Zienkiewicz O.C., Taylor R.L. Vol. 3. The finite - tiera.ru

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Volume 1: The basis 1. Some preliminaries: the standard discrete system 2. A direct approach to problems in elasticity 3. Generalization of the ®nite 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 ®eld problems ± heat conduction, electric and magnetic potential, ¯uid ¯ow, etc 8. `Standard' and `hierarchical' element shape functions: some general families of C 0 continuity 9. Mapped elements and numerical integration ± `in®nite' and `singularity' elements 10. The patch test, reduced integration, and non-conforming elements 11. Mixed formulation and constraints ± complete ®eld methods 12. Incompressible problems, mixed methods and other procedures of solution 13. Mixed formulation and constraints ± incomplete (hybrid) ®eld methods, boundary/Tre€tz methods 14. Errors, recovery processes and error estimates 15. Adaptive ®nite element re®nement 16. Point-based approximations; element-free Galerkin ± and other meshless methods 17. The time dimension ± semi-discretization of ®eld and dynamic problems and analytical solution procedures 18. The time dimension ± discrete approximation in time 19. Coupled systems 20. Computer procedures for ®nite element analysis Appendix A. Matrix algebra Appendix B. Tensor-indicial notation in the approximation of elasticity problems Appendix C. Basic equations of displacement analysis 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 Appendix H. Solutions exact at nodes Appendix I. Matrix diagonalization or lumping
Volume 2: Solid and structural mechanics 1. General problems in solid mechanics and non-linearity 2. Solution of non-linear algebraic equations 3. Inelastic materials 4. Plate bending approximation: thin (Kirchho€) plates and C 1 continuity requirements 5. `Thick' Reissner±Mindlin plates ± irreducible and mixed formulations 6. Shells as an assembly of ¯at elements 7. Axisymmetric shells 8. Shells as a special case of three-dimensional analysis ± Reissner±Mindlin assumptions 9. Semi-analytical ®nite element processes ± use of orthogonal functions and `®nite strip' methods 10. Geometrically non-linear problems ± ®nite deformation 11. Non-linear structural problems ± large displacement and instability 12. Pseudo-rigid and rigid±¯exible bodies 13. Computer procedures for ®nite element analysis Appendix A: Invariants of second-order tensors
Page 1 and 2: The Finite Element Method Fifth edi
Page 3 and 4: The Finite Element Method Fifth edi
Page 5 and 6: Dedication This book is dedicated t
Page 7 and 8: 3.7 The performance of two- and sin
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Page 13 and 14: xiv Preface to Volume 3 this algori
Page 15 and 16: 2 Introduction and the equations of
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48 Convection dominated problems ag
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50 Convection dominated problems To
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52 Convection dominated problems C
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54 Convection dominated problems Th
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56 Convection dominated problems an
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58 Convection dominated problems Th
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60 Convection dominated problems Ma
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62 Convection dominated problems 47
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3 A general algorithm for compressi
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66 A general algorithm for compress
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92 Incompressible laminar ¯ow Cons
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94 Incompressible laminar ¯ow and,
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96 Incompressible laminar ¯ow V/V
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98 Incompressible laminar ¯ow The
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100 Incompressible laminar ¯ow 1.5
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102 Incompressible laminar ¯ow p 1
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104 Incompressible laminar ¯ow �
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106 Incompressible laminar ¯ow x 2
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108 Incompressible laminar ¯ow Thi
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114 Incompressible laminar ¯ow (a)
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116 Incompressible laminar ¯ow (b)
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118 Incompressible laminar ¯ow wit
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120 Incompressible laminar ¯ow The
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122 Incompressible laminar ¯ow Fig
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124 Incompressible laminar ¯ow and
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126 Incompressible laminar ¯ow U U
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128 Incompressible laminar ¯ow C L
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130 Incompressible laminar ¯ow are
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132 Incompressible laminar ¯ow sha
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134 Incompressible laminar ¯ow Fig
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136 Incompressible laminar ¯ow 28.
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138 Incompressible laminar ¯ow 71.
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140 Incompressible laminar ¯ow 114
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142 Incompressible laminar ¯ow 153
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144 Free surfaces, buoyancy and tur
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170 Compressible high-speed gas ¯o
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7 Shallow-water problems 7.1 Introd
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220 Shallow-water problems reduced
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222 Shallow-water problems Approxim
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224 Shallow-water problems These si
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226 Shallow-water problems h = 2 η
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228 Shallow-water problems Surface
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230 Shallow-water problems FL: 578
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232 Shallow-water problems B Fig. 7
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234 Shallow-water problems Time = 0
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236 Shallow-water problems Fig. 7.1
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238 Shallow-water problems where no
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240 Shallow-water problems 14. T.D.
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8 Waves Peter Bettess 8.1 Introduct
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244 Waves the familiar form where
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246 Waves of 10 nodes or thereabout
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248 Waves and the Astley wave envel
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250 Waves agreement with the analyt
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252 Waves Fig. 8.3 General wave dom
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254 Waves Relative errors (%) 10 8
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256 Waves (The indirect boundary in
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258 Waves where m is the number of
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260 Waves Fig. 17.6 of Volume 1. La
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262 Waves to using such coordinate
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264 Waves r/a 5 4 3 2 1 0 0 2 4 6 8
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266 Waves 8.16 Three-dimensional ef
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268 Waves wave elevations in shallo
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270 Waves integrals. Preliminary re
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272 Waves 39. R.J. Astley. FE mode
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9 Computer implementation of the CB
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276 Computer implementation of the
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292 Appendix A Again substituting t
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294 Appendix B As usual the domain
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296 Appendix B 5. While the piecewi
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Appendix C Edge-based ®nite elemen
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Appendix D Multigrid methods It is
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Appendix E Boundary layer±inviscid
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304 Appendix E In Fig. E.2, Cp is t
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Author index Page numbers in bold r
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Gerdes, K. 259, 264, 265, 272 Ghia,
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Nakos, D.E. 146, 165 Narayana, P.A.
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Wu, J. 67, 90; 102, 108, 112, 137;
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316 Subject index Blurring of the s
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318 Subject index Convected coordin
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320 Subject index Elements ± cont.
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322 Subject index Flows: buoyancy d
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324 Subject index Incompressible St
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326 Subject index Metals: hot, 120
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328 Subject index Prescribed tracti
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330 Subject index Shock interaction
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332 Subject index Theorem ± cont.
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334 Subject index Wave ± cont. ste
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Zienkiewicz O.C., Taylor R.L. Vol. 3. The finite - tiera.ru

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