The Finite Element Method – Volume 1 : The Basis

The Finite Element Method – Volume 1 : The Basis
Fifth Edition
O.C. Zienkiewicz, CBE, FRS, FREng
UNESCO Professor of Numerical Methods in Engineering
International Centre for Numerical Methods in Engineering, Barcelona
Emeritus Professor of Civil Engineering and Director of the Institute for
Numerical Methods in Engineering, University of Wales, Swansea
R.L. Taylor
Professor in the Graduate School
Department of Civil and Environmental Engineering
University of California at Berkeley
Berkeley, CaliforniaContents
Preface xv
. Some preliminaries: the standard discrete system
. Introduction
. The structural element and the structural system
. Assembly and analysis of a structure
. The boundary conditions
. Electrical and fluid networks
. The general pattern
. The standard discrete system
. Transformation of coordinates
References
. A direct approach to problems in elasticity
. Introduction
. Direct formulation of finite element characteristics
. Generalization to the whole region
. Displacement approach as a minimization of total potential energy
. Convergence criteria
. Discretization error and convergence rate
. Displacement functions with discontinuity between elements
. Bound on strain energy in a displacement formulation
. Direct minimization
. An example
. Concluding remarks
References
. Generalization of the finite element concepts. Galerkin-weighted residual
and variational approaches
. Introduction
. Integral or ‘weak’ statements equivalent to the differential equations
. Approximation to integral formulations
. Virtual work as the ‘weak form’ of equilibrium equations for
analysis of solids or fluids
viii Contents
Partial discretization
Convergence
What are ‘variational principles’?
‘Natural’ variational principles and their relation to governing
differential equations
Establishment of natural variational principles for linear,
self-adjoint differential equations
. Maximum, minimum, or a saddle point?
. Constrained variational principles. Lagrange multipliers and
adjoint functions
. Constrained variational principles. Penalty functions and the least
square method
. Concluding remarks
References
. Plane stress and plane strain
. Introduction
. Element characteristics
. Examples – an assessment of performance
. Some practical applications
. Special treatment of plane strain with an incompressible material
. Concluding remark
References
. Axisymmetric stress analysis
. Introduction
. Element characteristics
. Some illustrative examples
. Early practical applications
. Non-symmetrical loading
. Axisymmetry – plane strain and plane stress
References
. Three-dimensional stress analysis
. Introduction
. Tetrahedral element characteristics
. Composite elements with eight nodes
. Examples and concluding remarks
References
. Steady-state held problems – heat conduction, electric and magnetic
potential, fluid flow, etc.
. Introduction
. The general quasi-harmonic equation
. Finite element discretization
. Some economic specializations
. Examples – an assessment of accuracy
. Some practical applications
Contents ix
, Concluding remarks
References
. ‘Standard’ and ‘hierarchical’ element shape functions: some general
families of C continuity
. Introduction
. Standard and hierarchical concepts
. Rectangular elements – some preliminary considerations
. Completeness of polynomials
. Rectangular elements – Lagrange family
. Rectangular elements – ‘serendipity’ family
. Elimination of internal variables before assembly – substructures
. Triangular element family
. Line elements
. Rectangular prisms – Lagrange family
. Rectangular prisms – ‘serendipity’ family
. Tetrahedral elements
. Other simple three-dimensional elements
. Hierarchic polynomials in one dimension
. Two- and three-dimensional, hierarchic, elements of the ‘rectangle’
or ‘brick’ type
. Triangle and tetrahedron family
. Global and local finite element approximation
. Improvement of conditioning with hierarchic forms
. Concluding remarks
References
. Mapped elements and numerical integration – ‘infinite’ and ‘singularity’
elements
. Introduction
. Use of ‘shape functions’ in the establishment of coordinate
transformations
. Geometrical conformability of elements
. Variation of the unknown function within distorted, curvilinear
elements. Continuity requirements
. Evaluation of element matrices (transformation in £, r (
coordinates)
. Element matrices. Area and volume coordinates
. Convergence of elements in curvilinear coordinates
. Numerical integration – one-dimensional
. Numerical integration – rectangular ( D) or right prism ( D)
regions
. Numerical integration – triangular or tetrahedral regions
. Required order of numerical integration
. Generation of finite element meshes by mapping. Blending functions
. Infinite domains and infinite elements
. Singular elements by mapping for fracture mechanics, etc.
x Contents
. A computational advantage of numerically integrated finite
elements
. Some practical examples of two-dimensional stress analysis
. Three-dimensional stress analysis
. Symmetry and repeatability
References
. The patch test, reduced integration, and non-conforming elements
. Introduction
. Convergence requirements
. The simple patch test (tests A and B) – a necessary condition for
convergence
. Generalized patch test (test C) and the single-element test
. The generality of a numerical patch test
. Higher order patch tests
. Application of the patch test to plane elasticity elements with
‘standard’ and ‘reduced’ quadrature
. Application of the patch test to an incompatible element
. Generation of incompatible shape functions which satisfy the
patch test
. The weak patch test – example
. Higher order patch test – assessment of robustness
. Conclusion
References
. Mixed formulation and constraints- complete field methods
. Introduction
. Discretization of mixed forms – some general remarks
. Stability of mixed approximation. The patch test
. Two-field mixed formulation in elasticity
. Three-field mixed formulations in elasticity
. An iterative method solution of mixed approximations
. Complementary forms with direct constraint
. Concluding remarks – mixed formulation or a test of element
‘robustness’
References
. Incompressible materials, mixed methods and other procedures of
solution
. Introduction
. Deviatoric stress and strain, pressure and volume change
. Two-field incompressible elasticity (u-p form)
. Three-field nearly incompressible elasticity (u-p-£„ form)
. Reduced and selective integration and its equivalence to penalized
mixed problems
. A simple iterative solution process for mixed problems: Uzawa
method
Contents xi
. Stabilized methods for some mixed elements failing the
incompressibility patch test
. Concluding remarks
References
. Mixed formulation and constraints – incomplete (hybrid) field methods,
boundary/Trefftz methods
. General
. Interface traction link of two (or more) irreducible form
subdomains
. Interface traction link of two or more mixed form subdomains
. Interface displacement ‘frame’
. Linking of boundary (or Trefftz)-type solution by the ‘frame’ of
specified displacements
. Subdomains with ‘standard’ elements and global functions
. Lagrange variables or discontinuous Galerkin methods?
. Concluding remarks
References
. Errors, recovery processes and error estimates
. Definition of errors
. Superconvergence and optimal sampling points
. Recovery of gradients and stresses
. Superconvergent patch recovery – SPR
. Recovery by equilibration of patches – REP
. Error estimates by recovery
. Other error estimators – residual based methods
. Asymptotic behaviour and robustness of error estimators – the
Babuska patch test
. Which errors should concern us?
References
. Adaptive finite element refinement
. Introduction
. Some examples of adaptive /(-refinement
. //-refinement and ///(-refinement
. Concluding remarks
References
. Point-based approximations; element-free Galerkin – and other
meshless methods
. Introduction
. Function approximation
. Moving least square approximations – restoration of continuity
of approximation
. Hierarchical enhancement of moving least square expansions
. Point collocation – finite point methods
. Galerkin weighting and finite volume methods
. Use of hierarchic and special functions based on standard finite
elements satisfying the partition of unity requirement
. Closure
References
. The time dimension – semi-discretization of field and dynamic problems
and analytical solution procedures
. Introduction
. Direct formulation of time-dependent problems with spatial finite
element subdivision
. General classification
. Free response – eigenvalues for second-order problems and
dynamic vibration
. Free response – eigenvalues for first-order problems and heat
conduction, etc.
. Free response – damped dynamic eigenvalues
. Forced periodic response
. Transient response by analytical procedures
. Symmetry and repeatability
References
. The time dimension – discrete approximation in time
. Introduction
. Simple time-step algorithms for the first-order equation
. General single-step algorithms for first- and second-order equations
. Multistep recurrence algorithms
. Some remarks on general performance of numerical algorithms
. Time discontinuous Galerkin approximation
. Concluding remarks
References
. Coupled systems
. Coupled problems – definition and classification
. Fluid-structure interaction (Class I problem)
. Soil-pore fluid interaction (Class II problems)
. Partitioned single-phase systems – implicit-explicit partitions
(Class I problems)
. Staggered solution processes
References
. Computer procedures for finite element analysis
. Introduction
. Data input module
. Memory management for array storage
. Solution module – the command programming language
. Computation of finite element solution modules
Contents xiii
. Solution of simultaneous linear algebraic equations
. Extension and modification of computer program FEAPpv
References
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 in two and three dimensions
(Green’s theorem)
Appendix H: Solutions exact at nodes
Appendix I: Matrix diagonalization or lumping
Author index
Subject index
Author index
Page numbers in bold refer to the list of references at the end of each chapter.
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Adee, J. ,
Ahmad, S. , ; ,
Ainsworth, M. , , ,
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Allwood, R.J. .
Andelfinger, U. ,
Anderson, R.G. ,
Ando, Y. , ; ,
Archer. J.S. ,
Argyris, J.H. , , ; , , ; , .
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Arlett, P.L. . . , ; . , .
Armstrong, C.G. ,
Arnold, D. ,
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Batina, J. , , , ,
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Baynham, J.A.W. , , ; , ,
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Beer, G. , ; ,
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Benz, W. .
Benzley, S.E. .
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Beresford, P.J. . ,
Bettencourt, J.M. , ,
Bettess, P. , ; , , , ; , ,
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Bey K .S. , ,
Bicanic, N. , , ; ,
Biezeno, O.C. , , ; ,
Bijlaard, P.P. ,
Biot, M.A. ,
Bischoff, M. ,
Blackburn, W.S. ,
Blacker, T.D. , , ; , ; ,
Bociovelli, L.L. ,
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Bonet, J. ,
Booker, J.F. ,
Boroomand, B. , ; , ; , , ,
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Babuska, I. , ; , , , ; ,
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Bachrach, W.E. , ; ,
Back. P.A.A. ,
Bahrani, A.K. , , ,
Bahrani. A.L. , , ,
Baiocchi, C. .
Balestra, M. ,
Bampton, M.C.C. ,
Banerjee, P.K. , ; ,
Bank, R.E. , , , Author index
Borouchaki, H. ,
Bossak , M. , ,
Braess, D. ,
Brauchli, H .J. , ; ,
Brebbia, C.A. . ; , ,
Brezzi, F. , , ; , , , ,
Brigham, E.O. ,
Brown, C. B. ,
Bruch, J .C. ,
Buck
, K.E. , ,
Bugeda, G. , ,
Butterfield, R . .
Byskov, E. ,
Cowper, G.R. ,
Cox, H . L. ,
Craig, A . , ; ,
Crandall, S .H. , ; , ; S, ,
Crank, J. ,
Crochet, M. ,
Crouzcix, M . ,
Cruse, T.A. ,
Dahlquist, G.G. ,
Daniel , W .J .T. , , ,
Davies
, A .J. ,
de Arrantes Oliveira, E.R. , ; , , :
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de Vries, G. , ,
Demkowiecz, L. , , ; . ,
Demmel , J. , ; , ; , ,
Desai, C.S. , ,
Dixon, J .R . ,
Doctors, L.J . ,
Doherty, W .P. , ; , , ,
Dolbow
, J . , .
Douglas, J . .
Duarte, A , , , , ,
Duarte, C .A. , . , , , . ,
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Duff, I .S. ,
Dungar, R. , ; ,
Dunham, R.S. ,
Dunne, P.C. , ,
Campbell, D.M . ,
Campbell, J. , ; , , , , , ,
; , . ; , ,
Canann, S. ,
Calitin, G . , , ; , ,
Caravani, P. ,
Carey, G. F. ,
Carlton, M.W. ,
Carpenter, C.J. ,
Carslaw, H.S. ,
Cassell. A.C. ,
Cavendish, J.C. ,
Chadwick, P. ,
Chan, A .H.C. , ; , ; , , ;
, , , , ,
Chan, S.T.K. ,
Chang, C.T. . , , ,
Chari. M .V. K . ,
Chen, C. M . ,
Chen, D.P. ,
Chen, H.-C. ,
Chen, H.S. . ; ,
Cheung, Y.K. . ; , , ; , , ; ,
: , ; , ,
Chiba, N. .
Chilton, L.K. , .
Chopra, A.K. , , , , ; ,
Chu, T.Y. ,
Ciarlet, P.G. , ; ,
Clough, R.W. , , , ; , , ; , ;
, ; , ; , , , ; ,
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Codina, R . , ,
Coffignal, G. ,
Collatz, L. ,
Collins, T. ,
Comincioli, V. .
Cook, R .D . ,
Coons, S.A.
Copps, K . , , , ,
Cornes, G .M .M. ,
Courant, R . , , ; , ; , ; ,
Eiseman, P.R. , ; , ; ,
Elias, Z .M . ,
Ely , J.F. ,
Emson, C. , ,
Engelman, M.S. ,
Ergatoudis, J.G. , , ; , , , .
, , ; , ,
Eriksson, K. ,
Evans. J.H. .
Evensen, D.A. ,
Farhat
, Ch. ,
Felippa, C.A. , ; . ; , , ,
,
Ferencz
, R.M. , , ; ,
Finlayson, B.A. , ; ,
Finn , N .D.L. ,
Fish, J. ,
Fix
, G .J . , , ; , ; . ,
Fjeld, S. ,
Fletcher, C.A.T. ,
Flores, F. ,
Formaggia, L. ,
Forrest, A.R. .
Forsythe, G .E. , Author index
Fortin, M. , , , ,
Fortin, N. ,
Fox, R . L. .
Fraeijs de Veubeke, B. , ; , ; , :
, , ,
Franca, L.P. . ; , , , ; ,
France, E.P. ,
Fraser, G.A. ,
Frazer, R.A. ,
Freund, J . ,
Fried, I . , , . ; , ; , ; ,
, ; ,
Friedmann, P.P. , . ,
Fujishiro, K . ,
Furukawa, T. ,
Hall, J.F. ,
Hammer, P.C. ,
Hansbo, P. ,
Hardy, O. , ,
Hause, J. , ; , ; ,
Hayes, LJ. , ,
Hearmon, R.F.S. ,
Heinrich, J .C. ,
Hellan. K . ,
Hellen
, T.K . , , ,
Hellinger, E. ,
Henrici, P. ,
Henshell, R.D. , ; ,
Herrera, I . ,
Herrmann, L. R. , ; . , , ; ,
, , ; , , ; , ,
Hestenes, M.R. ,
Hibbitt, H.D. ,
Hilber. H.M . , , ; , . ,
Hildebrand , F.B. , , . , : ,
Hine, N.W. ,
Hinton, E. , ; , , ; , ; ,
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Holbeche, J. .
Hood, P. .
Houbolt, J.C. , , ,
Hrenikoff, A. , ,
Hsieh, M.S. ,
Huang, Y. ,
Huck, J . , ,
Huebner, K.H. ,
Hughes, T.J . R . . ; , ; , , ,
, , , , ; , , , ,
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Gago, J .P. de S. R . , , ; , ; ,

