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

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instance, assume that the `viscous' ¯ow of the problem of Fig. 4.21 is that of an ideally plastic material under isothermal conditions modelling an extrusion process and obtain the solution shown in Table 4.1. For such a material exact extrusion forces can be calculated 130 and the table shows the errors obtained with the ¯ow formulation using di€erent triangular elements of Fig. 4.18 and two meshes. 93 The ®ne mesh here was arrived at using error estimates and a single adaptive remeshing. In general the problem of steady-state ¯ow is accompanied by the evolution of temperature (and other state parameters such as the total strain invariant ") and here it is necessary to couple the solution with the heat balance and possibly other evolution equations. The evolution of heat has already been discussed and the appropriate conservation equations such as Eq. (4.6). It is convenient now to rewrite this equation in a modi®ed form. Firstly, we note that the kinetic energy is generally negligible in the problems considered and that with a constant speci®c heat c per unit volume we can write E e ˆ ^cT …4:50a† where ^c is the speci®c heat. Secondly, we observe that the internal work dissipation Prescribed velocity (a) Steady rate Extrusion Rolling Fig. 4.20 Forming processes typically used in manufacture. Non-newtonian ¯ows ± metal and polymer forming 121 Prescribed traction
122 Incompressible laminar ¯ow Fig. 4.20 Continued. (b) Transient Moving mesh Extrusion Rolling Forging Cutting Sheet forming (deep drawing)
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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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68 A general algorithm for compress
Page 83 and 84: 70 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
Page 133: 120 Incompressible laminar ¯ow The
Page 137 and 138: 124 Incompressible laminar ¯ow and
Page 139 and 140: 126 Incompressible laminar ¯ow U U
Page 141 and 142: 128 Incompressible laminar ¯ow C L
Page 143 and 144: 130 Incompressible laminar ¯ow are
Page 145 and 146: 132 Incompressible laminar ¯ow sha
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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172 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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