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Article Dans Une Revue Engineering Analysis with Boundary Elements Année : 2001

Boundary element based formulations for crack shape sensitivity analysis

Marc Bonnet

Résumé

The present paper addresses several BIE-based or BIE-oriented formulations for sensitivity analysis of integral functionals with respect to the geometrical shape of a crack. Functionals defined in terms of integrals over the external boundary of a cracked body and involving the solution of a frequency-domain boundary-value elastodynamic problem are considered, but the ideas presented in this paper are applicable, with the appropriate modifications, to other kinds of linear field equations as well. Both direct differentiation and adjoint problem techniques are addressed, with recourse to either collocation or symmetric Galerkin BIE formulations. After a review of some basic concepts about shape sensitivity and material differentiation, the derivative integral equations for the elastodynamic crack problem are discussed in connection with both collocation and symmetric Galerkin BIE formulations. Building upon these results, the direct differentiation and the adjoint solution approaches are then developed. In particular, the adjoint solution approach is presented in three different forms compatible with boundary element method (BEM) analysis of crack problems, based on the discretized collocation BEM equations, the symmetric Galerkin BEM equations and the direct and adjoint stress intensity factors, respectively. The paper closes with a few comments.
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Dates et versions

hal-00092385 , version 1 (09-08-2008)

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Marc Bonnet. Boundary element based formulations for crack shape sensitivity analysis. Engineering Analysis with Boundary Elements, 2001, 25, pp.347-362. ⟨10.1016/S0955-7997(01)00025-X⟩. ⟨hal-00092385⟩
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