Galerkin, B.G. , , ; , ,
Gallagher, R . H . , ; , : ,
Gangaraj, S. K . , , , .
Gantmacher, F.R . , ,
Gauss, C.F. , ,
Gear, C.W. , , ,
George, P.L. .
Geradin, M . , ,
Ghaboussi, J . , , ,
GiD – the Personal Pre/Postprocessor , ;
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Gingold, R.A . ,
Girault, V. , ,
Glowinski, R . , ,
Godbole, P. N. ,
Gong, N.G. . , , , ,
Gonzalez, O. , ,
Goodier, J .N. , , ; , ; , , ; ,
; , ; ,
Gordon, W.J. ,
Gorensson, P. , ,
Gould, P.L. ,
Gourgeon, H . ,
Grammel, R . ,
Gresho, P.M. ,
Griffiths, A.A. .
Griffiths, D . ,
Griffiths, R .E. ,
Gu, L. , , ,
Gui, W. , ,
Guo, B. , ,
Gupta, A.K. , ; ,
Gupta, K .K . , ; ,
Gupta, S. ,
Gurtin, M. ,
Guymon, G.L. ,

Hulbert, G.M. , , , ; , ,
Humpheson, C. ,
Hurty, W.C. , ,
Hurwicz, K.J. ,
Hurwicz, L. , , ,
Hurwitz, A. , ,
Ibrabimbegovic, A. ,
Idelsohn, S . R . , , ,
Iding, R . ,
Irons, B.M. , ; , , ; , ; . ;
, , , , , , , , ,
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, ; , , ; , , ; ,

Jaeger, J.C. ,
Jameson, A. ,
Javandel, I. ,
Hall, C.A. , Jennings, A. , , , Author index
Jirousek, J. , , ,
Johnson , C. , , , , .
Johnson, M .W. ,
Jones, W.P. .
Jun, S. ,
Ligget, J.A. ,
Lin, Q. , ,
Lindberg, G.M . ,
.huger. W. , , , ,
Liszka, T. , , , , ,
Liu, P.L-F. ,
Liu, W.K. , ; ,
Livesley, R.K . ,
Lo, S.H. ,
Lok, T.-S.L. ,
Lomacky, O. ,
Loubignac, C. , ,
Lowther, D.A. ,
Lu, Y. , , ,
Lucy, L.B. ,
Luenberger, D.G. ,
Luke, J.C. ,
Lyness, J.F. ,
Lynn, P.P. , ,
Kamei, A. ,
Kantorovitch , L.V. ,
Kassos, T , ,
Katona, M. ,
Katz, I.N. ,
Kaupp, P. ,
Kazarian, L.E. ,
Kelly, D.W. , ; , ; , , ; ,
; , ; , ; ,
Key, S.W. , ; ,
Kikichi, F. , , ,
Kikuchi, N. , ; ,
Koch. J.J. , ,
Kong, D, ,
Koshgoftar, M . ,
Kosloff, D. , ; ,
Krizek, M. ,
Krok, J. ,
Kron, G. ,
Krylov, V.I. .
Kulasetaram , S. ,
Kvamsdal, T. , , ,
Kythe, P.K. ,
McDonald, B.H. ,
McHenry, D. , ,
MacKerle, J. ,
McLay, R.W. ,
Maione, V. ,
Makridakis, C.G. ,
Malleus, D.S. , , , ; ,
Mailed, R.H. ,
Mandel. J. ,
Margal, P.V. , , ,
Mareczek, G. , ; , ,
Marlowe, O.P. ,
Martin, H.C. , , , , ; , ; ,
Martinelli, L. ,
Mavriplis, D.J. ,
Mayer, P. ,
Meek. J.L. ,
Mei, C.C. , ; ,
Melenk, J.M. , , ,
Melosh, R.J. ,
Mikhlin, S.C. , ; , ,
Minich, M.D. ,
Miranda, I. , ,
Mitchell, A.R. . ; ,
Mitchell, S.A. ,
Moan, T. ,
Mohraz, B. ,
Monaghan, J.J. ,
Monk, P. , ,
Morand. H. , , ,
Morgan, K. , ; , ; , ; , ;
, . ; , ; , ,
Morton, K.W. , , ,
Mote, C.D. ,
Mowbray, D.F.
Mullen. R. ,
Ladeveze, P. , , , . . ; ,

Ladkany, S.G. ,
Lambert, T.D. , , ,
Lan Guex ,
Lancaster, P. , ,
Larock, B.E. ,
Leckie, F.A. ,
Ledesma, A. ,
Lee, K.N. , ,
Lee, Nam-Sua .
Lefcbvrc, D. , ,
Leguillon, D. . , ,
Lekhnitskii, S.G. . ,
Lesaint, P. ,
Leung, K.H. . , , ,
Levy, J.F. ,
Levy, N. , .
Lewis, R.W. , ; , , , ; .
, ,
Li, B. ,
Li, G.C. ,
Li, S. ,
Li, X.D. , ; , ,
Li, X.K. .
Liebman, H. , , Author index
Mullord, P. , ,
Munro, E. ,
Murthy Krishna, A. ,
Pelz, R.B. ,
Penzien , J. , , , , ,
Peraire, . . , ; , ; , ,
Perrone, N. , .
Phillips, D.V. ,
Pian, T.H.H. , ; , ; , ; , ,
, ; ,
Pierre, R. , ,
Piltner, R. ,
Ping Tong ,
Pister, K.S. , , ; ,
Pitkjiranta, J. , , ; , , ; .
Nagtegaal, J.C. , ,
Nakazawa, S. , ; , ; , , ,
; , , , ,
Nath, B. ,
Navert. U. . .
Nay, R.A. ,
Naylor, D.J. , : ,
Nayroles, B. , , ,
Neitaanmaki, P. ,
Newmark, N.M. , , ; , , , . ,
,
Newton, R.E. , ; , ; , ,
Nickell, R.E. , ; ,
Nicolson, P. ,
Nishigaki, I. ,
Nithiarasu, P. , ,
Norrie, D.H. , ,

Book. L.P. ,
Powell, M.J.D. ,
Prager, W. , , ; . ,
Price, M.A. ,
Przemieniecki, J.S. ,
Qu , S. , ; , ; ,
Rachowicz, W. , , ; , ,
Radau ,
Raju. I.S. ,
Ralston. A. . ; , ,
Ramin, E. ,
Randolf, M .F. ,
Rank, E. ,
Rao, A.K. ,
Rao. I.C. ,
Rashid, Y.R . . ; ,
Rausch , R.D. ,
Raviart, P.A. , ; , ; ,
Rayleigh, Lord , , ; , ; ,
Razzaque, A. , ; ,
Reddi. M.M. ,
Redshaw, J.C. ,
Reid, J.K. ,
Reinsch, C. , ; , .
Reissner, E. ,
Rheinboldt, C. , , ,
Rice, J.R. , , , ; , ,
Richardson, L.F. , , , ,
Riclitmyer, R.D. , ; ,
Rifai, M.S. ,
Ritz, W. , : , ; ,
Roberts, G. , ,
Robinson , J. .
Rock, T. ,
Rockenhauser, W. ,
Rohde, S.M. ,
Rougeot, P. , ,
Routh, E.J. , ,
Roux, F.-X. ,
Rubinstein, M.F. , ,
Rudin, W. . ; ,
Oden, J.T. , , , ; , , , ; ,
; , , ; , , , , ,
, ; , , , , ; , .
, , , , , , , , ;
,
Oglesby, J.J. ,
Oh , K.P. ,
Ohayon, R , . , , , ,
Onate, E. . ; , , ; . , ,
, ,
Orkisz, J. , , , , , ,
Ortiz, P. , ,
Osborn, J.E. ,
Ostergren, W.J. , ,
Owen, D.R.J. , , ; .
Padlog, J. ,
Paidoussis, M.P. , , ,
Parekh, C.J. , ; ,
Park, K.C. , , ,
Parks. D M. , ; , ,
Parlett, B.N. , ,
Pastor, M. , ; , , ,
Patil, B.S. , , ,
Paul, D.K. , , . , , , , ,

