Elément fini triangulaire de membrane avec degrés de liberté rotationnelsélément fini triangulaire de coque
Keywords:
Shell finite element, assembly of plates, normal rotationAbstract
For a long time, the coupling of non coplanar plates in space makes lot of difficulties because the normal rotations to the plane of the plate don’t occur as unknown. After recalling the main approaches which are actually used to solve these difficulties, we propose a finite element which explicitely takes into account the « drilling » parameters and passes the « hard » patch test. This one, associated to a bending finite element from Zienkiewicz and Specht is caracterized by three displacements and three rotations per node. The validation of this element is shown with the results of standard convergence tests. Some complementar results in static and dynamic which indicate the good accuracy of this element are presented in this paper.
Downloads
References
[ALL 84] ALLMAN D.J., « A compatible triangular element including vertex rotations for
plane elasticity analysis », Computer & Structures, vol. 19, n°1-2, 1984, p.1-8.
[ALL 88a] ALLMAN D.J., « The constant strain triangle with drilling rotations : a simple
prospect for shell analysis », Mathematics of finite elements and applications VI, LR
Whiteman (ed) Academic Press N.Y, 1988, p 233-240.
[ALL 88b] ALLMAN D.J., « Evaluation of the constant strain triangle with drilling rotations »,
International Journal for Numerical Methods in Engineering, vol. 26, 1988,
p. 2645-2655.
[AMI 92] AMINPOUR M.A., « An assumed-stress hybrid 4-node element with drilling degrees
of freedom », International Journal for Numerical Methods in Engineering, vol. 33, 1992,
p. 19-38.
[AYA 95a] AYAD R., « Une nouvelle approche variationnelle mixte-hybride pour les coques
avec effet de cisaillement transversal et un nouveau concept de rotation autour de la
normale pour améliorer la membrane », 2e Colloque National en Calcul des Structures 95,
Editions Hermès, 1995, p. 257-262.
[AYA 95b] AYAD R., BATOZ J.L., DHATT G., « Un élément quadrilatéral de plaque basé sur
une formulation mixte-hybride avec projection en cisaillement », Revue Européenne des
Eléments Finis, vol. 4, n°4, 1995, p. 415-440.
[BAT 88] BATOZ J.L., DHATT G., « Revue et bilan des éléments de plaque de type Kirchhoff
discret», Calcul des Structures et I.A., vol. 2, Fouet et al. Eds Pluralis, 1988, p. 137-160.
[BAT 90] BATOZ J.L., DHATT G., Modélisation des Structures par Eléments Finis, vol. 1 :
Solides élastiques, vol. 2 : Poutres et Plaques, Editions Hermès, 1990.
[BAT 92] BATOZ J.L., DHATT G., Modélisation des Structures par Eléments Finis, vol. 3 :
Coques, Editions Hermès, 1992.
[BER 85] BERGAN P.G., FELIPPA CA., « A triangular membrane element with rotational
degrees of freedom », Computer Methods in Applied Mechanics and Engineering, vol. 50,
, p.25-69.
[COO 74] COOK R.D., « Improved two-dimensionnal finite element », Journal Structural
Division ASCE, vol. 100, 1974, p.1851-1865.
[COO 87] COOK R.D., « A plane hybrid element with rotational d.o.f. and adjustable
stiffness », International Journal for Numerical Methods in Engineering, vol. 24, 1987,
p.1499-1508.
[COO 91] COOK R.D., « Modified formulations for nine D.O.F plane triangles that include
vertex rotations », International Journal for Numerical Methods in Engineering, vol. 31,
, p. 825-835.
[HUG 89] HUGHES T.J.R, BREZZI F., « On drilling degrees of freedom », Computer Methods
in Applied Mechanics and Engineering, vol. 72, 1989, p. 105-121.
[HUG 95] HUGHES T.J.R, MASUD A., HARAZI I., « Dynamic analysis and drilling degrees of
freedom », International Journal for Numerical Methods in Engineering, vol. 38, 1995,
p. 3193-3210.
[IBR 90] IBRAHIMBEGOVIC A., TAYLOR R., WILSON E., « A robust quadrilateral membrane
finite element with drilling degrees of freedom », International Journal for Numerical
Methods in Engineering, vol. 31, 1990, p. 445-457.
[IBR 91] IBRAHIMBEGOVIC A., WILSON E., « Thick shell and solide finite elements with
independant rotation fields », International Journal for Numerical Methods in
Engineering, vol. 31, 1991, p. 1393-1414.
[IBR 93] IBRAHIMBEGOVIC A., FREY F., REBORA B., « Une approche unifiée de la
modélisation des structures complexes : les éléments finis avec degré de liberté de
rotation », Revue Européenne des Eléments finis, vol. 2, n °3, 1993, p. 257-286.
[IRO 80] IRONS B., AHMAD S., « Techniques of finite elements », John Wiley and Son, 1980.
[LIU 95] LIU M.L., TO S.W.S., « Vibration of structure by hybrid strain-based three nodes flat
triangular shell elements », Journal of Sound and Vibration, vol. 18, n °5, 1995, p. 801-
[MAC 84] MACNEAL R.H., HARDER R.L., « A proposed standard set of problems to test finite
element accuracy », SDM Finite Element Validation Forum, 25th AIAA/ASME/ASCE/AHS
Structures, Structural Dynamics and Mpaterials Conference, Palm Springs, CA, 1984.
[MAC 88] MACNEAL R.H., HARDER R.L., « A refined four-noded membrane element with
rotational degrees of freedom », Computers & Structures, vol. 18, 1988, p. 75-84.
[OLS 79] OLSEN M.D., BEARDEN T.W., « A simple flat shell element revisited »,
International Journal for Numerical Methods in Engineering, vol. 14, 1979, p. 51-68.
[SAM 00] SAMCEF, User Manual 8.1, Samtech, Liège (Belgique), 2000.
[SPE 88] SPECHT B., « Modified shape functions for the three node plate bending element
passing the patch test », International Journal for Numerical Methods in Engineering,
vol. 26, 1988, p. 705-715.
[TAY 93] TAYLOR R.L. AURICHKIO F., « Linked interpolation for Reissner-Mindlin plate
elements- Part I : a simple triangle », International Journal for Numerical Methods in
Engineering, vol. 36, 1993, p. 3057-3066.
[TIM 51] TIMOSHENKO S., GOODIER J.N., Theory of Elasticity, McGraw-hill, New York,
[XU 94] XU Z., ZIENKIEWICZ O.C., ZENG L.F., « Linked interpolation for Reissner-Mindlin
plate elements - Part III : an alternative quadrilateral », International Journal for
Numerical Methods in Engineering, vol. 37, 1994, p. 1437-1443.
[YUN 89] YUNUS S.M., SAIGAL S., COOK R.D., « On improved hybrid finite elements with
rotational degrees of freedom », International Journal for Numerical Methods in
Engineering, vol. 28, n°4, p. 785-800.
[ZIE 91] ZIENKIEWICZ O.C., TAYLOR R.L., The finite element method, Four Edition, vol. 1 et
vol. 2, Mc Graw Hill, 1991.
[ZIE 93] ZIENKIEWICZ O.C., XU Z., ZENG L.F., SAMUELSON A., WIBERG N.E., « Linked
interpolation for Reissner-Mindlin plate elements - Part I : a simple quadrilateral »,
International Journal for Numerical Mmethods in Engineering, vol. 36, 1993,
p. 3043-3056.
