Une formulation symétrique pour le couplage éléments finis-éléments de frontière en mécanique
Keywords:
symmetrical coupling, finite elements, boundary elements, symmetric Galerkin BEM, fracture mechanicsAbstract
This article presents a formulation for the symmetrical coupling of finite element and boundary element methods, based on the symmetric Galerkin boundary integral equations for three-dimensional elasticity, in regularized form. The stiffness matrix of an elastic region is, as a result, expressed in terms of the boundary displacement DOFs. Its extension to elastic regions containing cracks is also presented. The procedure has been implemented in the FEM-based environment CAST3M. Three numerical examples are shown: a pressurized spherical cavity in an infinite elastic-plastic medium, an assembly structure, and a cracked cylindrical bar.
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References
[BIE 95] BIELAK J., MACCAMY R. C., ZENG X., « Stable coupling method for interface
scattering problems by combined integral equations and finite elements. », J. Comp. Phys.,
vol. 119, 1995, p. 374–384.
[BON 95] BONNET M., « Regularized direct and indirect symmetric variational BIE formulations
for three-dimensional elasticity. », Engng. Anal. with Bound. Elem., vol. 15, 1995,
p. 93–102.
[BON 99] BONNET M., Boundary Integral Equations Methods for Solids and Fluids, John
Wiley and Sons, 1999.
[BUR 99] BURGARDT B., « Contribution à l’étude des méthodes des équations intégrales et à
leur mise en oeuvre numérique en élastoplasticité », thèse, Ecole centrale de Nantes, France,
[HSI 90] HSIAO G. C., « The coupling of boundary element and finite element methods. », Z.
Angew. Math. Mech., vol. 70, 1990, p. 493–503.
[JOH 80] JOHNSON C., NEDELEC J. C., « On the coupling of boundary integral and finite
element methods. », Math. of Comput., vol. 35, 1980, p. 1063–1079.
[MOU 00] MOUHOUBI S., « Couplage symétrique éléments finis-éléments de frontière en mécanique
: formulation et implantation dans un code éléments finis », PhD thesis, Université
de Limoges, 2000.
[NED 85] NEDELEC J.-C., « Approximation des équations intégrales par éléments finis. Etude
d’erreur. », R. DAUTRAY J. L. L., Ed., Analyse mathématique et calcul scientifique pour
les sciences et les techniques (chap. 13), Masson, Paris, 1985, p. 953–968.
[SIR 93] SIRTORI S., MICCOLI S., KORACH E., « Symmetric coupling of finite elements
and boundary elements. », KANE J. H., MAIER G., TOSAKA N., ATLURI S. N., Eds.,
Advances in Boundary Element Techniques, p. 407–427, Springer-Verlag, 1993.