Pavlin, V. , ,
Pawsey, S.F. ,
Payne, N.A. ,
Peano, A.G. , ,
Peck, R.B. ,
Pedro, O. ,
Peiro, J. ,
Pelle, J.P. , , , , Author index
Sabin, M.A. ,
Sabina, F.J . ,
Sabo. B.A. ,
Sacco, C. , ,
Salkauskas, K . , ,
Salonen, E-M. ,
Samuelsson, A. ,
Sandberg, G. , ,
Sander, G. , ,
Sani, R .L. ,
Satya Sai, B.V.K.. , ,
Savin, G.N. ,
Scharpf, D.W. , . , ; , . ,
; ,
Schrnit, L.A. ,
Schrefler, B. ,
Schrefler, B.A. , , , .
Schweingruber, M. ,
Scott, F.C. , , , , , , , ;
, , , .
Scott, J .A. ,
Scott, V.H. ,
Seed, H.B. , ,
Sen, S.K. ,
Severn , R .T , : ,
Shaw, K.G. ,
Shen. S.F. ,
Shepard, D. , , ,
Shiomi, T. ,
Silvester, P. , ; , ; ,
Simkin, J . ,
Simo, J .C.. , ; , , ; , , ;
, , , ; , ,
Simon, B .R. ,
Sken, S.W. ,
Sloan, S.W. ,
Sloss, J.M. .
Snell, C. . ,
Sokolnikoff, I.S. ,
Sommer, M. ,
Soni, B.K . , ; , ; ,
Southwell, R.V . , , , , ; , , . ;
,
Specht, B. ,
Stagg, K .G. , ,
Stakgold, I. ,
Stanton, E.L. ,
Stegun, I.A. , ,
Steinberg, S. ,
Stephenson, M.B. ,
Strang, G. , , ; , ; , , ;
, ; , ,
Strannigan, J.S. ,
Strouboulis, T. , ; , , , , ,
Strutt, J.W. , , ; , ; ,
Stummel, F. , ,
Sumihara, K. ,
Suri, M. , ,
Swedlow, J .L. ,
Synge, J.L. , , : ,
Szabo, B.A. ,
Szmelter, J . ,
Tabbara, M. ,
Taig, I.C. ,
Takizawa, C. ,
Tanesa , D.V. ,
Tarnow, N. , ,
Tautges, T..I . ,
Taylor, C. , ; , , ,
Taylor, R .L. , ; , ; , , , ,
. ; , , , , , , ,
; , , . , , , . ;
, , , , , , ; . ;
, , , , ; . , ; ,

, , , , . . ; , ,
, , , ,
Teodorescu, P. , ,
Terzhagi, K. , ; ,
Thatcher, R .W. ,
Thomas, D.L. ,
Thomas, J.M. ,
Thomasset, F. .
Thompson, J.F. , ; . ; , ,

Thompson, J.P. ,
Thomson, H .T. ,
Tieu, A.K. ,
Timoshenko, S.P. , ; , , ; , , ;
, ; , ; ,
Todd, D.K. ,
Tong, P. , ; , ; , , ; , ;
,
Tonti, E. ,
Too, J. ,
Topp, L.J. , , ; ,
Touzot. C. . .
Touzot, G. , , ,
Toyoshima, S. , , , , ,
Tracey D.M. , , ,
Trefftz, E. ,
Treharne, C. , ,
Trowbridge, C.W, ,
Trujillo, D.M. ,
Turner, M.J. , , ; ,
Upadhyay, C.S. , ; , , , , ,

Utku, S. ,
Uzawa, H. , ; ,

Stroud, A.H. , Author index
Vahdati, M. , ; , ; , ,
Vainberg, M.M. ,
Valliappan, S. ,
Vanburen. W. ,
Vardapetyan, L. , ,
Varga, R.S. , , ; ,
Varogln, E. ,
Vazquez, M. , ,
Verfurth, R. ,
Vesey, D.G. , ,
Villon, P. , , ,
Vilotte, J.P. , ; , , .
Visser, W. , ; ,
Vogelius, M. ,
Wu, J.S-S. , , ; , , ; ,
Wyatt, E.A. ,
Xi Kui Li ,
Xie, Y.M ,
Xu, K. ,
Yagawa, G. ,
Yamada, T. ,
Yamashita, Y. ,
Yan, N. ,
Yang, H.T.Y. ,
Yokobori, T. ,
Yoshida, Y. ,
Wachspress, E.L. , ; ,
Wahlbin, L.B. .
Walker, S. , ,
Walsh, P.F. ,
Washizu, K . , ; , , ; , ; ,
; ,
Wasow
, W.R. ,
Watson, J.O. ,
Watwood, V.B. ,
Weatherill, N.P. , ; , ; , ,
Weiner, J.H. ,
Weiser, A , , , ,
Westergaard, H.M. ,
Westermann, A. , ,
Wexler, A. ,
Wiberg, N.E. , ; , , , , ;
,
Wilkinson, J.H. , ; , ,
Williams, F.W. ,
Wilson, E.L. , ; , ; , , , ,
, , ; , , , , . ,
, , , , , , ,
Winslow, A.M. , , ,
Witherspoon, P.A. ,
Wolf, J.P. , ,
Wong, K. , ,
Wood, W.L. , , , , , , ,
,
Wroblewski, A. ,
Zarate, F. ,
Zhang, Y.F. ,
Zhang, Z. , ,
Zhong, W.X. ,
Zhn, J.Z. , ; , , , , , ,
, ; , , , , , , ,
, , , ,
Zhu, Q.D. , ,
Zielinski, A.P. , ,
Zienkiewiez, O.C. , ; . , . ; , , ,
, , , ; , , , , , ;
, ; , , ; , , , ,
, , ; , , , , , ,
, , , , , , ; , ,
, , , , , , , , .
; , , , ; , , , ,
, , , , . , ; , ,
, , , , , , , , ,
, , ; , , , , , ,
, , , , , ; , , ,
, , , , , , . , :
, , , , , ; , , ,
, , , , , , ; , ,
, , , , , ; , , ,
, , , , , , , , ,
, , , , , ; , , ,

Ziukas
, S. , ,
Zlamal, M. , ; , , Subject index
a posteriori error estimator,
Absciss\ae, integration, , ,
Accelerator matrix, convergence, ,
Accuracy, local,
Acoustic problems,
Adaptive analysis,
Adaptive mesh refinement,
Adaptive methods,
Adaptive time stepping,
Adaptivity, h,
Added mass, ,
ADI (Alternating Direction Implicit ),
Adjoint functions and operators, . ,
Aerofoil, ,
Aircraft,
Airy stress function,
Algebraic equations:
linear,
non-linear,
simultaneous linear.
Algorithm (see also algorithms, methods):
Bossak-Newmark.
CBS, ,
Gear,
generalized Newmark,
GiD,
GN,
GN ,
GN , , , , , , , , ,
GNpj, ,
Hilber-Hughes-Taylor,
Houbolt,
Liniger,
Newmark (see SS ), , , ,
recurrence.
SS (Single Step), –
SSI , ,
SS , ,
SS ( see Newmark), , , , , ,
, ,
,
, ,
SS ,
SS / algorithms,
SSpj, ,
steady-stage,
three-step,
transient step-by-step,
Uzawa,
Wilson,
Zlamal,
Algorithmic damping,
Algorithms:
general single-step,
GNpj,
implicit,
multi-step,
multistep recurrence,
recurrence,
single-step,
transient recurrence,
transient step-by-step,
Alternating direction implicit (ADI),
Alternating direction of sweeps,
Amplification matrix. ,
Analysis procedure, modal,
Anchorages, cable,
Angular velocity,
Anisotropic elasticity,
Anisotropic materials,
Anisotropic media,
Anisotropic porous foundation,
Anisotropic problems,
Anisotropic seepage,
Anisotropic valley,
Anisotropy, stratified,
Approximation:
central difference,
discontinuous stress,
finite element, Subject index
Approximation – cant.
function,
incomplete,
least square,
mixed,
multi-step polynomial,
partial field, ,
point,
point-based,
three-field, ,
Approximation error,
Approximation in time,
Arbitrary tetrahedral meshes,
Arbitrary weighting function,
Arch dam in rigid valley, , ,
Area:
elements of,
tributary,
Array computations, element,
Area coordinates, – , –
Array storage,
Arrays:
dynamically dimensioned,
global,
residual load,
Artificial harbour. ,
ASCII file,
Assembly equations,
Assembly process, general,
Asymptotic convergence rate, , , ,
B, strain matrix, – , ,
B-bar method ,
Babuska patch test,
Babuska-Brezzi conditions, ,
Back substitution,
Background grid,
Backward difference four-step algorithm,
Backward difference implicit scheme,
Band:
variable,
Bandwidth, , ,
Bandwidth minimization,
Bar:
pin-ended, ,
Barlow points,
Bars:
elastic,
pin-jointed,
Base polynomial solutions, .
Basic shape function routines,
Batch processing,
Beam:
cantilever,
narrow,
simply supported,
Beam reactions, simple,
Beam shape function,
Beam vibration,
Bearing pad,
Bending moment, .
Bending moments, internal,
Bending of prismatic beams,
Best fit stresses,
Bhakra dam-reservoir system,
Bilinear mapping,
Bilinear shape functions,
Bimetallic shaft, hollow,
Biomechanics, ,
Blade cascade, infinite,
Blade, cooled rotor,
Blending functions, ,
Blocks of elements,
Blocks of nodes,
Body force components,
Body force potential,
Body force vectors,
Body forces, , , , , ,
D distributed,
distributed, ,
Body of revolution,
Bone-fluid interaction,
Bossak-Newmark algorithm,
Boundaries:
external,
internal,
repeating,

Atmospheric pressure,
Augmented Lagrangian form,
Automatic element subdivision,
Auxiliary bending shape functions,
Auxiliary functions,
Average dynamic equation,
Average stress error,
Axes:
orthogonal,
principal,
Axial co-ordinates,
Axial tension,
Axisymmetric elasticity matrix, D,

