bibliography - springer978-1-4684-9143-2/1.pdf · bibliography adm1s, r.a. [1975] : ... de plaques...
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BI BLIOGRAPHY
ADM1S, R. A. [1975] : SoboZev Spaces , Ac?demic Press, New Yor k .AHMAD, S. ; I RONS, B.M. ; ZI ENKI EWICZ, O.C. [ 1970] : Ana lys i s of thick
and thin she l l structures by curved finite e l ements , Internat . J .Numer . Met hods Engrg. ~' pp. 419-451.
ARGYRIS, J.H. ; FRIED, I . ; SCHARPF, D.W. [1968] : The TUBA family ofplate elements for the matrix displacement metho d, Aero. J . RoyaZAeronauticaZ Societ y 72, pp. 701-709.
ARGYRI S, J.H. ; HAASE, M. ; MALEJ ANNAKI S, G. A. [19 73] : Natural geome t ryof sur faces wi t h specific reference to the matrix displacementanal ys i s of shells, I, II and I I I , Proc . Kon . Ned . Akad. Wetensch . ,Ser ies B, 76, pp . 36 1-4 10.
ARGYRI S, J .H. ; LOCHNER , N. [ 1972] : On the applica t ion of the SHEBAshell element, Comput. Met hods Appl. Mech. Engrg. 1, pp. 317-347 .
ASHWELL, D.G. ; GALLAGHER, R. H. [ 1976] : Fini te eZements f or t hin sheZZsand curved member s , J. Wi l ey and Sons , London.
BEGIS, D. ; PERRONNET, A. [1980 ] : Presentation du Club MODULEF,Notice 50 , Ver s ion 3. 2, I NRIA.
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BERNADOU, M. [1 978] : Sur Z'ana Zyse numer ique du modeZe Zineair e decoques minces de W.T. KOITER, Thes e d 'Etat, Universite Pierre etMar i e CURIE, Paris.
BERNADOU, M. [1980] : Convergence of conforming finite element methodsfor general ,she l l problems, In ternat. J . Engrg. Sci . , 18, pp 249-276.
BERNADOU, M. ; BOISSERIE, J.M. [1978a] : Implementation de l'elementfini d'ARGYRIS - Exemples, Rapport IRIA-LABORIA lQi.
BERNADOU, M. ; BOI SSERIE, J.M. [ 1978b] : Sur l'implementation deproblemes gener aux de coques, Rapport I RIA-LABORIA 211.
BERNADOU, M. ; BOISSERIE, J. M. ; HASSAN, K. [1980], Sur l'implementationdes elements finis de HSIEH-CLOUGH-TOCHER, complet et reduit, Rapportsde Recherche INRIA, i .
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BERNADOU. 11. ; CIARLET, P.G. [19 76J : Sur l'ellipticite du modelelineaire de coqu es de W. T. Koite~ in Computing Me t hods in Appl iedSciences and Engineering (R. Glowinski and J .L. Lions, Editors ),pp. 89-1 36, Lecture Notes in Economics and Ma t hema t ica l Syst ems,Vol . ~, Springer-Verlag, Berlin.
BERNADOU , M. ; DUCATEL, Y. [1978J : Methodes d'elements finis avecintegration numerique pour des problemes e l l ipt i ques du quatriemeordre, Rev . Fran9aise Automat . Informat . Recherche Operationne l l e,Analyse Numerique , ~, Numer o I, pp. 3-26 .
BERNADOU, M. ; HASSAN, K. [1981J : Basis functions for general HSIEH-CLOUGH-TOCHER triangles, compl et e or reduc ed, In ternat . J . Numer .Methods Engrg . , 12, pp . 784-789.
BOGNER, F .K. ; FOX, R.L. ; SCHMIT, L. A. [1965J : The generation ofinterelement compa t i b l e s t i f f ness and mass matrices by the us e ofinterpolation formulas, in Proceedi ngs of the Conference on Matr i xMethods in Structural Mechanics , ~lr ight Patterson A.F . B. , Ohi o .
BRAMBLE, J.H. ; HILBERT, S.R. [1970J : Estimation of linear functionalson Sobolev spaces wi th app lication to Fourier transforms and s pl i neinterpolation , SIAM J . Numer . Anal . 2, pp . 113-124 .
CARLSON, D. E. [ 1972J : Linear The rmoelas tic i ty , Handbuch der Physi k ,Vol. VI a-2, Springer-Verlag, Berlin, pp . 297-345.
