Nouvel element secteur base sur le modele de deformation avec rotation dans le plan
Keywords:
sector element, rotational degree of freedom, assumed strain model, membrane, plane elasticityAbstract
Elements, as beams and membranes, could be used in finite element modelling of complex structural systems such as buried drain pipes or tunnels. These elements of different kind, based on classical formulations, generally do not share the same nodal degrees of freedom, which complicates construction of a compatible model. To solve this modelling problem, we propose to develop a new sector membrane element based on the assumed strain model with three degrees of freedom at each node including inplane rotation as an additional degree of freedom. This helps enormously to solve easily, general plane elasticity problems having a circular contour.
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References
[ALL 84) ALLMAN D.J., A compatible triangular element including vertex rotations for plane
elasticity, Computer & Structures, 19, p. 1-8, 1984.
[ALL 88a] ALLMAN D.J., Evaluation of the constant strain triangle with drilling rotations, Int.
lou. Num. Meth. Eng.. 26, p. 2645-2655, 1988.
[ALL 88b] ALLMAN D.J., A quadrilateral finite element including vertex rotations for plane
elasticity analysis, Int. lou. Num. Meth. Eng., 26, p. 717-730, 1988.
[ASH 72] ASHWELL D.G., SABIR A.B., A new cylindrical shell finite element based on simple
independent strain functions, Int. J. Mech. Sci., vol. 14, p. 171-183, 1972.
[ASH 71] ASHWELL D.G., SABtR A.B., ROBERTS T.M., Further studies in the application of
curved finite clements to circular arches, Int. J. Alech. Sci. vol.l3, p. 507-517, 1971.
[BAT 90] BATOZ Jean Louis, DHA TI Go uri, Modelisation des structures par elements finis,
Editions Hermes, Paris, 1990.
[BER 85] BERGAN P.G., FELIPPA C.A., A triangular membrane element with rotational
degrees of freedom, Comput. Meth. App. Mech. Eng., vol. 50, p. 25-69, 1985.
(BOU 87] BOUZERIRA C., Finite element analysis for general plane elasticity, Msc. thesis
university of Walles College ofCardiff(G.B), 1987.
[CAR 85] CARPENTER N., STOLARSKI H., BELYTSCHKO T., A flat triangular shell element with
improved membrane interpolation, Comm. App/. Num. Meth., vol. I, p. 161-168, 1985.
[COO 86] CooK R.D., On the Allman triangle and a related quadrilateral element, Comput. &
Struct., vol. 22, p. 1065-1067, 1986.
[COO 87] CooK R.D., A plane hybrid element with rotational d.o.f and adjustable stiffness,
Int. lou. Num. Meth. Eng., vol. 24, p. 1499-1508, 1987.
[DJO 90] OJOUDI M.S., Strain based Finite Elements for linear and geometrically non-linear
analysis of structures, PhD thesis university of Walles College of Cardiff (GB), 1990.
[IBR 93)1BRAHIMBEGOVIC A., FREY F., REBORA B., Une approche unifiee de Ia modelisation
des structures complexes, Revue Europeenne des Elements Finis. vol. 2, p. 257-287,
[RAJ 69] RAm l.S., RAo A.K., Stiffness matrices for sector elements, A.l.A.A.J. 7, p. 156-
, 1969.
[RAJ 73] RAJU I.S., KRISHNA A.V., RAO A.K., Sector elements for matrix displacement
analysis, Int. J. of Num. Met h. in Eng .. vol. 6, p. 553-563, 1973.
[REK 80] REKATCH V., Problemes de Ia theorie de l'elasticite, Edition MIR Moscou, 1980.
[SAB 85] SABIR A.B., A rectangular and triangular plane elasticity element with drilling
degrees of freedom, Chapter 9 in Proceeding of the 2nd international conference on
variational methods in engineering, Southampton University, Springer-Verlag, Berlin,
p. 17-25, 1985.
[SAB 86] SABIR A.B., SALHI H.Y., A strain based finite element for general plane elasticity in
polar coordinates, Res. Mechanica, 19, p. 1-16, 1986.
[TAY 86) TAYLOR R.L, S!MO J.C., ZIENKIEWICZ O.C., CHAN A.C., The patch test : A
Condition for Assessing Finite Element Convergence, Int. lou. Num. Meth. Eng., vol. 22,
p. 39-62, 1986.
[TIM 51) TIMOSHENKO S., GOUDIER J.N., Theory of elasticity, Me Graw Hill New York,
[ZIN 91) ZIENKIEWICZ O.C., TAYLOR R.L., The Finite Element Method, fourth edition, vol. I,
Me Graw Hill London, 1991.