Axisymmetric heat flow,
Axisymmetric initial strain,
Axisymmetric loading,
Axisymmetric solids,
Axisymmetric stiffness matrix.
Axisymmetric strain matrix, B,
Axisymmetric stress analysis,
Axisymmetric thermal strain,
Axisymmetrical pressure vessel,
Axisymmetry plane strain,
Axisynnnetry plane stress, Subject index
Boundary:
flux,
internal element,
radiation,
Boundary condition:
forced, , , ,
natural, , , , ,
prescribed ,
radiation,
traction,
Boundary condition data, ,
Boundary elements, ,
Boundary methods, , .
Boundary traction,
Boundary Trefftz-type elements,
Boussinesq problem, , ,
Box product,
Brick elements, hierarchical,
Brick-type elements,
Bubble function, , ,
cubic,
hierarchical,
Bubble mode, , , ,
Bubbles, distributed (cavitation),
Bubnov-Galerkin method ( see also Galerkin),
Bulk modulus, , ,
Buttress dam,
Characteristic equation, ,
Characteristic polynomial,
Characteristic value,
Checking, mesh data,
Circular hole,
Circular subdomains,
Circumferential strain,
Co-ordinates:
axial,
radial
,
Coalescing two nodes,
Coefficient array, sparse,
Coefficient matrix, global,
Coefficient of thermal expansion,
Cofactors,
Collocation:
point, , , , , ,
subdomain, , . ,
Taylor series,
Command programming language, ,
Compact storage operation,
Compatibility, , , ,
Complementary elastic energy principle,
Complementary forms,
Complementary heat transfer,
Complete field methods,
Complete polynomial, ,
Completeness,
Complex form,
Complex impedance,
Complex mesh generation,
Complex pairs,
Composite elements,
Compressibility, , ,
Compressibility matrix, fictitious,
Computer procedures,
Concrete reactor pressure vessel,
Condition: ( see also boundary condition),
constant gradient,
constant strain,
Routh-Hurwitz, , ,
stability, , , .
Condition number, ,
Condition of stationarity,
Conditional stability, , , , ,
Conditioning,
Conditioning of hierarchical forms,
Conditioning, matrix,
Conditions:
Babuska-Brezzi, ,
constraint,
equilibrium, , .
initial, ,
natural,
stability, ,
support,
C programming language,
C_! continuity,
C continuity, , , ,
C continuous shape functions. –
dimensional, S –
dimensional, –
dimensional, –
C, continuity, , , , ,
Cable anchorages,
Cancellation of error,
Cantilever. ,
Cartesian tensors:
first rank,
second rank,
Cascade, infinite blade,
Cavitation, , ,
Cavities,
Cavity problem:
driven, ,
Cavity zones,
CBS (Characteristic Based Split ), algorithm, ,
, ,
Central difference approximation,
Centrifugal action,
Centrifuge, ,
Chain rule,
Characteristic Based Split (CBS), , , ,
Subject index
Conduction:
heat, , , , , , , , , ,
, , , , ,
transient heat. , ,
Conduction-convection, steady-state heat,
Conductivity, ,
Conductors, electric,
Conformability, geometrical,
Conical water tank,
Connection data,
Connection:
element, , ,
Conservation equation,
Conservation, energy,
Consistency, , , , , , ,
order of, ,
P,
rate of, , ,
ultra,
Convergence accelerator, ,
Convergence criteria,
Convergence of elements,
Convergence rate,
asymptotic, , ,
Convergence requirements,
Cooled rotor blade,
Coordinate transformation,
Coordinates,
area,
curvilinear,
global,
nodal, ,
parametric curvilinear,
parent,
transformation of,
triangle normalized,
volume,
Corner shape functions, , ,
Corners, re-entrant.
Coupled analyses, . , ,
Coupled metal forming,
Coupled systems weak form ,
Couples, rotary inertia,
Coupling, ,
Coupling forms, symmetric,
Cracking,
Crank-Nicolson scheme, , , ,
Crest gates (spillway),
Crime,
Critical damping ration,
Cross criterion,
Cross product,
Crystal growth, ,
Cubic bubble,
Cubic elements,
Cubic tetrahedron,
Cubic triangle,
Cubic variation,
Current, ,
Current balance,
Current, electric,
Curvature,
Curved strata,
Curvilinear coordinates,
parametric,
Curvilinear mapping,
Cutouts,
Cyclic permutation, ,
Cylinder, pressure loaded,

Consistent damping matrix,
Consistent mass matrix, , ,
Constant:
radiation ,
spring,
Constant At form,
Constant energy norm density,
Constant gradient condition,
Constant jacobian,
Constant strain,
Constant strain condition ,
Constitutive equations, elastic,
Constitutive relation, ,
Constrained functional,
Constrained Lagragian forms,
Constrained variational principle, ,
Constraint conditions, ,
Constraint variable, , , ,
Continuity: (see also shape functions)
C_ i ,
C , , , ,
C,. , , , ,
displacement,
excessive,
interelement,
stress flux,
subdomain,
Continuity equation, , ,
Continuity of flux,
Continuous interpolation,
Continuous systems,
Continuum domain,
Continuum , three-dimensional,
Contravariant transformation,
Contrived variational principle,
Control data,
Control program,
Convective diffusion equation,
Convergence, , ,
h, D’Alembert principle, Subject index
D: elasticity matrix, , , ,
Dam ,
buttress,
gravity,
perforated,
perforated gravity,
Dam-reservoir system, Bhakra,
Dam/reservoir interaction,
Damped dynamic eigenvalues,
Damped wave equation,
Damping:
algorithmic,
linear,
modal,
Rayleigh,
zero,
Damping element,
Damping matrix, , , , , ,
consistent,
element,
Damping ratio, critical,
Damping terms,
Darcy’s law,
Data:
boundary condition,
connection,
control,
element,
Data checking, mesh,
Data input module, , ,
Data input modules,
De-refine (finite element mesh|,
DEC Fortran ,
Decomposed, modally,
Decomposition of matrix,
Decomposition:
modal. – , ,
triangular, –
Deficiency, rank,
Definition of error,
Definition of matrix,
Definition, pointwisc,
Deflection,
lateral,
Degenerate isoparametric®,
Degree of freedom count,
Degree of robustness,
Degrees of freedom,
Delauney triangulation,
Delta function, Dirac,
Delta:
Kronecker
, , ,
Densification,
Density:
flux,
mesh,
Determinant, jacobian,
Deviatoric projection matrix,
Deviatoric strains, , ,
Deviatoric stress, , ,
Diagonal matrix,
Diagonal scaling,
Diagonal terms, zero,
Diagonal:
principal,
zero, ,
Diagonality,
Diagonalization,
matrix. ,
Diagonals, unit,
Differential equations,
adjoint,
Euler,
non-linear,
ordinary,
self-adjoint,
Differential volume,
Differential, time,
Diffuse elements,
Diffuse finite element method,
Diffusion,
Diffusive term,
Dilatation, thermal,
Dimension:
time, ,
Dimensioned arrays, dynamically,
Dirac delta function,
Direct elimination,
Direct rank test,
Direct solution, , ,
Direction cosine array inverse,
Direction cosine array transpose,
Direction cosines,
Directional mesh refinement,
Disc:
rotating,
rotating,
Discontinuities, load,
Discontinuity,
element,
Discontinuous Galerkin method, , ,

Discontinuous slope,
Discontinuous stress approximation,
Discrete analysis,
Discrete coupled system,
Discrete elements, ,
Discrete pressure equation,
Discrete system: , ,
Discrete variables,
Discretization, ,
finite element, Subject index
Discretization
partial,
Discretization error,
Displacement,
prescribed,
radial,
virtual, ,
Displacement compatibility,
Displacement continuity,
Displacement field,
Displacement formulation,
Displacement frame, interface,
Displacement function, ,
Displacement gradient,
Displacement potential,
Displacement shape functions,
Displacements:
nodal, ,
prescribed,
rigid body, ,
SPR for,
Distorted four-noded element,
Distorted Lagrangian elements,
Distorted serendipity elements,
Distorted triangular prism,
Distortion:
gross,
violent,
Distributed body forces, ,
Distributed bubbles (cavitation),
Distributed loads, nodal forces,
Domain:
analysis,
continuum.
L-shaped, , , ,
space-time,
square,
time,
Domain element, polygonal,
Domain integral,
Domain of influence, ,
Domains:
infinite,
interpolation,
multiple,
overlapping,
Domains overlap,
Dome, hemispheric,
Double summation (numerical integration).
Dynamic memory allocation,
Dynamic problems,
Dynamically dimensional arrays,
Dynamics:
explicit,
soil,
cont.
E\ Young’s Modulus of elasticity, , , ,

• , – , – , ,
  Earthed trough,
  Earthquake,
  Earthquake forcing motion,
  Earthquake motion.
  Earthquake, simulated ,
  Effective stress, ,
  Effectivity index. , , ,
  Effects, surface wave,
  Eigenpairs, real,
  Eigenproblem, , .
  Eigenvalue computations,
  Eigenvalue participation factors,
  Eigenvalue problem,
  standard,
  Eigenvalues, , , , ,
  damped dynamic,
  real,
  zero,
  Eigenvector, , , ,
  Elastic bars,
  Elastic constants,
  Lame ,
  Elastic constitutive equations,
  Elastic foundation,
  string on, ,
  Elastic membrane,
  Elastic wave propagation,
  Elasticity, , ,
  anisotropic,
  incompressible, , ,
  linear, , ,
  two-field incompressible,
  Elasticity matrix D, , ,
  Elastodynamics.
  Electric conductors,
  Electric current,
  Electric potential,
  Electrical networks,
  Electrical resistance,
  Electromagnetics, ,
  Electrostatic potential,
  Electrostatics,
  Element:
  damping,
  distorted four-noded,
  enhanced strain.
  general triangular,

Driven cavity problem, ,
Dummy index,
Dyke foundation,
Dynamic analysis, implicit-explicit,
Dynamic eigenvalues, damped.
Dynamic equation, average, Subject index
incompatible,
line,
linear,
non-robust,
Pian-Sumihara,
polygonal domain,
quadratic,
quadratic triangular,
Simo-Rifai,
tetrahedral, ,
triangular, ,
Element analysis,
Element array computations.
Element boundary, internal,
Element connection, , ,
Element damping matrix,
Element data ,
Element discontinuity,
Element invariance,
Element mass matrix,
Element matrix, ,
singular,
Element modes:
singular,
zero energy,
Element partition,
Element patch {see also SPR ), , ,
Element residual,
Element residual error estimator,
Element residual, recovery by,
Element robustness, ,
Element routines,
multiple,
Element shape functions, –
Element singularities, local,
Element size, required ,
Element stiffness calculation,
Element stiffness matrix, , ,
Element stiffness matrix computation,
Element subdivision, ,
automatic,
Element test, single,
Element-free Galerkin method, . ,
Elements of area,
Elements of volume,
Elements:
blocks of,
boundary, ,
boundary Trefftz-type,
brick-type.
composite,
convergence of,
cubic,
diffuse,
discrete, ,
distorted Lagrangian,
distorted serendipity,
exterior,
finite, not indexed because too pervasive
hierarchical brick,
hierarchical rectangle,
hierarchical tetrahedron,
hierarchical triangle,
hybrid-stress,
infinite, ,
interior
,
irreducible, ,
isoparametric,
linear,
mapped,
non-conforming, ,
one-dimensional,
patch of,
rectangular,
singular,
singularity,
superparametric,
suspect,
tetrahedral,
three-dimensional,
Trefftz-type, , ,
triangular prism,
two-dimensional,
Elimination:
direct,
forward,
Gaussian
, ,
Elimination of internal variables,
Elimination of singularities,
ELMLIB (Element Library),
Elongation,
relative period ,
Energy bound, ,
Energy conservation,
Energy functional,
Energy loss, radiation,
Energy norm, , , ,
Energy principle, complementary elastic,
Enhanced strain element. ,
Enhanced strain stabilization, ,
Equation:
adjoint differential,
average dynamic,
characteristic,
characteristic,
conservation,
continuity,
continuity, ,
convective diffusion,
damped wave,
discrete pressure,
equilibrium, Subject index
Equation – coni.
first-order,
heat,
Helmholtz, , ,
hyperbolic,
Laplace, – , , ,
Maxwell’s,
parabolic,
Poisson, – , , . .
quasi-harmonic, – ,
Reynolds,
second-order,
wave,
Equations:
assembly,
constraint,
coupled,
differential.
elastic constitutive,
equilibrium, , , , ,
Euler, , ,
linear algebraic,
non-linear algebraic,
non-linear differential.
ordinary differential,
quasi-harmonic,
self-adjoint differential,
singular,
slope-deflection,
symmetric,
system,
Equilibrated element residual estimator, , ,
Error estimates by recovery,
Error estimation, , , , ,
Error estimator,
a posteriori,
element residual,
energy norm,
equilibrated residual, ,
explicit residual,
global,
implicit residual,
residual,
residual based, ,
Error magnitudes, permissible,
Error norms,
Escher modes,
Euler equations. , ,
Exact integration,
Exact nodal answers,
Excessive continuity,
Expansion:
isotropic thermal,
polynomial,
quadratic,
stress field,
thermal,
three-dimensional thermal,
Explicit dynamics,
Explicit residual error estimator,
Explicit scheme, , ,
Explicit-split process,
Exponential Gauss function,
Exterior elements,
External boundaries,
External loading.
External nodal forces,
External water pressure,
External work,
Extrapolation:
Richardson,
stress,
Extrusion problem ,
Extrusion, metal,