CIARLET, P. G. [1976J : Conforming finite element methods for the sh ellproblems, in The Mathematics of Finite El ements and Applicati ons II(J .R. Whiteman, Editor), Academic Press, London, pp . 105-123.
CIARLET, P.G. [1978J : The Fin ite Element Method f or Elliptic Probl ems ,Nor t h- Hol l and , Amsterdam.
CIARLET, P.G. ; DESTUYNDER, P. [1979J : "Appro ximation of three-dimensional model s by two-dimensional models in plate theory",Energy Methods in Finite Element Analysis , Edited by R. Glowinski,E.Y. Rodin, O.C. Zienkiewicz; John Wiley & Sons , Chi chester,pp. 33- 45 .
CLOUGH, R.W . ; JOHNSON, C.P. [1970J : Finite element analys is ofarbitrary thin shells, Proceedings ACI Symposium on concrete thinshells , New-York, pp . 333-363 .
CLOUGH, R.W. ; TOCHER, J. L. [1965J : Finite element stiffness matricesfor analysis of plates in bending, in Proceedings of the Conferenceon Matrix Methods in Structural Mechanics , Wright Patterson A.F.B.Ohio .
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COUTRIS, N. [1976J : Theoreme d'existence et d'unic ite pour un problemede flexion elastique de coques dans Ie cadre de la modelisation deP.M. Naghdi . C.R. Acad. Sci. Paris, Ser. A, ~, pp . 951-953.
COUTRIS, N. [19 78J : Theoreme d'existence et d'unicite pour un problemede coque elastique dans Ie cas d'un modele lineaire de P.M. Naghdi,Rev. Fran9ai se Automat . Informat. Recherche Operationne l le, Analys eNumerique , ~, nO I, pp. 51-58.
COv~ER, G.R. [1973J : Gaussian quadrature formulas for triangles,Internat . J . Numer. Methods Engng., 1, n° 3, pp. 405-408.
COYNE & BELLIER, [1977J : Barrage de GRAND'MAISON, Dos sier pre liminai re.CRAINE, R.E. [1968J : Spherically symmetric problem i n finite thermo-
elastostatics, Quart. J. Mech . App l. Math . , ~, Pt. 3, pp . 279-291.DESTUYNDER, P. [1980J : Sur une j ust ifi cati on mathematique des theor i es
de plaques e t de coques en elasticite lineaire, These d'Etat,Universite Pierre et Marie Curie, Paris.
DESTUYNDER, P. ; LUTOBORSKI, A. [1980J : A penalty method for theBUDIANSKY-SANDERS shell model. Rappor t Interne, £2, Centre deMathematiques Appliquees de l'Ecole Polytechnique.
DUPUIS, G. [1971J : Application of Ritz method to thin elastic shellanalysis, J. Appl. Mech . , 71-APM- 32, pp. 1-9.
DUPUIS, G. ; GOEL, J. -J. [1970aJ : Finite elements with a high degreeof regularity, Internat. J . Numer. Me thods Engrg. ~, pp. 563-577.
DUPUIS, G. ; GOEL, J .-J. [1970bJ : A curved finite element for thinelastic shells, Internat. J . Sol i ds and Struct ures ~ , pp . 1413-1428 .
DUVAUT, G. ; LIONS , J .L. [ 1972J Les In equations en Mecanique et enPhysi que, Dunod, Paris.
ERICKSEN, J.L. [1960J : Appendix- Tensor Fields, Handbuch der Physik,Vol. III/I, Spr inger-Verlag, Berlin, pp. 793-858.
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GERMAIN, P. [1973J : Cours de Mecanique des Mili eux Continus, Tome I,Theorie Generale, Masson, Paris.
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~
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Symbol
a
a(. , .)
a .1.
