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

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Updated mesh 636 DOF η = 15% Updated mesh 1200 DOF η = 18% Initial mesh Non-newtonian ¯ows ± metal and polymer forming 127 Adaptive refinement 808 DOF η = 11% Adaptive refinement 1242 DOF η = 10% t = 0 t = 1.1 s t = 7.7 s Fig. 4.24 (a) A material grid and updated and adapted meshes with material deformation ( percentage in energy norm).
128 Incompressible laminar ¯ow C L C L (b) Contours of state parameters at t = 2.9 s Load (MN) 0.4 0.3 0.2 0.1 624 ‘Effective’ strain (ε) t = 2.9 s 623 624624 624 643 649 644 Temperature (T) t = 2.9 s 2 (c) Load versus time 4 6 8 Time (s) 10 12 14 16 forming process. It is of interest simply to observe that here the energy norm of the error is the measure used. <strong>The</strong> details of various applications can be found in the extensive literature on the subject. This also deals with various sophisticated mesh updating procedures. One particularly successful method is the so-called ALE (arbitrary lagrangian±eulerian) method. 135ÿ139 Here the original mesh is given some prescribed velocity v in a manner ®tting the moving boundaries, and the convective terms in the equations 0.2 0.2 0.8 0.8 Fig. 4.24 (continued) A transient ext<strong>ru</strong>sion problem with temperature and strain-dependent yield. 132 Adaptive mesh re®nements uses T6/1D elements of Fig. 4.18.
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The Finite Element Method Fifth edi
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The Finite Element Method Fifth edi
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Dedication This book is dedicated t
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3.7 The performance of two- and sin
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...................................
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Volume 2: Solid and structural mech
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xiv Preface to Volume 3 this algori
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2 Introduction and the equations of
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10 Introduction and the equations o
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12 Introduction and the equations o
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14 Convection dominated problems We
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16 Convection dominated problems wh
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18 Convection dominated problems ch
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20 Convection dominated problems i.
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22 Convection dominated problems 2
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24 Convection dominated problems 2.
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26 Convection dominated problems ar
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28 Convection dominated problems Th
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30 Convection dominated problems co
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32 Convection dominated problems 2.
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34 Convection dominated problems ha
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36 Convection dominated problems an
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38 Convection dominated problems ac
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40 Convection dominated problems An
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42 Convection dominated problems U
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44 Convection dominated problems (a
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46 Convection dominated problems sp
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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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56 Convection dominated problems an
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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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Page 89 and 90: 76 A general algorithm for compress
Page 105 and 106: 92 Incompressible laminar ¯ow Cons
Page 107 and 108: 94 Incompressible laminar ¯ow and,
Page 109 and 110: 96 Incompressible laminar ¯ow V/V
Page 111 and 112: 98 Incompressible laminar ¯ow The
Page 113 and 114: 100 Incompressible laminar ¯ow 1.5
Page 115 and 116: 102 Incompressible laminar ¯ow p 1
Page 117 and 118: 104 Incompressible laminar ¯ow �
Page 119 and 120: 106 Incompressible laminar ¯ow x 2
Page 121 and 122: 108 Incompressible laminar ¯ow Thi
Page 127 and 128: 114 Incompressible laminar ¯ow (a)
Page 129 and 130: 116 Incompressible laminar ¯ow (b)
Page 131 and 132: 118 Incompressible laminar ¯ow wit
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Page 135 and 136: 122 Incompressible laminar ¯ow Fig
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Page 147 and 148: 134 Incompressible laminar ¯ow Fig
Page 149 and 150: 136 Incompressible laminar ¯ow 28.
Page 151 and 152: 138 Incompressible laminar ¯ow 71.
Page 153 and 154: 140 Incompressible laminar ¯ow 114
Page 155 and 156: 142 Incompressible laminar ¯ow 153
Page 157 and 158: 144 Free surfaces, buoyancy and tur
Page 183 and 184: 170 Compressible high-speed gas ¯o
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178 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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