Equilibrating form subdomains.
Equilibrating stresses,
Equilibrium and energy,
Equilibrium conditions, , ,
Equilibrium equations. , , , , ,

Equilibrium equations weak form,
Equilibrium, overall,
Equivalent nodal forces,
Error:
approximation,
average stress,
cancellation of,
definition of,
discretization,
energy norm, ,
local stress,
local truncation,
order of,
RMS stress,
total permissible,
true,
truncation, ,
Factors, eigenvalue participation,
Fast Fourier transform,
FEAPpv (Finite Element Analysis Program ), ,
, ,
Fibreglass,
Fick’s law,
Fictitious compressibility matrix,
Field:
displacement,
incomplete,
oil,
thermal,
uniform stress, Subject index
Field approximation:
partial, –
Field expansion, stress,
Field methods:
complete,
incomplete hybrid,
Field problems, steady-state,
Field strength , magnetic,
File:
Fluid-structure time-stepping scheme,
Fluids, incompressible,
Flutter,
Flux, . , , , ,
continuity of,
normal, ,
Flux boundary,
Flux continuity, stress,
Flux density,
Force:
inertia,
lateral inertia,
Force matrix,
Forced boundary condition , , , ,
Forced periodic response, ,
Forces:
body, , , , , ,
distributed body, ,
equivalent nodal,
external nodal,
inertia.
interelement,
lateral inertia,
nodal, , , ,
prescribed nodal,
Forcing motion, earthquake,
Forcing term , , ,
Forcing, continuous,
Formula, two-point recurrence,
( also see algorithms, methods, formulations)
Formulation:
displacement,
enhanced strain,
Galerkin,
hybrid,
incompatible,
irreducible, , , , , ,
mixed, , , , , ,
stress function,
two-field mixed,
three-field mixed,
Fortran,
Fortran , DEC.
Forward elimination,
Foundation:
anisotropic porous,
dyke,
elastic,
rock,
stratified,
Foundation pile,
Foundation response,
Four-noded element, distorted,
Four-point interpolation,
Four-step algorithm, backward difference,
Fourier series, ,
ASCII,
output,
Fill-in (matrix), S
Film thickness,
Films, squeeze,
Finite differences, , , , , , , ,

Finite element analysis program,
Finite element approximation,
Finite element discretization,
Finite element program schematic,
Finite element solution modules,
Finite element not indexed because too pervasive
Finite increment calculus,
Finite point method,
Finite volume, , ,
First rank cartesian tensors,
First-order equation ,
First-order problem,
Fixed weighting function,
Flexible wall,
Flow,
axisymmetric heat,
fluid,
heat.
ideal fluid,
plastic,
slow viscous,
sphere heat,
Stokes, ,
Flows:
free surface,
incompressible,
irrotational,
Fluid:
interstitial,
pore,
Fluid flow,
ideal,
Stokes,
Fluid interaction, soil-pore.
Fluid networks,
Fluid oscillating with wall,
Fluid phase, ,
Fluid problems,
Fluid-structure interaction, , , ,
Fluid-structure systems, Subject index
Fourier transform, fast,
Fourier’s law,
Fracture mechanics,
Frame links,
Frame of specified displacements,
Frame parameters,
Frame, interface displacement,
Free index,
Free jet,
Free response, ,
Free surface, , ,
Free surface flows,
Free vibration, ,
Frequencies, natural,
Frequency response procedure,
Frictional resistance,
Frontal method,
Fully reduced matrix,
Function: see under names of functions, e.g.
Green’s, shape
Functional, , , ,
constrained,
energy,
maximum of,
minimum of.
quadratic,
variational,
GiD algorithm, program ,
Global arrays,
Global coefficient matrix,
Global coordinates,
Global energy norm,
Global energy norm error,
Global error estimator,
Global finite element approximation,
Global functions, ,
Global matrix,
Global shape functions,
Global stiffness matrix,
Global tangent matrix,
GLS {see Galerkin Least Squares),
GN algorithm ,
GN algorithm,
GN algorithm, , , , , , ,
, ,
GNpj algorithm , , , ,
Gradient singularities,
Gradients:
interface,
potential,
recovery of,
Gravity dam:
perforated,
Gravity loading,
Gravity waves, surface,
Green’s functions,
Green’s theorem, , , ,
Grid:
background,
Grids, nesting,
Gross distortion,
Growth:
crystal, .
Gurtin’s variational principle,
Galerkin approximation, time discontinuous,
Galerkin form, ,
Galerkin formulation,
Galerkin least square (GLS), . , ,
Galerkin method, , , ,
discontinuous, , ,
element-free, , ,
Galerkin method , , , , . ,
( see also Petrov-Galerkin, Bubnov-Galerkin)
Gates, crest (spillway),
Gauss function:
exponential,
truncated,
Gauss points, .
Gauss quadrature, , , , , ,
Gauss-Legendre points,
Gauss-Lobatto quadrature,
Gaussian elimination, ,
Gear algorithm,
General assembly process,
General single-step algorithms,
General triangular element,
General variational principle,
Generalised patch test,
Generalized Newmark algorithm,
Generalized strain,
Generators, hexahedral mesh,
Geometrical conformability,
h adaptivity,
h convergence,
//-refinement, , , ,
Half-space, semi-infinite,
Hamilton’s variational principle.
Hanging points,
Harbour:
artificial, ,
Harmonic wave functions,
Head:
hydraulic, ,
Heat conduction, , , , , , ,
. . , , ,
steady-state, ,
transient, , ,
weak form,
Heat conduction-convection, steady-state,
Heat equation, Subject index
Heat flow,
axisymmetric,
sphere,
Heat storage,
Heat transfer problem,
Heat transfer, complementary,
Hellinger-Reissner variational principle, ,
Helmholtz equation, , ,
Hemispheric dome,
Hermitian interpolation function,
Herrmann theorem, ,
Hexahedral mesh generators,
Hierarchical brick elements,
Hierarchical bubble function,
Hierarchical enhancement,
Hierarchical forms, ,
Hierarchical interpolation, , ,
Hierarchical method, polynomial,
Hierarchical moving least square,
Hierarchical polynomials,
Hierarchical rectangle elements,
Hierarchical shape functions, , , ,
Hierarchical tetrahedron elements,
Hierarchical triangle elements,
Hierarchical variables, . ,
High Poisson’s ratio,
fvi : also almost incompressible, Poisson’s
ratio = / )
High-frequency responses,
Higher derivatives,
Higher order patch test, , ,
Higher order stability,
Hilber-Hughes-Taylor algorithm,
Hinged member,
Hole, circular,
Hollow bimetallic shaft,
Horace Walpole,
Houbolt algorithm,
Hourglass control,
ftp-clouds,
/ip-refinement, ,
Hybrid:
superelement,
Hybrid form,
Hybrid formulations,
Hybrid-stress elements,
Hydraulic head, ,
Hydrodynamic pressure,
Hydrodynamics, smooth particle,
Hydrostatic pressure,
Hyperbolic equation,
Implicit algorithms,
Implicit methods.
Implicit residual error estimator,
Implicit scheme:
backward difference,
Implicit schemes,
Implicit-explicit dynamic analysis,
Implicit-explicit partitions, ,
Implicit-explicit solution,
Implicit-implicit schemes,
Inclined pile wall,
Incompatible element, ,
Incompatible element patch test,
Incompatible formulation,
Incompatible mode, ,
Incomplete approximation,
Incomplete field,
Incomplete hybrid field methods,
Incompressibility, , , , ,
Incompressibility patch test,
Incompressibility:
near, , , , , ,
( see also large Poisson’s ratio, Poisson’s
ratio = / )
Incompressible constraint,
Incompressible elasticity, . ,
three-field nearly
two-field,
Incompressible flows. ,
Incompressible material, . ,
Independent linear relations.
Independent strain relations,
Index:
dummy,
effectivity, ,
free,
robustness, ,
Indicial and matrix notation, ,
Indirect methods,
Inertia couples, rotary,
Inertia force,
lateral,
Inertia, rotatory,
Inexact integration,
Infinite blade cascade,
Infinite domains.
Infinite elements, ,
Infinite line,
Infinitesimal patch,
Infinity, ,
Initial conditions, ,
Initial strain, , ,
axi-symmetric,
Initial strains, volumetric,
Initial stress,
Initial value problem,
Ideal fluid flow,
Ideal fluid irrotational flow,
Impedance, complex,
Impeller, Subject index
Input module:
data, , , ,
mesh,
Instability. ,
Insulator, porcelain,
Integral:
domain,
volume, ,
surface,
Integrating factor,
Integrating points,
Integration:
exact,
Gauss,
gaussian,
inexact,
numerical, , , , , ,
order of,
prism numerical,
rectangular numerical,
reduced, , , , , ,
selective, , ,
standard,
tetrahedral numerical,
triangle numerical,
Integration by parts, , , , , , ,
Internal element boundary,
Internal nodes,
Internal parameters, nodeless,
Internal variables, ,
Internal water pressure,
Internal work, ,
Interpolation:
continuous,
domains,
four-point,
hierarchical, , ,
Lagrange.
local,
Shepard,
three point,
two point,
Interpolation function, Hermitian,
Interstitial fluid,
Invariance, element,
Inverse of matrix,
Irreducible elements, ,
Irreducible form, , , ,
Irreducible form subdomains,
Irreducible formulation, , , ,
Irregular mesh.
Irregular partitions,
Irrotational flow:
ideal fluid,
Isoparametric element, – ,
Isoparametrics, degenerate,
Isotropic behaviour,
Isotropic material, ,
transversely,
Isotropic thermal expansion,
Iteration, predictor-corrector,
Iterative method , , , , ,
Iterative solution, ,
Iterative solvers,