...-a a
+aa
GLOSSARY OF SYMBOLS
Name or description
bilinear form associated with theshell strain energy
approximate bilinear form
vertices of a triangle
covariant basis of the tangent
plane to the undeformed mi dd l e
surface
contravariant basis of the tangent
plane to the undeformed middle
surface
covariant basis of the tangentplane to the deformed middle
surface
first fundamental form
elements of the inverse matrix-I
[aA ]r
normal vector to the undeformed
middle surface
Place of definitionor first occurence
(1.1.18) (I .5.13)
(1.3.26)
(2.2.4) (2.4.15)
pages 30, 66
(I. 1.2)
(1.1.6)
(1.3.3)(1.3.15)(1.3.18)
(I .1.4) (I .5.12)
(I. I. 7) (1.5.14)
(1.1.3)
Symbol
AS
b .1
174
Name or description
normal vector to the deformed
middle surface
matrix of shape functions for
ARGYRIS triangle
matrix of shape functions for
complete H.C.T. triangle
matrix of shape functions for
reduced-H.C.T. triangle
denotes parameters which are
antisymmetric with respect to
the plane x = 0
matrix coefficient associated with
the bilinear form
midpoints of the sides of a
triangle
nodes of a numerical integration
scheme
second fundamental form
mixed components of the second
fundamental form
contravariant components of the
second fundamental form
mixed components of the second
fundamental form of the de formedmiddle surface
Place of definitionor first occurence
(1.3.4)(1.3.19)
{3.1 .19),
Figure 3. I. 2
{3.1.33),
Figure 3.1.3
(3.1.41) ,
Figure 3.1.4
(6.4.17) to (6.4 .20)
(I.5.3)(I.5.1O)
page 30
(2.2.2) (2.4.10)
(I.1.5) (I.5.15)
(1.1.8)
(1.1.8)
(I.3.5) (I.3. 7)
Symbol
B.~
c .i.
175
Name or descript ion
matrix as soc iated with the l inearf orm f h ( . )
t he point of intersection of a l i nef r om a vertex a i perpendicular to
the oppo s i t e side of a triangle
mix ed components of the third
fundam ental form
conf i guration of the undeforrned
she ll
Place of de finitionor f i r s t occurence
( 3 .3 . 9)(3 . 4 . 9)
(3. 5 . 9)(3 . 6. 9)
page 30
(1.5.17)
(1 . 2 . 2 ) ; pa ge 10
c,. * conf i guration of t he de formed sh e ll pa ge 10
c,.m, m=O, l
ds
dS
as
dV
d .i.
s pac e of funct i ons m times
continuously differentiab l e
l ine e l emen t
area e lement
area element of t he middle surf ace
bound ary of t he middle sur fa ce
clamped part of the boundaryof t he middle surface
volume e l ement
compone nts of a change ma t r ix
c ompone nt of a chan ge mat r ix
page 29
( 4 .3 . 16)
(5 .2 .8)
( 1. 1. 19 )
page 5
(1 .3 .28 )
(5. 3.1 8)
(3 . 1.23)
(3 . 1.24)
Symbol
DC
D,\.~
DC .~
DLCLC.~
DLCLR.~
176
Name or description
set of global degrees of freedom
change matrix associated withARCYRIS triangle
change matrix associated withcomplete-H.C.T. triangle
change matrix associated with
reduced-H.C.T. triangle
change matrices
change matrices
sets of global degrees of freedom
set of global degrees of freedom
associated with ARCYRIS triangle
set of global degrees of freedomassociated with complete-H.C.T.triangle
set of global degrees of freedomassociated with reduced-H.C.T.
triangle
set of local degrees of freedom
associated with ARCYRIS triangle
set of local degrees of freedom
associated with complete-H.C.T.triangle
Place of definitionor first occurence
(3.2.6)
(3.1.22)(3.2.7)
(3.1.36)
(3.1.44)
(3.3.4)(3 .4.4)
(3.5 .4)(3.6.4)
(3.3.2)
(3.1.20)
(3.1.34)
(3.1.43)
(3 .1.18)
(3.1.32)
Symbol
DLLCR.1
DT
DT.1
e
....e i , i =I ,2,3
177
Name or description
set of ZoeaZ degrees of freedomassociated with reduced-H.C.T.triangle
change matrix
change matrices
a-th (FRECHET) derivative of afunction v at a point a
thickness of the shell
orthonormal basis
permutation matrices
Place of definit ionor first occurence
(3 .1.40)
(3.2.8)
(3 .3 .3)
page 3
(1.2 .1)(4 .4.3)
page 5
(1.1.17)
E
E( . )
E(. )
YOUNG 1 S modulus
error functionals as so c i a t ed withthe use of a numerical integrationscheme
strain energy of the arch dam
pure deformation component of thestrain energy
page 15,page 123
(2 .4 .12)
(2.4.11 )
(5.3 .4)
(5 .3 .6)
(5.3 .2)
thermal component of the strainenergy
Euclidean plane
Euclidean space
(5.3.7)(5.3 .20)
pages 3, 5
page 5
Symbol
f c.:
F
g
....g.~
....g.~
178
Name or description
linear form giving the work ofexternal loads
approximate linear form
matrix associated with the linearform f(.)
