Finite Element Method - The Basis (Volume 1)

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DedicationThis book is dedicated to our wives Helen and MaryLou and our families for their support and patienceduring the preparation of this book, and also to all ofour students and colleagues who over the years havecontributed to our knowledge of the ®nite elementmethod. In particular we would like to mentionProfessor Eugenio OnÄ ate and his group at CIMNE fortheir help, encouragement and support during thepreparation process.
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Page 5: The Finite ElementMethodFifth editi
Page 9 and 10: viiiContents3.5 Partial discretizat
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Page 17 and 18: xviPrefaceIn Volumes 1, 2 and 3 the
Page 19 and 20: 2 Some preliminaries: the standard
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40 Generalization of the ®nite ele
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88 Plane stress and plane strainymv
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90 Plane stress and plane strainSub
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92 Plane stress and plane strainyzx
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94 Plane stress and plane strainfro
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96 Plane stress and plane strainAga
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98 Plane stress and plane strain®n
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100 Plane stress and plane strainy
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102 Plane stress and plane strain4.
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104 Plane stress and plane strainBu
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106 Plane stress and plane strainEq
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Fig. 4.14 An underground power stat
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110 Plane stress and plane strainA
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5Axisymmetric stress analysis5.1 In
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114 Axisymmetric stress analysis5.2
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116 Axisymmetric stress analysiszrF
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118 Axisymmetric stress analysisIn
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122 Axisymmetric stress analysis100
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126 Axisymmetric stress analysisRef
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128 Three-dimensional stress analys
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Computed valueExact value45 tonsSec
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7Steady-state ®eld problems ± hea
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142 Steady-state ®eld problemswhic
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144 Steady-state ®eld problemswith
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146 Steady-state ®eld problemsymsL
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148 Steady-state ®eld problems2042
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H = 100H = 094.093.694.2 93.7 94.48
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C L0 0 0 0 0 0152 Steady-state ®el
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154 Steady-state ®eld problemsφ =
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156 Steady-state ®eld problemsFig.
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158 Steady-state ®eld problemsElem
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160 Steady-state ®eld problemsand
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162 Steady-state ®eld problems8. J
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8`Standard' and `hierarchical'eleme
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166 `Standard' and `hierarchical' e
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9Mapped elements and numericalinteg
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yη = 1 ξ = 1ηη = 1ζηζξξη
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204 Mapped elements and numerical i
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1010zyσ z(r = 0)0-10 0lb/in 24030l
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10The patch test, reduced integrati
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252 The patch test, reduced integra
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11Mixed formulation and constraints
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278 Mixed formulation and constrain
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308 Incompressible materials, mixed
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13Mixed formulation and constraints
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366 Errors, recovery processes and
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5000300020001000500300200100NDF400.
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Nodal values determinedfrom the pat
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402 Adaptive ®nite element re®nem
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430 Point-based approximations(a)(b
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432 Point-based approximations®t a
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434 Point-based approximations86u v
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436 Point-based approximations1.00.
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438 Point-based approximationsdisco
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440 Point-based approximationsx1.5u
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442 Point-based approximationsappro
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444 Point-based approximationsatten
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446 Point-based approximationsThus,
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448 Point-based approximations15105
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450 Point-based approximationsCollo
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452 Point-based approximationsCollo
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454 Point-based approximationsprese
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456 Point-based approximationsGaler
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458 Point-based approximations2. Ha
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460 Point-based approximationsrelat
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462 Point-based approximations(a) 2
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464 Point-based approximationsby Eq
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466 Point-based approximationspoint
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17The time dimension ± semidiscret
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470 The time dimension ± semi-disc
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494 The time dimension ± discrete
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a n - p +1a n - 1a na n +1t∆t∆t
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19Coupled systems19.1 Coupled probl
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544 Coupled systemsImposed position
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546 Coupled systemsIn such problems
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548 Coupled systemsand on eliminati
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550 Coupled systemsThe discrete str
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552 Coupled systemsMode 1Frequency:
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554 Coupled systemstedious. Neverth
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556 Coupled systems19.2.7 Special c
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558 Coupled systemsFrom the momentu
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560 Coupled systems19.3.2 The forma
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562 Coupled systemsupFig. 19.6 `Rob
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564 Coupled systemsExcess porepress
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566 Coupled systems2. Conditional s
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568 Coupled systemsconsider the pro
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570 Coupled systemsT c0.80.60.40.2I
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572 Coupled systemsbefore solving f
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574 Coupled systems38. O.C. Zienkie
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20Computer procedures for ®niteele
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578 Computer procedures for ®nite
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Appendix AMatrix algebraThe mystiqu
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622 Appendix Awhich will also follo
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624 Appendix AA symmetric matrix mu
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Appendix BTensor-indicial notation
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628 Appendix BDerivatives and tenso
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630 Appendix BIndeed we can also us
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632 Appendix Bwhich yields the stre
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634 Appendix Bin Chapter 6 as Tr
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Appendix DSome integration formulae
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Appendix FSome vector algebraSome k
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640 Appendix FDirection cosinesDire
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642 Appendix FSimilarly, if we have
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644 Appendix GFig. G.1 De®nitions
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646 Appendix Hpoints the discrete v
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Appendix IMatrix diagonalization or
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650 Appendix IThe third procedure u
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652 Appendix Ithe form (I.6) gives
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Author indexPage numbers in bold re
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Author index 657Fortin, M. 314, 323
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Author index 659Mullord, P. 429, 44
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Author index 661Vahdati, M. 138, 13
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664 Subject indexApproximation ± c
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666 Subject indexConduction:heat, 4
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668 Subject indexDiscretization ±
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670 Subject indexEquation ± cont.
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672 Subject indexFourier transform,
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674 Subject indexInput module:data,
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676 Subject indexMapped mesh genera
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678 Subject indexMoment:bending, 7,
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680 Subject indexPile, foundation,
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682 Subject indexQuadrature ± cont
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684 Subject indexShape functions ±
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686 Subject indexStrati®ed materia
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688 Subject indexTriangle numerical
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