Integration formulae for tetrahedron,
Integration formulae for triangle,
Integration formulae:
tetrahedra numerical,
triangle numerical,
Integration limits,
Integration orders, low,
Integration points, minimum,
Integration procedures, numerical,
Interaction:
bone-fluid,
dam/reservoir,
fluid-structure, , , ,
reservoir-dam,
soil-fluid,
soil-pore fluid,
soil-pressure,
structure-structure,
Intcrclcmcnt continuity,
Interelement forces,
Interface displacement frame,
Interface gradients,
Interface line,
Interface traction, ,
Interface traction link, ,
Interface with solid,
Interior elements,
Internal bending moments,
Internal boundaries,
Jacobian, , ,
Jacobian determinant,
Jacobian matrix, ,
transformation,
Jacobian, constant,
Jet overflow,
Jet, free,
Joints, rigid,
Jump,
K matrix, singular,
k\ permeability,
Kernel method, reproducing,
Kronecker delta, , ,
L-shaped domain, , , ,
Lr norm. Subject index
L~ projection of stress,
Lagragian forms, constrained,
Lagrange interpolation,
Lagrange interpolation in time,
Lagrange multiplier, , , ,
Lagrange polynomials ,
Lagrange shape functions
Lagrangian elements, distorted,
Lagrangian form, augmented,
Laminar flow regime,
Laminations,
Lame elastic constants ,
Lanczos methods
Language statements, programming command ,
Language:
C programming,
command.
command programming,
Laplace equation, – , , ,
Lateral deflection,
Lateral inertia force,
Lateral load,
Law:
Linear polynomials,
Linear relations, independent,
Linear steady-state problems,
Linearly varying stress field,
Liniger algorithm,
Link:
interface traction, ,
Links, frame,
Liquefaction, soil,
Listings, source,
Load:
lateral,
Load arrays, residual,
Load discontinuities,
Load matrix, D,
Loaded cylinder, pressure,
Loaded sphere, pressure,
Loaded string,
Loading, ,
axisymmetric,
external,
gravity,
non-symmetrical.
Local accuracy,
Local element singularities,
Local finite element approximation,
Local interpolations,
Local stability,
Local stress error,
Local truncation error,
Localization,
Locally based functions,
Locking, , , , , , , , ,
Darcy’s,
Fick’s,
Fourier’s,
Least square,
Least square approximation,
Least square fit, ,
Least square forms,
Least square method, ,
Least square minimization,
Least square smoothing,
Least square:
Galerkin (GLS),
hierarchical moving,
Legendre polynomials, .
Length scale,
Limit:
stability,
vapour pressure.
Limitation:
principle of, , , ,
Limits:
integration,
stability,
Line:
infinite,
interface,
Line element,
Linear algebraic equations,
Linear damping,
Linear elastic model,
Linear elasticity, , ,
Linear element, ,
Linear operator,

Logarithmic terms,
Low integration orders,
Low reynolds number flow,
Lower bound solution,
Lower triangular matrix,
Lubrication,
Lubrication of pad bearings,
Lumped mass matrix, , ,
Lumped mass, negative,
Lumping, , ,
Lumping procedures,
Lumping:
mass, ,
Lunar waveguide,
Machine part,
Magnet,
Magnetic field strength,
Magnetic permeability,
Magnetic potential,
Magnetostatics, ,
Mapped elements, Subject index
Mapped mesh generation,
Mapped shape functions,
Mapping:
bilinear,
curvilinear,
uniqueness of, ,
Mapping function, , ,
Mass:
added.
lumped,
negative lumped,
Mass array,
Mass lumping, ,
Mass matrix, , ,
added,
consistent, , ,
element,
lumped, ,
Material:
anisotropic,
incompressible, , ,
isotropic, ,
stratified,
transversely isotropic,
Material properties, , ,
Material property specification,
Matrix:
D load,
D stiffness,
D stress,
added mass,
amplification,
axi-symmetric stiffness,
B
, D strain ,
B, D strain
B
, axi-symmetric strain,
bubble,
consistent damping,
consistent mass, , ,
convergence accelerator,
D, D elasticity ,
D, D elasticity
D, axi-symmetric elasticity,
damping, , , , , .
decomposition,
definition of,
deviatoric projection,
diagonal,
element damping,
element mass,
element stiffness, , ,
fictitious compressibility,
force,
fully reduced ,
global,
global coefficient,
global stiffness,
global tangent,
inverse of,
jacobian, ,
lower triangular,
lumped mass, ,
mass, , ,
non-singular,
positive definite,
profile,
singular element,
singular K,
skew symmetric, , ,
stiffness, , , , , , ,
strain-displacement,
symmetric, , ,
tangent,
three-dimensional strain,
transformation jacobian,
unsymmetric stiffness,
upper triangular,
Matrix algebra,
Matrix conditioning,
Matrix diagonalization, ,
Matrix notation,
Matrix singularity, , ,
Matrix subtraction,
Maximum of functional,
Maximum primary variables,
Maximum principle.
Maxwell’s equation,
Maxwell-Betti reciprocal theorem,
Mechanics, fracture,
Mechanisms, spurious,
Media:
anisotropic,
non-homogeneous,
porous,
Medium:
porous, ,
Member, hinged,
Membrane, elastic,
Memory allocation, dynamic,
Memory management.
Mesh:
irregular,
optimal,
regular,
Mesh data checking,
Mesh density,
Mesh enrichment, ,
Mesh generation:
complex,
mapped,
Mesh generators, hexahedral,
Mesh input module, Subject index
Mesh refinement:
adaptive,
directional,
Mesh regeneration, , ,
Meshes, arbitrary tetrahedral,
Meshless methods, , ,
Metal extrusion,
Metal forming, coupled,
Method of weighted residuals,
Method: (see also algorithm)
B-bar,
Bubnov-Galerkin,
discontinuous Galerkin, , ,
element-free Galerkin, , ,
finite point,
finite volume,
frontal,
Galerkin, , , , ,
iterative, , , . ,
iterative solution,
least square, ,
Petrov-Galerkin,
polynomial hierarchical,
Rayleigh-Ritz,
relaxation,
reproducing kernel,
row sum, ,
subspace,
Uzawa,
weighted residual,
Methods:
adaptive,
boundary, ,
complete field,
explicit,
finite difference.
finite point,
finite volume,
Galerkin solution,
implicit,
indirect,
Lanczos,
meshless, , ,
mixed,
multistep,
Newton’s,
stabilized,
stress recovery,
transient solution,
Trefftz,
variational,
Mid-edge nodes,
Mid-face nodes,
Mid-side shape functions,
Mid-side shift.
Middle half rule,
Middle third rule,
MINI,
Minimization,
bandwidth,
least square,
Minimum constraint variables,
Minimum integration points,
Minimum of functional,
Minimum order of integration,
Minimum principle,
Minimum span,
Miracles,
Miscellaneous weight functions,
Mixed approximation,
Mixed form, , , , , ,
Mixed form subdomains, ,
Mixed formulation , , , , , ,

two-field,
Mixed formulations, ,
three-field,
Mixed methods,
Mixed patch test, , .
Mixed problem,
Mixtures, water/oil,
Modal analysis, ,
Modal damping,
Modal decomposition, , , , ,

Modal orthogonality,
Modally decomposed,
Mode:
bubble, , , ,
incompatible,
spurious,
zero-energy,
Model:
linear elastic,
physical,
Modes:
Escher,
normal.
participation of,
quadratic,
rigid body, ,
singular element,
vibration,
wild,
zero energy,
Modified variational principle,
Module:
data input, –
mesh input,
results,
solution, ,
Molification, Subject index
blocks of,
coalescing two,
for comer,
internal,
mid-edge,
mid-face,
Non-conforming elements. ,
Non-homogeneous media,
Non-homogeneous shaft.
Non-linear algebraic equations,
Non-linear differential equations,
Non-linear problems,
Non-robust element,
Non-self adjoint operators,
Non-self-adjoint problem,
Non-singular matrix,
Non-square integrable,
Non-symmetrical loading,
Non-trivial solutions,
Non-unique mapping,
Norm density, constant energy,
Norm:
energy,
global energy,
L ,
Norm error,
energy,
energy,
global energy,
relative energy,
Normal flux, .
Normal modes,
Normalized coordinates, triangle,
Notation:
Moment:
bending, ,
Moments, internal bending,
Motion:
earthquake,
earthquake forcing,
rigid body, ,
Moving least square approximation, , ,

Moving weight function, ,
Multi-step algorithms,
Multi-step polynomial approximation,
Multigrid procedures,
Multiple domains,
Multiple element routines,
Multiplication, vector,
Multiplier:
Lagrange, , , , , , , , ,
,
Multistep methods, ,
Multistep recurrence algorithms,
Narrow beams,
Natural boundary condition, , , , ,
Natural conditions,
Natural frequencies,
Natural variational principle, , ,
Near incompressibility, , , , , ,

( see high Poisson’s ration. Poisson’s ratio= / )
Negative lumped mass,
Neighbour criterion , Voronoi, ,
Nesting grids,
Networks:
electrical,
fluid,
Neutron transport,
Newmark , , ,
Newmark algorithm
Newmark algorithm (GN ),
Newmark algorithm, generalized,
Newton’s methods
Newton-Cotes quadrature
Newton’s laws of motion
Nodal coordinates, ,
Nodal displacements, , ,
Nodal forces, , , , ,
equivalent,
external,
prescribed,
Nodal forces distributed loads,
Nodal point quadrature,
Nodal points,
Nodeless internal parameters,
Nodeless variables,
Nodes,
indicial, ,
Nuclear pressure vessel, ,
Number:
condition, ,
penalty, ,
Numerical integration, , , , , ,

( see also Gauss, integration, quadrature )
Numerical integration procedures,
Numerical integration:
prism,
rectangular,
tetrahedral,
triangle,
Numerical oscillation,
Numerical patch test,
Numerically integrated finite elements,
Oil field,
Oil recovery,
One-dimensional elements,
Opening, reinforced, Subject index
Particle hydrodynamics, smooth,
Partition of unity, , , , ,
Partition:
element,
Partitioned single-phase systems,
Partitioning, ,
Partitions:
implicit-explicit,
implicit-explicit,
irregular,
Pascal triangle patch,
Patch equilibrium, recovery by,
Patch:
element, , ,
infinitesimal,
superconvergent,
Patch of elements,
Patch recovery:
superconvergent, ,
Patch test, , – ,
Patch test A,
Patch test B, ,
Patch test C,
Patch test:
Babuska,
generalised,
higher order, , ,
incompatible element,
incompressibility,
mixed, , ,
numerical,
simple,
weak, ,
Pathological arrangements of elements,
PCG,
Penalty function, , , ,
Penalty number, ,
Penalty parameter,
Penalty term,
Perforated dam, ,
Periodic response,
forced,
Permeability, , ,
Permeability, magnetic,
Permissible error, ,
Permutation:
cyclic, ,
Petrov—Galerkin method,
Phase:
fluid, ,
Physical model,
Pian-Sumihara, –
Piecewise constant shape functions,
Piers,
Pile in stratified soil,
Pile wall, inclined,
Operator:
linear,
non-self adjoint,
self-adjoint,
small strain,
Optimal mesh,
Optimal sampling points, ,
Optimal superconvergent sampling,
Optimization,
Order of convergence, ,
Order of error,
Order of integration,
Order stability, higher,
Ordinary differential equations,
Orifice, ,
Orthogonal axes,
Orthogonal form,
Orthogonal series,
Orthogonality, ,
modal,
Oscillation, , ,
numerical,
Oscillations of natural harbour,
Oscillations, three-dimensional,
Oscillatory results,
Outgoing waves,
Output file,
Output module, solution and.
Overall equilibrium,
Overflow, jet,
Overlapping domains,
Overspill,
p convergence.
^-refinement, , , , ,
p-step algorithm , weighted residual,
Pad:
bearing,
stepped (lubrication),
Pairs, complex,
PALLOC (memory management ),
Parabolic equation,
Parallel computation,
Parameter:
frame,
nodelcss internal,
penalty,
system ,
undetermined,
weighting,
Parametric curvilinear coordinates,
Parent coordinates,
Partial discretization,
Partial field approximation, ,
Participation factors, eigenvalue,
Participation of modes, Subject index
Pile, foundation,
Pin-ended bar, ,
Pin-jointed bars,
PINPUT (program input command),
Pipes,
Pivot,
Plane strain,
axisymmetry,
Plane stress, .
axisymmetry,
Plastic flow,
Plate, slopes of,
PMACRn routines,
PMESH,
Point:
collocation,
quarter,
saddle,
superconvergent,
Point approximation,
Point-based approximation,
Point collocation, , , ,
Pointers, ,
Points:
Barlow,
collocation,
Gauss, ,
Gauss-Legendre,
hanging,
integrating,
minimum integration,
nodal,
optimal sampling, ,
quadrature,
sampling,
superconvergent,
Pointwise definition,
Poisson equation, – , , , ,
Poisson’s ratio, ,
Poisson’s ratio = / , , , , ,
Poisson’s ratio, high,
Polygonal domain clement,
Polynomial:
characteristic,
complete,
stability, ,
Polynomial approximation, multi-step,
Polynomial expansion,
Polynomial hierarchical method,
Polynomial order. ,
Polynomials:
completeness of,
hierarchical,
Lagrange, ,
Legendre, ,
linear,
Porcelain insulator,
Pore fluid,
Pore pressure,
Porous foundation, anisotropic,
Porous media, , ,
seepage through,
Positive definite matrix, ,
Positive valued weighting function ,
Potential:
body force,
displacement,
electric,
electrostatic,
magnetic,
scalar,
vector,
Potential energy:
total, ,
Potential gradients,
Potential temperature,
Power station:
underground, ,
Preconditioned conjugate gradient method. ,