mapping which associates triangleA
K with the reference triangle K
= det (g .. )~J
gravitational acceleration
covariant basis of the undeformedshell
covariant basis of the deformedshell
metric tensor of the undeformedshell
Place of definitionor first occurence
(1.3.29) (5.4.2)
(2.2.5) (2.4.16)
(1.5.20) (5 .5.2)(6.4.21)
(2.4.1)
(5.1.2)
(5.1.2) (5.2.2)page 123
(1.2.3)
(1.3.5)
(1.3.7)
g ..~J
metric tensor of the deformed shell (1.3.7)
functions which give AIJ (1.5.3)
....G
h
volume density of the weight of
the dam
= max hKK € "Ifh
(5.1.1 )
(2.1.2)
Symbol
k
(K,P,E)
2.r,
LAMBD
LAMBD.~
M
M
M
M.~
179
Name or description
= diam (K)
SOBOLEV space
upstream wall of the dam
energy of the shell associated with
a displacement field ~
thermal conductivity coefficient
finite element
reference finite element
length of the side a i_ 1 a i + 1
matrix of barycentric coordinatesand their derivatives
matrix of barycentric coordinatesand their derivatives
position of a particle of theundeformed shell
number of subdivisions of theinterval [O,IJ of the x-axis
position of the particle M after
deformation
matrices associated with theapproximate bilinear form
Place of definitionor first occurence
(2.1.1)
page 4
page 113
(1.4.6) (5.4.1)
page 116
page 40
page 40
(3.1.16)
(3.2.9)
(3.3.5) (3.4.5)
(3.5.5)(3.6.5)
page II
page 124
page II
(3.3.7) (3.4.7)
(3.5.7)(3.6.7)
Symbol
->-n
->-n
n.1
N
p
P
Pm(K)
180
Name or description
matrix associated with the change
of curvature tensor
unit normal vector to the upstreamwall directed to the external part
of the arch dam
unit normal vector to the
boundary f.
parameters used to construct
matrix DA
number of subdivisions of the
interval [O,IJ of the y-axis
pressure upon the upstream wall
of the dam
basis polynomials for ARGYRIS
triangle
position of a particle of the
undeformed middle surface
position of the particle P after
deformation
space of all polynomials of degree
space of shape functions for
element K
symmetry plane of the arch dam
Place of definitionor first occurence
(1.5.9)
page 112(5.2.4)
(6.3.4)
(3.1.22) (3.1.25)
page 124
(5.2.2)
(3. I. 19)
page II
page II
pages 30, 40
page 30
page 132
Symbol
s
S
S
S,S
->-t
T
~h
Tup
181
Name or description
curvature radius of the middle
surface of the arch dam
shape functions for the complete-
H.C.T. triangle
shape functions for the reduced-
H.C.T. triangle
arc length of the middle line
denotes parameters which aresymmetric with respect to t heplane x = 0
upper-triangular matrix
middle surface of the shell
un it tangent vector to the
boundary f o
half-tangents at a salient point
change of temperature field
triangulation of the polygonal
domain n
downstream wa l l temperature
up stream wall temperature
work of gravitational load ing of
the arch darn
Place of definitionor first occurence
(4.3.17)
(3.1.33)
(3 .1.41 )
(4.4.1)
(6.4. 17)
to(6.4.20)
page 143
page 5
(6.3 .3 )
(6.3.7)
(5.3.10)(5.3.12)
(2.1.1)
(5.3.11)(7 .1.1 )
(5.3.11)(7.1.1)
(5 .1.3) (5.1.6)(5.1. 7)
Symbol
182
Name or description
wor k of wa t er pr e s sur e l oading
mean-value of the upstr eam anddownstream wall temperatures
moment of order 1 associated wi t hthe upstream and downstr eam wal ltemperatures
Place of definitionor first oc curence
(5 .2 .6 ) (5 .2 . 10)
(5 .3 .1 3)
(5 .3.14)
-+u
u
-+U
covariant derivatives ( 1. 1. 11)
covariant derivatives ( 1. 1.12)
displacement field of the particlesof the middle surface S ( 1.3 . 13)
column matrix of components of thedisplacement ~ and their derivative (1. 5 .1)(1.5. 2)
d isplacement field of the particles page 11 ;
of C (1 .3 . 12) (1. 3.20)
v
-+V
approximate displacement fi eld (6.6.2)
