ......Page 294 15.3 Displacement Models for Plate Analysis ......Page 295 15.4 Rectangular Plate Element with 12 Degrees of Freedom ......Page 297 15.5 Rectangular Plate Element with 16 Degrees of Freedom ......Page 302 15.6 Mindlin's Plate Element ......Page 305 References ......Page 312 16.2 Forces on Shell Element ......Page 314 16.3 Finite Elements of Shell Analysis ......Page 315 16.4 Finite Element Formulation Using Four Noded Degenerated Quadrilateral Shell Element ......Page 320 References ......Page 330 17.2 Non-Linear Problems ......Page 331 17.3 Analysis of Material Non-Linear Problems ......Page 333 17.4 Analysis of Geometric Non-Linear Problems ......Page 338 References ......Page 341 18.2 Commercially Available Standard Packages ......Page 342 18.3 Structure of a Finite Element Analysis Program ......Page 343 18.4 Pre and Post Processors ......Page 344 Questions ......Page 346 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.