CONTENTS PREFACE ix INTRODUCTION TO FINITE ELEMENTS 1.1Finite-Element Concepts 1 1.2Stresses and Strains in Elastic Continua 6 1.3Virtual Work Basis of Finite-Element Method 9 1.4Shape Functions and Generalized Displacements 15 1.5One-Dimensional Elements 17 1.6Generalized Stresses and Strains 27 1.7Axis Transformations 29 1.8Assemblage of Elements and Solution 35 1.9Potential-Energy Bases of Finite-Element Method 37 1.10Convergence Criteria 40 1.11Computer Programs 42 References 43 Problems 44 2 PLANE STRESS AND PLANE STRAIN 51 2.1Two-Dimensional Stresses and Strains 51 2.2Triangular Elements 61 2.3Rectangular Elements 72 2.4 Quadrilateral Elements 82 2.5 Program PSCST and Applications 84 References 98 Problems 99 ISOPARAMETRIC FORMULATIONS 103 3.1 Introduction 103 3.2Natural Coordinates 104 3.3 Numerical Integration 111 3.4 Quadrilateral Elements 115 3.5 Triangular Elements 123 3.6 Programs PSQ4 and PSQ8 and Applications 127 References 140 Problems 141 4 GENERAL SOLIDS 144 4.1 Stresses and Strains in Solids 144 4.2 Natural Coordinates 149 4.3 Numerical Integration 154 4.4 Hexahedral Elements 156 4.5 Tetrahedral Elements 161 4.6 Programs SOH8 and SOH20 and Applications 165 References 176 Problems 177 5 AXISYMMETRIC SOLIDS 180 5.1 Axisymmetric Stresses and Strains 180 5.2 Triangular and Rectangular Sections 182 5.3 Quadrilateral Sections 186 5.4 Nonaxisymmetric Loads 189 5.5 Programs AXSOQ4 and AXSOQ8 and Applications 192 References 197 Problems 197 FLEXURE IN PLATES 200 6.1 Flexura! Stresses and Strains in Plates 200 6.2 Rectangular Elements 205 6.3 Triangular Elements 212 6.4 Quadrilateral as Specialization of Hexahedron 214 6.5 Annular Element 222 6.6 Program PBQ8 and Applications 226 References 232 Problems 233 7 GENERAL SHELLS 236 7.1 Introduction 236 7.2 Flat-Facet Elements 238 7.3 Specialization of Hexahedron 240 7.4 Program SHQ8 and Applications 248 References 253 8AXISYMMETRIC SHELLS 255 8.1 Introduction 255 8.2 Straight Section 256 8.3 Curved Section 262 8.4 Nonaxisymmetric Loads 269 8.5 Program AXSH3 and Applications 273 References 278 7VIBRATIONAL ANALYSIS 279 9.1 Introduction 279 9.2 Consistent Mass Matrices 282 9.3 Eigenvalue Problem for Vibrations 296 9.4 Reduction of Stiffness and Mass Matrices 298 9.5 Program VIBPQ8 and Applications 305 References 310 Problems 311 10 INSTABILITY ANALYSIS 315 10.1Introduction 315 10.2 Initial Stress Stiffness Matrices 316 10.3 Linear Instability and Vibrations 326 10.4 Nonlinear Instability Analysis 331 10.5 Program BUCPQ8 and Applications 333 References 338 Problems 339 Notation 342 Appendix A: Integration Formulas 346 A.1 Line 346 A.2 Triangle 346 A.3 Tetrahedron 347 Appendix B: Gaussian Quadrature 349 Appendix C: Computer Solution Routines 353 C.1 Factorization of Symmetric Matrices 353 C.2 Subprogram VECFAC 355 C.3 Subprogram VECSOL 358 C.4 Subprogram SKYFAC 358 C.5 Subprogram SKYSOL 359 Appendix D : Flow Chart for Program PSCST 365 Answers to Problems 387 General References: Textbooks on Finite Elements 393 Index395