column matrix of components of thedisplacement; and their derivative (1. 5.1)(1. 5.2)
space of admi ssible displacements ( 1. 4 . 2)(5 .4 . 3)
-+V
-+
V
-+antisymmetric subspace of V
-+symmetric subspace of V
approximate space of admissibledisplacements
(6 . 4 . 10)
(6. 4.11 )
page 29 ;( 2 . 1 . 6) (2.1.7)
Symbol
Z
Zo
a
a
*y . .~J
r
183
Name or description
subspace of Xh l
subspace of Xh2
SOBOLEV sp aces
finite element subspace of thespace HI m )
finite element su bs pa ce of t he2space H (n)
co ordinate along t he vertical
height of the arch dam
level of wat er in the reservoir
parameter of t he arch dam
coef f i c ient of l inear expans ion
strain t en sor of t he she ll e
mixed component s of the s t rain
tensor of the shell
strain t enso r of the middl e
surfac e
mixed component s of t h e s t r ain
tensor of t he middle su rface
boundary of the domain n
Pl ace of definitionor first occurence
(2 . 1.4)
(2.1.5)
page 3
(2.1. 3)
(2. 1. 3)
Fig . 4 . I . 3 ; (4 .2.3)
(4. 2.5)
page 151
(4 . 2. 5)
(5. 3. 3) ; page 124
(I . 3 . 6) ; pa ge I 15
(6.7. 3)
(1.3 .10) (1 .3 .2 1)
( I. 3 .25) ( 6 .7 • I )
pag e 5
Symbol
raBy
184
Name or description
fa = clamped part of the boundary f
CHRISTOFFEL's symbols
CHRISTOFFEL's symbols
KRONECKER's symbols
I~I = 2.(area of the triangle)
Place of definitionor first occurence
page 16
(1.1.10)(1.5.16)(4.3.24)
(4.3.18) to (4.3.23)
(1.5.7)
(3.1.5)
->-£ a
e
~ll = ~22 = 0 ; ~12 = ~21 = I .( 1. 5 . 7)
orthonormal basis in the Euclidean2plane lR (3.1.2)
£-system for the middle surface (1.1.16)
eccentricity parameters (3.1.14)
parameter used in the definitionof the middle surface of the arch
e
dam
parameter used in the definitionof the middle surface of the archdam
temperature function of the archdam
initial uniform temperature of thearch dam
(4.2.3)
(4.2.3)(4.2.5)
(5.3.1)
(5.3.1 )
Symbol
A.~
po
185
Name or description
barycentric coordinates of t he
triangle
matrix associated with the straintensor of the middle surface
POISSON's coefficient
system of orthonormal coordinates2of the 8 -plane
system of curvilinear coordinates
for space 8 3
new system of curvilinear
coordinates used in the descriptionof the deformed shell
interpolation operator
interpolation operator associated
with ARGYRIS triangle
interpolation operator associated
with complete-H .C.T. triangle
i nt er pol a t i on operator associatedwith reduced-H.C.T. t riangle
~-interpolant of a function ; € V
parameter used in the definition of
the middle surface of the arch dam
Place of def i nit i onor firs t occurence
(3.1.3) to (3 .1.5)
(I.5 .6)
(I .3.24) (5 .3.2)
page 123
page 3
page 9
page 12
page 30
(3.1.17)(3 .1 .28)
(3. 1 .31)(3 .1.37)
(3.1.39) (3 .1 .45)
(2 . 2 .6)
(4.2.6)
Symbol
...<P
w
186
Name or description
mass density of the concrete in
the undeformed configuration
mass density of the water
change of curvature tensor of themiddle surface
mixed components of the change ofcurvature tensor of the middlesurface
s t r es s tensor of the shell
set of de grees of freedom
mappi ng used i n t he definition ofthe middle surface
functional used in the (infinite-simal) rigid bod y motion lemma
equivalent norm on the space(HI(n)) 2 x H2cn)
angle used i n order to take i ntoaccount boundary condi t i ons
weights of the numerical
integration scheme
Place of defini tionor f irst occurence
(5 .1. 2); page 123
(5 . 2 . 2) ; page 123
(1 .3 .11) (1.3 . 22)
(1 .3 .25) (6.7. 2)
(5 .3 . 1) (6 .7 .4)
pa ge 30
(1.1.1)
(1.6. 3)
(1 .6.1)(1 .6 .2)
(6.3 .3)(6.3.4)
(2.2.2) (2 . 4. 10)
open bounded subset in a plane 8 2
which is used as a reference domain page s I, 5 ;Figure 4 .2 .2
Symbol
187
Name or description