Preconditioned conjugate gradient solver,
Preconditioning,
Predictor-corrector iteration,
Preprocessor,
Prescribed boundary condition,
Prescribed displacement, ,
Prescribed nodal forces,
Prescribed tractions,
Pressure, ,
Pressure equation, discrete,
Pressure limit, vapour,
Pressure loaded cylinder,
Pressure loaded sphere,
Pressure stabilization,
Pressure vessel,
axisymmetrical,
concrete reactor,
nuclear, . ,
Pressure:
atmospheric,
external water,
hydrodynamic,
hydrostatic,
internal water,
pore,
Primary variable, , ,
Primary variables, maximum,
Princes of Serendip,
Principal axes,
Principal diagonal,
Principle:
constrained variational. , Subject index
contrived variational,
d’Alembert,
Galerkin,
general variational,
Curtin’s variational,
Hamilton’s variational,
Hellinger-Reissner variational, ,
maximum,
minimum.
modified variational,
natural variational, , ,
variational, , , , . , ,
Principle of limitation, , , ,
Prism elements, triangular.
Prism numerical integration,
Prism:
distorted triangular,
rectangular,
triangular,
Problem:
acoustic,
anisotropic,
Boussinesq, , ,
continuous,
discrete,
driven cavity, ,
dynamic,
eigenvalue,
extrusion,
first-order,
fluid,
heat transfer,
initial value,
linear steady-state,
magnetostatic,
mixed,
non-linear,
non-self-adjoint,
saddle point,
seepage,
self-adjoint,
slot,
standard discrete,
standard eigenvalue,
steady-state field,
Stokes,
three-dimensional,
transient,
two-dimensional,
waveguide,
Procedure: ( see also methods, algorithms)
analytical,
computer,
frequency response,
lumping,
modal analysis,
multigrid,
numerical integration,
Rayleigh-Ritz,
recovery,
REP,
single-step,
SSpj,
stabilized,
weighted residual,
Process:
explicit-split,
general assembly,
recovery,
stabilization,
staggered solutions,
weighted residual,
Processing, batch,
Product:
box,
cross,
scalar,
tensor,
triple,
vector, ,
Products:
sum of,
PROFIL (program command ),
Profile matrix,
Profile solution scheme,
Profile storage,
Program:
control,
GiD,
Programming command language statements.

Programming language:
C,
command,
Projection matrix, deviatoric,
Propagation, elastic wave,
Properties:
material, , ,
stability,
Property specification, material,
Quadratic element,
Quadratic expansion,
Quadratic functional,
Quadratic modes,
Quadratic tetrahedron,
Quadratic triangle,
Quadratic triangular element,
Quadrature: (see also integration)
Gauss, ,
Gauss-Legendre, , ,
Gauss-Lobatto, Subject index
Quadrature – cam!.
gaussian,
Newton-Cotes,
nodal point,
selective reduced,
Quadrature points,
Quadrature weight,
Quadrilateral:
Pian-Sumihara, , ,
Simo-Rifai, ,
Quarter point,
Quasi-harmonic equation, , , , ,
Recurrence relation, . , ,
single-step,
Reduced integration, , , , , ,
Reduced quadrature, selective,
Reduction of eigenvalue system,
Refinement,
adaptive mesh,
directional mesh,
Regeneration:
mesh, , ,
Regular mesh,
Reinforced opening,
Relative energy norm error,
Relative period elongation,
Relaxation method,
Relaxation solution,
Remainder, Taylor series,
Remeshing,
REP procedure,
Repeatability, ,
Repeatability segments,
Repeating boundaries,
Reproducing kernel method ,
Required element size,
Reservoir, ,
Reservoir bottom,
Reservoir-dam interaction,
Residual, ,
element,
form,
stresses
tolerance on,
weighted, , ,
Residual based error estimator. ,
Residual error estimator,
Residual estimator, equilibrated element,
Residual load arrays,
Residual method:
Galerkin weighted, ,
weighted,
Residual procedures, weighted, ,
Resistance.
electrical,
frictional,
Resolution ( of matrix equations ),
Response:
forced periodic,
foundation,
free, ,
high-frequency,
periodic,
transient, ,
Response procedure, frequency,
Results module,
Results, oscillatory,
Revolution, body of,
/ -refinement,
Radial co-ordinates,
Radial displacement,
Radiation,
Radiation boundary,
Radiation boundary condition,
Radiation coefficient,
Radiation constant,
Radiation energy loss,
Radiation of reflected waves,
Radius:
spectral, ,
Rank deficiency,
Rank test, direct,
Rate:
asymptotic convergence, , ,
convergence,
Rate of convergence, , ,
Rayleigh damping,
Rayleigh-Ritz method , ,
Re-entrant corners,
Reactions,
simple beam,
Reciprocal theorem, Maxwell-Betti,
Recovery:
oil,
superconvergent patch (SPR), , ,
Recovery based estimator,
Recovery by element residual,
Recovery by patch equilibrium,
Recovery methods, stress,
Recovery procedures, , , , , ,
,
Rectangle elements, hierarchical,
Rectangular elements,
Rectangular numerical integration,
Rectangular prism,
Rectangular prisms, serendipity family,
Rectangular shaft torsion,
Recurrence algorithm, ,
multistep,
transient,
Recurrence formulae, two-point, Subject index
Reynolds equation,
Richardson extrapolation,
Right-hand rule,
Rigid body constraints,
Rigid body displacements, ,
Rigid body modes, ,
Rigid body motion, ,
Rigid joints,
Rigid valley and arch dam, . ,
RMS stress error robustness index, ,
Robustness:
assessment of,
degree of,
element, ,
Robustness of error estimator,
Robustness requirements,
Rock foundation,
Root mean square error (RMS),
Rotary inertia couples.
Rotating disc, ,
Rotating solids,
Rotating sphere, ,
Rotational symmetry,
Rotatory inertia ,
Rotor blade, cooled,
Round-off, ,
Routh-Hurwitz condition, , ,
Routines:
element,
multiple element,
PMACRn,
Row sum method, ,
Second rank cartesian tensors,
Second rank symmetric tensors,
Second-order equation,
Seepage, , , , , ,
Seepage, anisotropic,
Selective integration, , ,
Selective reduced quadrature,
Self-adjoint, , ,
Self-adjoint differential equations,
Self-adjoint operator,
Self-adjoint problem ,
Self-equilibrating,
Self-starting scheme,
Semi-discretization , ,
Semi-infinite half-space,
Serendip, Princes of,
Serendipity,
Serendipity cubic shape functions,
Serendipity elements, distorted,
Serendipity family rectangular prisms,
Serendipity linear shape functions,
Serendipity quadratic shape functions,
Serendipity quartic shape functions,
Serendipity shape functions,
Series collocation:
Taylor,
truncated Taylor,
Series remainder, Taylor,
Series:
Fourier, ,
orthogonal,
Taylor, ,
Shaft torsion, rectangular,
Shaft:
hollow bimetallic,
non-homogeneous,
Shape function,
Shape function subprograms,
Shape function:
beam,
Shape functions, , , , , ,
auxiliary bending,
bilinear,
C continuous,
corner,
displacement,
element,
global,
hierarchical. , , ,
incompatible,
Lagrange,
mapped,
mid-side,
piecewise constant,
serendipity.
serendipity cubic,
Saddle point, ,
Safe zone for midpoint,
Sampling points,
optimal, ,
Sampling:
optimal superconvergent.
stress,
Scalar potential,
Scalar products,
Scale, length,
Scaling, diagonal,
Scheme:
Crank-Nicolson, , ,
explicit, ,
finite difference,
fluid-structure time-stepping,
implicit,
implicit —implicit,
multistep,
profile solution,
self-starting,
sparse solution,
staggered, , Subject index
Shape functions – coni.
serendipity linear,
serendipity quadratic,
serendipity quartic,
standard, ,
tetrahedron,
tetrahedron cubic,
tetrahedron linear,
tetrahedron quadratic,
triangle,
Shear strain singularity,
Shedding of vortices,
Shells,
Shepard interpolation shift, mid-side,
Shrinkage, ,
Simo-Rifai element,
Simo-Rifai quadrilateral, ,
Simple beam reactions,
Simple patch test,
Simply supported beam ,
Simpson one third rule,
Simulated earthquake,
Simultaneous linear algebraic equations.
Skew symmetric matrix, , ,
Slope:
discontinuous,
Slope-deflection equations,
Slopes of plate,
Slot problems,
Slotted tension strip,
Slow viscous flow,
Small strain operators,
Smooth particle hydrodynamics,
Smoothed stress, ,
Smoothing,
least square,
Soil dynamics,
Soil liquefaction ,
Soil skeleton,
Soil-fluid interaction,
Soil-fluid system,
Soil-pore fluid interaction,
Soil-pressure interaction,
Solid:
elastic,
interface with,
Solids:
axisymmetric,
rotating,
Solid skeleton,
Solution:
base, ,
boundary,
direct, , ,
implicit-explicit,
iterative,
lower bound,
relaxation,
staggered ,
Trefftz-type,
Solution and output module,
Solution iteration number,
Solution method:
iterative,
Solution methods:
Galerkin,
transient,
Solution module, ,
Solution modules, finite element,
Solution scheme:
profile,
Solution schemes, sparse,
Solutions exact at nodes,
Solution processes, staggered,
Solvers, iterative,
Sound, speed of,
Source listings,
Space-time domain,
Span, minimum,

