Preface to the Adapted Edition xi Preface xiii 1. MATHEMATICAL BACKGROUND 1.1-1.33 1.1 Introduction- 1.1 1.2 Vector Analysis.. 1.1 1.3 Matrix Theory . 1.2 1.4 Differential Equations . 1.4 1.5 Cartesian Tensors.. 1.6 Solved Problems 1.7 Multiple Choice Questions 1.23 Short Answer Questions .. 1.24 Supplementary Problems.. 1.25 Answers to Multiple Choice Questions 1.28 Answers to Supplementary Problems 1.28 2. ONE-DIMENSIONAL FINITE ELEMENTS 2.1-2.54 2.1Introduction 2.1 2.2Mathematical Equations of Engineering 2.2 2.3 Variational Functions 2.5 2.4Interpolation Function .. 2.6 2.5Shape Functions .. 2.7 2.6Stiffness Matrix..- .. 2.7 2.7Connectivity ..- .. 2.7 2.8 Boundary Conditions .. 2.8 2.9 Problems in Cylindrical Coordinates 2.9 2.10 The Direct Method . 2.9 Solved Problems 2.10 Multiple Choice Questions.. 2.48 Short Answer Questions . 2.50 Supplementary Problems.. 2.51 Answers to Multiple Choice Questions 2.52 Answers to Supplementary Problems 2.52 3. TWO-DIMENSIONAL FINITE ELEMENTS 3.1-3.58 3.1Introduction .. 3.1 3.2Two-Dimensional Boundary-Value Problems. 3.2 3.3Connectivity and Nodal Coordinates. 3.2 3.4 Theory of Elasticity 3.3 3.5Variational Functions.. 3.4 3.6 Triangular Elements and Area Coordinates 3.5 3.7Transformations 3.5 3.8Cylindrical Coordinates.. 3.6 Solved Problems . 3.7 Multiple Choice Questions 3.45 Short Answer Questions 3.47 Supplementary Problems 3.48 Answers to Multiple Choice Questions 3.52 Answers to Supplementary Problems 3.52 4. BEAM AND FRAME FINITE ELEMENTS 4.1-4.43 4.1 Introduction.. .. 4.1 4.2Governing Differential Equation . 4.2 4.3The Displacement Method for Beam Analysis . 4.3 4.4Beam Finite Elements 4.5 4.5Matrix Transformations .. 4.5 Solved Problems 4.6 Multiple Choice Questions.. 4.35 Short Answer Questions .. 4.37 Supplementary Problems 4.37 Answers to Multiple Choice Questions . 4.41 Answers to Supplementary Problems 4.41 5. VARIATIONAL PRINCIPLES, GALERKIN APPROXIMATION, AND PARTIAL DIFFERENTIAL EQUATIONS 5.1-5.39 5.1 Introduction- .. 5.1 5.2Variational Principles . 5.2 5.3Galerkin Approximation 5.4 5.4 Coupled Partial Differential Equations . 5.5 5.5Initial-Value Problems- .. 5.5 Solved Problems . 5.5 Multiple Choice Questions.. 5.29 Short Answer Questions . 5.31 Supplementary Problems. 5.32 Answers to Multiple Choice Questions .. 5.34 Answers to Supplementary Problems 5.34 6. ISOPARAMETRIC FINITE ELEMENTS 6.1-6.45 6.1 Introduction 6.1 6.2 Numerical Integration 6.2 6.3 Interpolation Formulas and Shape Function Formulas.. 6.2 6.4 Generalized Coordinates . 6.3 6.5 Isoparametric Elements 6.4 6.6 Axisymmetric Formulations 6.5 Solved Problems . 6.5 Multiple Choice Questions.. 6.33 Short Answer Questions 6.35 Supplementary Problems 6.35 Answers to Multiple Choice Questions 6.38 Answers to Supplementary Problems . 6.38 7. SELECTED TOPICS IN FINITE ELEMENT ANALYSIS 7.1-7.41 7.1 Introduction. 7.1 7.2 Initial-Value Problems 7.2 7.3 Eigenvalue Problems 7.3 7.4 Three-Dimensional Finite Elements 7.3 7.5 Higher-Order Finite Elements 7.4 7.6 Element Continuity .. 7.5 7.7 Plate Finite Elements 7.5 Solved Problems .. 7.9 Multiple Choice Questions 7.30 Short Answer Questions .. 7.32 Supplementary Problems 7.32 Answers to Multiple Choice Questions .. 7.35 Answers to Supplementary Problems 7.35 Appendix A.I-A. 19 Bibliography B.1-B.3 Solved Preblem Index of Applications S.1-S.2 Index 1.1-1.3