reference domain of the middlesurface of the arch dam beforesimplifications
half-domain n
Place of definitionor first occurence
Figure 4.2.2
Figure 6.4.1
11-llm,p,n norm on the space rf,pcn), that is page 3
Ilvl~,p =( L In Inctvl P d~)\/P, \~p<coIctl~m
semi-norm on the space "f,pcn),that is page 3
lvl =( L I InctvlP d~)\/P, \~p<com,p nIctl=m
«- ,-» m n,
I-I
norm in the dual of the space~,PCQ)
scalar product on the space RmCn)= "f,2 cn), that is
«u,v»m,n = L In nctu nctv d~Ictl~m
norm on the space L 2 cn) , that is
\vi = \vIo,nor
Euclidean norm in 8 3
Lemma 2.4.\
page 4
page 4
page 4
(1.6.2)
C1. 1.3)
Symbol
188
Name or description
1 1 d . 3 .usua sca ar pro uct i n 8 , that as
(~,b) = -:·b
Place of definitionor first occurence
page 6
inclusion with continuous injection page 4
covariant derivatives ; for
instance Ta iY • T, aBlY (I . I • II) (I . I. 12)
[OJ
[IJ
this exponent indicates adifference between tensors in 8 3
and tensors defined on the middle
surface
corresponding degree of freedom
is known
corresponding degree of freedom
is unknown
(1.3.6)
page 128
page 128
page 43pages 112, 123pages 17, 120
elements pages 39, 40
INDEX
Abstract error estimateAcceleration (gravitational -)Admissible displacement spaceAffine regular family of finiteAlmost-affine regular family of finite elements
Approximation (conforming -)Arc lengthArch dam
- simulationsdefinition of the -variational formulation of the - problem
Area element of the surfaceARGYRIS triangle
basis polynomials for the -boundary conditions associated with -criterion on the choice of numericalintegration scheme associated with -energy functional modules associated with -implementation of the -second member modules associated with -shape function for the -symmetry conditions associated with -
Asymptoticerror estimate theoremexpansions
Bandwith (sky-line - factorization)Barycentric coorrlinatesBasis polynomials for the
- ARGYRIS trianglecomplete-H.C.T. trianglereduced-H.C.T. triangle
page 40page 29page 106
page 3pages 89,91,94,95pages 109,119,1 21
page 9page 32page 7!page 130page 38page 38page 80
page 69
page 80page 71page 141
page 56page 15
pages 90, 143
page 66
page 71page 76page 79
190
Border degr ee s of freedomBoundary condit ions associated with the
- ARGYRIS triangle- complete-H.C.T. triangle- reduced-H.C.T. triangle
t riangle of type ( 1)t r i angl e of t ype (2)
Boundar y condit ions
clamped -free -ps eud o -
Boundary (curved - )BRAMBLE-HILBERT lemmaCalculation of
- displacementsstrain tensorstress tensor
Cartesian coordinatesChange s
effect of - of numerical integration s chemeeffect of - of temperatureeffect of - of triangulation- of curvature tensor- of temperature field
CHOLESKI method
C~~ISTOFFEL symbolsClamped condi tionsClampe d condi tions associa ted wi th
- ARGYRI S triangle- complete-H.C .T. triangle- reduced-H.C .T . triangle
triangle of t ype (I)
triangle of t yp e (2)Coefficient of therma l conductivityCoefficient of linear expansion of the concrete
Combined effect of loads
pages 75,82,126
page 130page 131page 131
page 129page 129
page 125page 125
page 139pa ge 63pa ge 45
page 144
page 145page 145page 66
pages 158, 166
pages 154, 157pa ges 157, 160
pa ge 13page 117pages 90 ,139 ,1 43
pages 8 ,104,105
pages 16 , 139
page 130page 131
page 131
page 129
page 129
page 116page 124
page ISS
191
Complementary hypotheses of KOlTER
Component (thermal - of the energy)
Component s of a tensorcont ravariantcovariantmi xed -
Conductivity (thermal - coef f i c i ent )
Configur ation of a shell
ne w -reference
Conforming approximation sConf or mi ng finite element me t hods
Cons i s tency of an integration schemp.
