FINITE ELEMENTS FOR ANALYSIS AND DESIGN
CONTENTS PREFACE 1 SOME PRELIMINARIES: THE STANDARD DISCRETE SYSTEM 2 A DIRECT APPROACH TO PROBLEMS IN ELASTICITY 3 GENERALIZATION OF THE FINITE ELEMENT CONCEPTS GALERKIN-WEIGHTED RESIDUAL AND VARIATIONAL APPROACHES 4 PLANE STRESS AND PLANE STRAIN 5 AXISYMMETRIC STRESS ANALYSIS 6 THREE-DIMENSIONAL STRESS ANALYSIS 7 STEADY-STATE FIELD PROBLEMS - HEAT CONDUCTION, ELECTRIC AND MAGNETIC POTENTIAL, FLUID FLOW, ETC 8 'STANDARD' AND 'HIERARCHICAL' ELEMENT SHAPE FUNCTIONS: SOME GENERAL FAMILIES OF C0 CONTINUITY 9 MAPPED ELEMENTS AND NUMERICAL INTEGRATION - 'INFINITE' AND 'SINGULARITY' ELEMENTS 10 THE PATCH TEST, REDUCED INTEGRATION, AND NON-CONFORMING ELEMENTS 11 MIXED FORMULATION AND CONSTRAINTS - COMPLETE FIELD METHODS 12 INCOMPRESSIBLE MATERIALS, MIXED METHODS AND OTHER PROCEDURES OF SOLUTION 13 MIXED FORUMATION AND CONSTRAINTS - INCOMPLETE (HYBRID) FIELD METHODS, BOUNDARY/TREFFTZ METHODS 14 ERRORS, RECOVERY PROCESSES AND ERROR ESTIMATES 15 ADAPTIVE FINITE ELEMENT REFINEMENT 16 POINT-BASED APPROXIMATIONS; ELEMENT-FREE GALERKIN - AND OTHER MESHLESS METHODS 17 THE TIME DIMENSION - SEMI-DISCRETIZATION OF FIELD AND DYNAMIC PROBLEMS AND ANALYTICAL SOLUTION PROCEDURES 18 THE TIME DIMENSION - DISCRETE APPROXIMATION IN TIME 19 COUPLE SYSTEMS 20 COMPUTER PROCEDURES FOR FINITE ELEMENT ANALYSIS APPENDIX A MATRIX ALGEBRA APPENDIX B TENSOR-INDICIAL NOTATION IN THE APPROXIMATION OF ELASTICITY PROBLEMS APPENDIX C BASIC EQUATIONS OF DISPLACEMENT ANALYSIS (CHAPTER 2) APPENDIX D SOME INTEGRATION FORMULAE FOR A TRIANGLE APPENDIX E SOME INTEGRATION FORMULAE FOR A TETRAHEDRON APPENDIX F SOME VECTOR ALGEBRA APPENDIX G INTEGRATION BY PARTS IN TWO OR THREE DIMENSIONS (GREEN'S THEOREM) APPENDIX H SOLUTIONS EXACT AT NODES APPENDIX I MATRIX DIAGONALIZATION OR LUMPING AUTHOR INDEX SUBJECT INDEX BLANK PAGE