BIBLIOGRAPHY - Springer978-1-4684-9143-2/1.pdf · BIBLIOGRAPHY ADM1S, R.A. [1975] : ... de plaques...

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.

BELL, K. [196 9] : A refined tr iangular pl at e bend ing element, Internat .J . Numer. Me t hods Engrg. l, pp . 101-122 .

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 .

Theorie des corps deformabl es , Herman,

168

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 .

COSSERAT, E. and F. [ 1909JParis.

169

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.

FRAEIJS DE VEUBEKE, B. [1965aJ : Bending and stretching of plates, inFroceedi ngs of the Conference on Mat rix Methods i n St ruct uralMechanics , Wright Patterson A.F .B., Ohio.

GERMAIN, P. [1973J : Cours de Mecanique des Mili eux Continus, Tome I,Theorie Generale, Masson, Paris.

GREEN, A.E. ; ADKINS, J.E . [1970J : Large Elastic Deformations, secondedition, revised by A.E. GREEN, Clarendon Press, Oxford.

GREEN, A.E. ; NAGHDI, P.M. [1970J : Non-isothermal theory of rods, platesand shells, In terna t . J. Solids and Structures, ~, pp. 209-244 .

Theorie de l 'Elast i ci t e , Editions

170

GREEN, A.E. ; NAGHDI, P.M. [ 1978J : On thermal effects i n the t he ory ofshells, Office of Naval Research Report nO UCB/~M-78-4.

HAASE, M. [1977J : On t he construction of Gauss ian quadrature formul aefor triangular r egions , ISD Inter nal Report, Univ . Stuttgart.

HA}ft1ER, P.C. ; STROUD , A.H. [1956J : Numer i ca l integration over simplexes .Math. Tabl es Aids Comput. , LQ, pp . 137-1 39 .

HILLION, P. [1977J : Numer ical i nt egr a t i on on a triangle, I nt erna t . J.NUmer . Methods Engrg., l! , pp . 797-8 15.

HLAVACEK , I. ; NECAS, J. [1970J : On i nequalit i es of Kor n' s t ype I andII , Arch. Rational Mech . Anal . , }2, pp . 305-334 .

JENNI NGS, A. [1 971J : Solution of variable bandwidth positive defini t es imultaneaous equations, Comput. J ., ~' p. 446 .

JOHNSON, C. [J 975J "On finite element methods fo r curved shell s usingflat element s", NUmerische Behandlung von Differentialgleichungen ,International Series of Numerical Mathematics, Vol . 11, Bi rkhauserVerlag, Basel and Stuttgart, pp . 147-154.

KIRCHHOFF, G. [1 876J : Vorlesungen uber Mathematische Physik , Mechanik ,Leipzig.

KNOWLES, N.C. ; RAZZAQUE, A. ; SPOONER, J .B . [l976J : "Experience off inite element analysi s of shell s t r uc t ur es", Finite El ement s forthin shells and curved members , Edited by D. G. ASH~mLL , R.H.GALLAGHER, J . Wil ey & Sons , London, pp. 245-2 62 .

KOlTER, W.T. [1966J : On the nonlinear theory of thin elastic shells,Proc , Kon , Ned. Akad. Wetensch., B 69 , pp , I-54 .

KOlTER , W.T. [1970J : On the foundations of the l inear theory of thinelastic shells, Proc . Kon . Ned. Akad. Wetensch. , ~' pp. 169-195.

KOlTER, W.T . ; SIMMONDS, J.C. [1973J : Foundations of shel l theor y,Proceedings of Thi r t eent h International Congress of Theor et i caland Appl i ed Mechani cs, Mo scow, Aout 1972, Springer-Verlag, Berlin,pp , 150-176 .

LANDAU, L. ; LIFCHITZ , E. [1967JMIR , Moscou.

LAURSEN, M.E . ; GELLERT, M. [1978J : Some criteria for numericallyintegrated matrices and quadrature formula s for triangles, Internat.J. NUmer . Methods Engng. , 12, pp . 67-76.

LIONS, J.L. ; MAGENES, E. [1968J : Probleme s aux limites non homogeneset applications, Vol. I, Dunod, Paris .

171

LOVE, A.E.H . [193 4J : The Mathematica~ Theory of E~asticity , CambridgeUni ver s i ty Press .