Continuous prob l emContravari ant components of
a t ensor
s t rainstre ss
Convergen c e of a finite element method
Coordinatesbaryc entric
cartesian -curvilinear -ne w system of cu rvil i ne ar
no rmal _ . system
orthonormal -
COSSERAT surf ac e theory
Covar i an t- componen t s of a tensor- der i vatives .
Cr i t e r i on on the choice of numerical integration
s chemef or ARGYRIS tr i an glefo r complete-H. C. T. tr i angle
for r educ ed-H.C.T . triangle
i n general case
paee 11
paee 116
page 7pag e 7page 7
page 116
page 10
page 10pa ge 29
pages 2,28,30page 44page 5
pa ge 7
page 115pa ge 115
page 39
page 66
page 66
pa ge 2
pag e 12
pag e 9pa ge 3
page
pa ge 7pag e 8
pag e 38pa ges 38 ,62
pages 38,62
pa ges 37, 39
192
Curvature
change of - tensor
- radius RC of the damnormal -
Curved boundary
Curved shell elements
Curvilinear coordinates
new system of -Degrees of freedom of a finite element
global -local -set of
Definition
geometrical of the arch dam- of the arch dam
- of the middle surface of a shellDensity
mass - of concretemass - of water
Discrete problem
new -
Displacement (admissible - space)Displacement field
calculation of theDomain (reference -)Eccentricity parameters
Effect of changes of
- numerical integration schemetemperaturetriangulation
Effect of
combined - loads- gravitational loads
- hydrostatic loads
page 13page 103,104page 106page 63pages 27,28page 2
page 12
pages 69,72pages 69,70page 30
pages 91,94,95page 89pages 5,97
page 123pages 112,123pages 27,33page 33pages 17, 120pages 2, 11, 13page 144page 2
pages 69 ,70
pa ges .158,166pages 154,157pages 157,160
page 155page 152page 153
193
Ellipticity...V- -...Vh- -
Energy functional modules associated with- A.RGYRIS triangle- complete-H.C.T. triangle- triangle of type (2) and complete-H.C.T.
triangle- reduced-H .C.T. triangle
triangle of type (1) and reduced-H.C.T.triangle
Energy of the damEnergy (potential - of external loads)Energy (shell strain -)Error estimate
abstract -asymptotic - theoremexamples of -local -- theorem
Error functionalsExistence and uniqueness of a solutionExpansions (asymptotic-)Expansion (coefficient of linear - of theconcrete)Factorization (sky-line bandwith -)Family of finite elements
regular -affine regular -almost .a f f i ne regular -
Family of shell theoriesfirst -second -
Finite elementaffine regular family of - salmost-affine regular family of - sconforming - method
page 25pages 43,54
page 80page 82
page 84page 85
page 87pages 115, 119pages 3,16page 15page 39page 43page 56page 38page 45page 56pages 41,42pages 21,22,121page 15
page 124pages 90,143
page 29pages 39,40page 40
pagepage
pages 39,40page 40pages 2,28,30
194
curved shell -flat - for shellsisoparametric solid - for shells
reference -~
space VhForm
first fundamental -other expression fo r the bilinear -o ther expression for the linear -
second fundamenta l -
Formulationequivalent variational
minimization -
variational -
FRENET-SERRET formulae
GAUSS relations
Gravitationalacceleration
loads
H.C .T. trianglecomplete -criterion on the choice of numerical
integration scheme for -energy functional modules associated with
complete -energy functional modules associated with
t riangle of type (2) and complete -energy functional modules as soc i a t ed wi th
reduced -energy functional modules associated with
triangle of type (1) and reduced
implementat ion of complete -
implementation of reduced -
reduced -second member modules associated with
complete -
pages 27,28pages 27,28pages 27,28page 40page 30
pages 7,103page 18pages 18,21,121pages 7 ,103
pages 17,137pages 17,121pages 17,90,109,pages 119,121page 104page 8
pages I 12, 123page 109
page 32
page 38
page 82
page 84
page 85
page 87pa ge 75page 77
page 32
page 82
195
second member modules associated withtriangle of type (2) and complete -second member modules associated withreduced -second member modules associated withtriangle of type (I) and reduced -
HOOKE's lawHybrid methods for general shellsHydrostatic loads
