The Finite Element Method Set. Its Basis and Fundamentals

Content: 
Preface for Volume I, Pages xiii-xiv
Preface for Volume II, Pages xiii-xv
Preface for Volume III, Pages xi-xii
Acknowledgements, Page xiii
1 - The standard discrete system and origins of the finite element method, Pages 1-18
2 - A direct physical approach to problems in elasticity: Plane stress, Pages 19-53
3 - Generalization of the finite element concepts. Galerkin-weighted residual and variational approaches, Pages 54-102
4 - ‘Standard’ and ‘hierarchical’ element shape functions: Some general families of C0 continuity, Pages 103-137
5 - Mapped elements and numerical integration — ‘infinite’ and ‘singularity elements’, Pages 138-186
6 - Problems in linear elasticity, Pages 187-228
7 - Field problems — heat conduction, electric and magnetic potential and fluid flow, Pages 229-263
8 - Automatic mesh generation, Pages 264-328
9 - The patch test, reduced integration, and non-conforming elements, Pages 329-355
10 - Mixed formulation and constraints — complete field methods, Pages 356-382
11 - Incompressible problems, mixed methods and other procedures of solution, Pages 383-428
12 - Multidomain mixed approximations — domain decomposition and ‘frame’ methods, Pages 429-455
13 - Errors, recovery processes and error estimates, Pages 456-499
14 - Adaptive finite element refinement, Pages 500-524
15 - Point-based and partition of unity approximations. Extended finite element methods, Pages 525-562
16 - The time dimension — semi-discretization of field and dynamic problems and analytical solution procedures, Pages 563-588
17 - The time dimension — discrete approximation in time, Pages 589-630
18 - Coupled systems, Pages 631-663
19 - Computer procedures for finite element analysis, Pages 664-667
1 - General problems in solid mechanics and non-linearity, Pages 1-16
2 - Galerkin method of approximation — irreducible and mixed forms, Pages 17-45
3 - Solution of non-linear algebraic equations, Pages 46-61
4 - Inelastic and non-linear materials, Pages 62-126
5 - Geometrically non-linear problems — finite deformation, Pages 127-157
6 - Material constitution for finite deformation, Pages 158-190
7 - Treatment of constraints — contact and tied interfaces, Pages 191-227
8 - Pseudo-rigid and rigid—flexible bodies, Pages 228-244
9 - Discrete element methods, Pages 245-277
10 - Structural mechanics problems in one dimension — rods, Pages 278-322
11 - Plate bending approximation: Thin (Kirchhoff) plates and C1 continuity requirements, Pages 323-381
12 - ‘Thick’ Reissner—Mindlin plates — irreducible and mixed formulations, Pages 382-425
13 - Shells as an assembly of flat elements, Pages 426-453
14 - Curved rods and axisymmetric shells, Pages 454-474
15 - Shells as a special case of three-dimensional analysis — Reissner—Mindlin assumptions, Pages 475-497
16 - Semi-analytical finite element processes — use of orthogonal functions and ‘finite strip’ methods, Pages 498-516
17 - Non-linear structural problems — large displacement and instability, Pages 517-546
18 - Multiscale modelling, Pages 547-589
19 - Computer procedures for finite element analysis, Pages 590-596
1 - Introduction to the equations of fluid dynamics and the finite element approximation, Pages 1-27
2 - Convection dominated problems — finite element approximations to the convection—diffusion-reaction equation, Pages 28-78
3 - The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow, Pages 79-109
4 - Incompressible Newtonian laminar flows, Pages 110-140
5 - Incompressible non-Newtonian flows, Pages 141-169
6 - Free surface and buoyancy driven flows, Pages 170-196
7 - Compressible high-speed gas flow, Pages 197-247
8 - Turbulent flows, Pages 248-273
9 - Generalized flow through porous media, Pages 274-291
10 - Shallow water problems, Pages 292-316
11 - Long and medium waves, Pages 317-348
12 - Short waves, Pages 349-381
13 - Computer implementation of the CBS algorithm, Pages 382-388
Appendix A - Matrix algebra, Pages 668-673
Appendix B - Tensor-indicial notation in the approximation of elasticity problems, Pages 674-682
Appendix C - Solution of simulataneous linear algebraic equations, Pages 683-691
Appendix D - Some integration formulae for a triangle, Page 692
Appendix E - Some integration formulae for a tetrahedron, Page 693
Appendix F - Some vector algebra, Pages 694-698
Appendix G - Integration by parts in two or three dimensions (Green\'s theorem), Pages 699-700
Appendix H - Solutions exact at nodes, Pages 701-703
Appendix I - Matrix diagonalization or lumping, Pages 704-709
Appendix A - Isoparametric finite element approximations, Pages 597-603
Appendix B - Invariants of second-order tensors, Pages 604-608
Appendix A - Non-conservative form of Navier-Stokes equations, Pages 389-390
Appendix B - Self-adjoint differential equations, Page 391
Appendix C - Postprocessing, Pages 392-394
Appendix D - Integration formulae, Pages 395-396
Appendix E - Convection—diffusion equations: verctor-valued variables, Pages 397-404
Appendix F - Edge-based finite element formulation, Pages 405-406
Appendix G - Multigrid method, Pages 407-408
Appendix H - Boundary layer—inviscid flow coupling, Pages 409-412
Appendix I - Mass-weighted averaged turbulence transport equations, Pages 413-415
Author index for Volume I, Pages 711-718
Subject index for Volume I, Pages 719-733
Author index for Volume II, Pages 609-617
Subject index for Volume II, Pages 619-631
Author index for Volume III, Pages 417-425
Subject index for Volume III, Pages 427-435
Color Plates for Volume I, Pages I-IV
Color Plates for Volume II, Pages I-IV
Color Plates for Volume III, Pages I-VI