LYNESS, J. N. ; JESPERSEN, D. [19 75J : Moder a t e de gree symmetric quadra-ture rules for the triangle, J . Inst . Math. App~ . , ~, pp. 19-3 2 .

MALVERN, L.E. [1969J : Introduction t o the mechanics of a continuousmedium, Prentice-Hall, Inc., Englewood Cliffs .

Mc CONNELL, A.J. [1931J : App~ications of the abso~ute differentia~

ca~eu~us , Blackie, London and Glasgow.NAGHDI, P.M. [1963 J : Foundations of elastic shell theory, Progr ess in

So ~id Mechanics , Vol . ~, North-Holland, Amsterdam, pp . 1-90 .NAGHDI , P.M. [ 1972J : The Theory of Shel l and Plates , Handbuch der Physik ,

Vol. VI a-2 , Springer-Verlag, Berlin, pp . 425-640.NAYLOR, D.J . ; STAGG, K.G. ; ZIENKIEWICZ , O.C. [ 1975 J : Criteria and

assumptions f or numerica~ ana~ysis of dams , Proceedings of anI nternational symposium held at Swansea, U. K., 8-11 September, 1975,University College, Swansea.

~

NECAS, J . [1967J : Les Methodes Directes en Theor i e des Equat i onsE~ ~iptiques , Masson, Paris.

aDEN, J .T . ; REDDY, J . N. [ 1976J An In troduct i on t o t he Mathematica ~

Theory of Finite E~ements , Wi l ey Interscience, New-York .PERRONNET, A. [1979J, The Club MODULEF : "A library of subroutines fo r

finite element analysis" , Computing Methods in App~ied Science s ar4Engi neer i ng, Edited by R. Glowinski and J.L. Lions, Lectures Not esin Mathematics, ~, Springer- Verlag, Berlin, pp . 127-153.

RUTTEN, H.S. [1973 J : Theory and design of she~~s on the basis ofasymptotic ana~ysis, Rutten + Kruisman , Consulting engineers,Ri jswijk , Holland.

RYDZEWSKI, J.R. [1965J : Theory of Arch Dams , Pergamon Press, Oxford .SANDER, G. [ 1969J : Appl i cations de la methode des elements finis a la

f lexion des plaques, Co~~ection des pub ~ications de ~a Facu ~te de sSci ences de Li ege, ~.

STEPHAN , E. ; WEISSGERBER, v. [19 78J : Zur approximation von schalem mithybriden elementen, Computing , 20, nO I, pp . 75-95 .

STROUD, A.H. [1971 J : Approximate Ca~eu~ation of Mu ~tip ~e Integra ~s ,

Prentice-Hal l, Englewood Cliffs.TRUESDELL, C. [1953J : The physical components of ve c t or s and tensors,

Z. Angew. Math . Mech . , l2, nO 10-1 1, pp . 345-356 .

172

WEMPNER, G.R. ; ODEN, J.T. ; KROSS, D. [1968] : Finite Element Analysisof Thin Shells, J. Engrg. Mech. Div., ASCE, Vol . 21, nO EM6,pp. 1273-1294.

ZIENKIEWICZ, O.C. ; TAYLOR, R.L. ; TOO, J.M. [1971] : Reducedintegration technique in general analysis of plates and shells,Internat . J. NUmer. Methods Engrg.,~, pp. 275-290.

/ZLAMAL, M. [1974] Curved elements in the finite element method, Part II,

SIAM J. NUmer. Anal ., ll, pp. 347-362.

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


complete H.C.T. triangle


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


(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


(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


(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


(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


(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


(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)


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


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


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

pages 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 56page 15

pages 90, 143

page 66


190

Border degr ee s of freedomBoundary condit ions associated with the

- ARGYRIS trianglecomplete-H.C.T. trianglereduced-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 trianglecomplete-H.C .T. trianglereduced-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 129page 129

page 125page 125

page 139pa ge 63pa ge 45

page 144


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


193

Ellipticity...V- -...Vh- -

Energy functional modules associated with- A.RGYRIS trianglecomplete-H.C.T. triangle- triangle of type (2) and complete-H.C.T.

trianglereduced-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 trianglecomplete-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 trianglecomplete-H .C.T . trianglereduced-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 trianglecomplete-H.C.T. trianglereduced-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


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

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