Singing wire,
Single element test,
Single-phase systems,
partitioned,
Single-step algorithms,
general,
Single-step procedures.
Single-step recurrence relations,
Singular element matrix,
Singular element modes,
Singular elements,
Singular elements by mapping,
Singular equations,
Singular functions,
Singular k matrix,
Singular solutions,
Singularities,
elimination of,
gradient.
local element,
Singularity elements,
Singularity, . , , , ,
avoidance of,
matrix,
matrix,
matrix,
shear strain,
weak
,
Size, required element,
Skeleton:
soil,
solid, Subject index
Sparse coefficient array,
Sparse solution schemes,
Specification, material property,
Spectral form,
Spectral radius, ,
Speed of sound,
Sphere:
pressure loaded,
rotating, ,
Sphere heat flow,
SPR (Superconvergent Patch Recovery), –
SPR for displacements,
Spring constant,
Spurious mechanisms,
Spurious mode,
Spurious solutions,
Square domain
Squeeze films, S
SS (Single Step ), algorithms, –
SSI algorithm , ,
algorithm, ,
algorithm, , , , , , , ,
, .
algorithm,
algorithm, ,
SS algorithm,
SS / f algorithms,
SSpj algorithm ,
Stability, , . , , , ,
conditional, , ,
higher order,
local,
unconditional, , , , , , ,
Stationary point of functional,
Steady-stage algorithm,
Steady-state field problems,
Steady-state heat conduction, ,
Steady-state heat conduction-convection,
Steady-state problems, linear,
Steady-state solutions,
Step-by-step algorithm:
transient, ,
Stepped pad bearing (lubrication),
Stiffness array,
Stiffness calculation, element,
Stiffness matrix, . . , , , ,
D,
axi-symmetric,
element, , ,
global,
unsymmetric,
Stiffness, tangent,
Stokes flow, ,
Storage:
array,
heat,
profile.
Storage allocation,
Storage operation, compact,
Strain , , ,
axi-symmetric initial,
axi-symmetric thermal,
circumferential.
constant,
deviatoric,
generalized,
initial, , ,
plane,
thermal,
volumetric, , , ,
Strain element, enhanced,
Strain energy,
Strain formulation, enhanced,
Strain matrix, B, axi-symmetric
Strain matrix, B, D ,
Strain matrix, B, D
Strain operators, small,
Strain relations, independent,
Strain stabilization:
enhanced, ,
Strain tensor,
Strain-displacement, ,
Strains:
deviatoric, ,
volumetric initial,
Strata,
curved,
Stratified anisotropy,
Stratified foundation,

Stability check,
Stability condition, , , , , ,
Stability criteria, ,
Stability limit, ,
Stability of general algorithms,
Stability of mixed approximation,
Stability polynomial, ,
Stability properties,
Stability requirements, ,
Stabilization:
enhanced strain, ,
pressure,
Stabilized methods, ,
Stabilizing terms,
Stable:
conditionally, ,
unconditionally,
Stagger,
Staggered schemes, , ,
Standard discrete system, ,
Standard eigenvalue problem,
Standard shape functions, , Subject index
Stratified material,
Stratified soil, pile in,
Stream function,
Streamline,
Strength, magnetic field,
Stress:
axisymmetry plane,
deviatoric, ,
effective,
initial,
plane, ,
smoothed, ,
techtonic,
total,
Stress approximation, discontinuous,
Stress components,
Stress concentration,
Stress error:
average,
local,
RMS,
Stress evaluation,
Stress extrapolation,
Stress field expansion,
Stress field:
linearly varying,
uniform,
Stress flux continuity,
Stress function,
Stress function formulation,
Stress function, Airy,
Stress matrix, D,
Stress recovery methods,
Stress sampling,
Stress tensor, symmetric cartesian,
Stress-strain relation, ,
Stresses:
best fit,
deviatoric,
effective,
equilibrating,
recovery of,
residual,
tectonic,
thermal, ,
String on clastic foundation, ,
String, loaded,
Strip, slotted tension ,
Structure-structure interaction,
Subdivision:
automatic element,
element, ,
Subdomain, , ,
Subdomain collocation , , , ,
Subdomain continuity.
Subdomains with standard elements,
Subdomains, , ,
circular,
equilibrating form,
irreducible form,
mixed form, ,
Submatrix,
Submerged surface,
Subparametric,
Subprograms, shape function,
Subspace method,
Substitution, back,
Substructures, ,
Substructuring,
Subtraction:
matrix,
vector,
Sufficient condition for convergence,
Sum of products,
Sumihara, Pian and,
Summation convention,
Summation, double (integration),
Superconvergence, , , ,
Superconvergent patch,
Superconvergent patch recovery (SPR), ,
Superconvergent point, ,
Superconvergent sampling, optimal,
Superelement hybrid ,
Superelements,
Superparametric elements,
Support conditions,
Surface:
free, , ,
submerged,
Surface flows, free,
Surface gravity waves,
Surface integrals,
Surface traction,
Surface wave effects,
Suspect elements,
Symmetric cartesian stress tensor,
Symmetric coupling forms,
Symmetric equations,
Symmetric matrix, , ,
skew, ,
Symmetric tensors, second rank ,
Symmetry, , .
rotational,
T elements (Trefftz),
Tangent matrix,
global,
Tangent stiffness,
Tank, conical water,
Taylor series collocation, ,
Techniques, recovery,
Techtonic stress. . Subject index
Temperature, , , , ,
Temperature change, , ,
Temperature, potential,
Tension strip with slot, ,
Tension, axial,
Tensor:
strain,
Tensor product,
Tensor-indicial notation,
Tensorial relations,
Tetrahedra numerical integration formulae.
TINPUT, ,
Tolerance on residual,
Torsion of prismatic shafts,
Torsion, rectangular shaft,
Total permissible error,
Total potential energy, ,
Total stress,
Traction,
boundary,
interface,
surface,
Traction boundary condition,
Traction link:
interface, ,
Tractions, ,
interface,
prescribed,
Transfer coefficient,
Transfer problem, heat,
Transfer, complementary heat,
Transform:
fast Fourier,
Transformation jacobian matrix,
Transformation of coordinates,
Transformation:
contravariant,
coordinate,

Tetrahedral element, ,
Tetrahedral elements,
Tetrahedral meshes, arbitrary,
Tetrahedral numerical integration,
Tetrahedron:
cubic,
quadratic,
Tetrahedron cubic shape functions,
Tetrahedron elements, hierarchical,
Tetrahedron linear shape functions,
Tetrahedron quadratic shape functions,
Tetrahedron shape functions,
Theorem:
Green’s, , , ,
Herrmann, ,
Maxwell—Betti reciprocal,
variational,
Thermal conduction,
Thermal dilatation,
Thermal expansion,
isotropic,
three-dimensional,
Thermal field,
Thermal strain,
axi-symmetric,
Thermal stresses, ,
Three point interpolation,
Three-dimensional continuum,
Three-dimensional elements,
Three-dimensional oscillations,
Three-dimensional problem,
Three-dimensional strain matrix,
Three-dimensional stress analysis,
Three-dimensional thermal expansion,
Three-dimensional transformer,
Three-field approximation, ,
Three-field mixed formulations,
Three-field nearly incompressible elasticity,
Three-step algorithm,
Time differential,
Time discontinuous Galerkin approximation,
Time domain,
Time stepping, adaptive,
Time stepping scheme, fluid-structure,
-,
Transformations,
Transformer,
three-dimensional,
Transient computations,
Transient heat conduction, , ,
Transient heat conduction equation,
Transient heating of bar,
Transient problem,
Transient recurrence algorithms,
Transient response, ,
Transient solution methods,
Transient step-by-step algorithm,
Transient step-by-step algorithms,
Transpose of a matrix,
Transpose of a product,
Transversely isotropic material,
Trapezoidal rule,
Trefftz methods, , , ,
Trefftz-type elements, boundary,
Trefftz-type solution,
Trial function, ,
Triangle:
cubic,
Pascal, , , ,
quadratic,
Triangle elements, hierarchical,
Triangle normalized coordinates,
Triangle numerical integration, Subject index
Triangle numerical integration formulae,
Triangle shape functions,
Triangular decomposition, , , ,
Variational methods,
Variational principle, , , , , , ,

complementary energy,
constrained, ,
contrived,
general,
Gurtin’s,
Hamilton’s,
Hellinger-Reissner, ,
modified,
natural, . ,
Variational theorem,
Vector addition, ,
Vector algebra,
Vector multiplication,
Vector potential,
Vector product, ,
Vector subtraction,
Vectors components,
Velocity,
angular,
virtual,
Vessel:
axisymmetrical pressure,
nuclear pressure,
pressure,
reactor pressure,
Vibration modes,
Vibration of earth dam,
Vibration:
beam ,
forced,
free, ,
Violent distortion,
Virtual displacement, ,
Virtual velocity,
Virtual work, , , , , ,
Viscosity, , ,
Viscous flow, slow,
Voltage,
Volume coordinates, –
Volume integral. ,
Volumetric initial strains,
Volumetric strain, , , ,
Voronoi neighbour criterion ,
Vortices, shedding of,

Triangular element, ,
general,
quadratic,
Triangular matrix:
lower,
upper.
Triangular prism elements,
Triangular prism:
distorted.
Triangular prisms,
Triangulation, Delauney,
Tributary area,
Triple product,
Trough, earthed,
True error,
Truncated gauss function,
Truncated taylor series collocation,
Truncation error, .
local,
Two nodes, coalescing,
Two point interpolation,
Two-dimensional elements,
Two-dimensional problem,
Two-field incompressible elasticity,
Two-field mixed formulation,
Two-point recurrence formulae,
Ultra convergence,
Unconditional stability, , , , , ,
, ,
Underground power station. ,
Undetermined parameters,
Undrained behaviour,
Uniform stress field,
Uniqueness of mapping,
Unit diagonals,
Unity:
partition of, , , , ,
Universal shape function routines,
Unreduced coefficient,
Unsymmetric stiffness matrix,
Upper triangular matrix,
User manual,
Uzawa algorithm ,
Uzawa method, Wall:
flexible.
inclined pile,
Walpole, Horace,
Water pressure:
external,
internal,
Water tank, conical,
Valley, anisotropic,
Vapour pressure limit,
Variable band,
Variational approaches,
Variational forms,
Variational functional, Subject index
Water/oil mixtures,
Wave effects, surface,
Wave equation,
damped,
Helmholtz, ,
Wave functions, harmonic,
Wave propagation, elastic,
Wave transmission,
Waveguide problem,
Waveguide, lunar.
Waves:
outgoing,
surface gravity,
Weak form, , , ,
Weak form heat conduction,
Weak form:
coupled systems,
equilibrium equations,
Weak patch test, ,
Weak patch test satisfaction,
Weak singularity,
Weak statements,
Weight coefficient,
Weight function:
moving, ,
Weight functions, miscellaneous,
Weight:
quadrature,
Weighted least square fit,
Weighted residual,
Weighted residual finite element, ,
Weighted residual method ,
Weighted residual p-step algorithm,
Weighted residual procedures,
Weighted residual process,
Weighted residuals, ,
Weighting coefficient,
Weighting function, , , , , , ,
,
arbitrary,
fixed,
positive valued,
Weighting method, Galerkin,
Weighting parameter,
Weighting:
collocation,
Galerkin,
Wild modes,
Wilson algorithm
Windows based systems
Wire, singing,
Work:
external,
internal, ,
virtual. , , , . ,
X-window applications
Young’s modulus, E, , , , – , – ,

• , ,
  Z transformation,
  Zero damping,
  Zero diagonal, ,
  Zero diagonal terms,
  Zero eigenvalues,
  Zero energy element modes,
  Zero energy modes, ,
  Zlamal algorithm
  Zone:
  active.
  v.
  Poisson’s ratio, ,

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