work of -Hypotheses (complementary - of KOlTER)Implementation
- of ARGYRIS triangle- of complete-H.C.T. triangle
- of reduced-H.C;T. triangle
- of triangle of type (I)
- of triangle of type (2)
Integrationnode.. of a numerical - schemenumerical - schemenumerical - scheme over a reference set Knumerical - techniquesweight of a numerical - schemecriterion on the choice oEnumerical - schemeeffect of changes of numerical - schemes
Interpolant e1J'"--)hInterpolation
- modules- operator
KOlTERcomplementary hypotheses ~f -linear model of -
KORN inequalityLAX and MILGRM1 theoremLoads
gravitational
page 84
page 85
page 87page 13
page 28page III
page 113,114page II
pages 3,65,90,123page 69page 75page 77
page 67
page 68
page 33page 33page 41page 2page 33pages 37,38,39pages 158, 166page 34
pages 3,65page 30
page II
page 10page 22
page 25
page 109
196
hydrostatic
surface -t her ma l -
volume -work done by external -
Mass density of- concrete
- water
Middle surfacedefinition of the -
Minimization formulat ionMi xed components of a tensor
Mixed methods of finite elements
Momentsof orderof order ~ 2
surface -Node s of a numerical integration scheme
Nor ma lcurvatures
- vectorOperator ( i n t er polat i on - )
Orthonormal f i xed systemPhy s i ca l components of stresses
left- -right- -
Physical (values of - cons t ant s )
Plate (equation of -)
Point (salient -)POI SSON' s co efficientPo t en t i a l en ergy of exter na l loads
Problemcontinuous
discrete -
new di screte
page I I Ipage 16page 114page 16page 16
page 123page 123page I
pages 5,97page 121page 7pa ge 28
page IIIpage IIIpage 16pa ge 33
pa ge 106page 6page 30pag e 5pa ge 90,144page 148page 147page 123page 63page 127pages 2 , 13, 15, I 23pages 3,16
pa ge 5pages 27 ,33page s 33,42
197
Profile of a matrix
Pseudo-boundary conditionsRadius (curvature - of the arch dam)Reference
local - system
- configuration- domain- triangle
Regular pointResultant of the surface and volume loadsRigid body lemma (infinitesimal-)
Salient pointScheme 1Scheme 2Scheme 3Second member modules associatef with
- ARGYRIS triangle- complete-H.C .T. triangle
triangle of t ype (2) and complete-H .C.T.triangle
- reduced-H.C.T. triangle- triangle of type (1) and reduced-H.C .T.
triangleShape funct ionsShape functions for
- ARGYRIS triangle- complete-H .C.T . triangle- reduced-H .C.T. triangle
ShellShell theories
first family of -second family of -thick -thin -
pages 143,144
page 139pages 103, 104
pages 6, 10, 12
page 10page 2page 39page 5page 16pages 21,23
page 75page 34page 35page 36
page 80page 82
page 84page 85
page 87page 30
page 71page 76page 79pages 1,9
pagepagepagepage
198
Sky-line bandwith factorizationSOBOLEV's imbedding theoremSOBOLEV spacesSolution methodStrain energy of the arch damStrain tensor of the
- middle surface
- shellStress-strain-temperature relationsStress tensorStresses
calculation of the - in the damphysical components of the -
Surface (COSSERAT's)Symmetry conditionsSymmetry conditions and clamped conditions for
- ARGYRIS triangle- complete-H.C.T. triangle- reduced-H.C.T. triangle
triangle of type (I)
triangle of type (2)Tangent planeTemperature (change of - field)Thermal
- conductivity coefficient- loads
Thermoelasticity (equations of -)Thickness of
- a shell- the arch dam
Triangle of- type (I)
- type (2)
pages 90,143pages 4,48,53page 3page 139page 115
pages 13,145~al:les 11,12,145
page 115pages 11,115
pages 144,145pages 90,144,146page I
page 132
page 141page 142page 142page 140page 140page 6page 117
page 116page 114page 115
pages 1,9page 106
pages 31 ,67pages 3 1, 68
199
Triangulationeffect of change of -regular family of - s
Variational formulation
Variational formulation (equivalent -)Volume elementWeight of a numerical integration schemeWEINGARTEN (relation of -)Work of
- external loads- gravitational loads- hydrostatic loads- thermal loads
YOUNG's modulus
page 124
pages 157,160page 29pages 17,90,109,pages 119,121page 137page 118page 33page 8
page 16pages I 10, IIIpages I 13 , 114pages 114,118
pages 2, 15,123