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The standard topological derivative methodology developed by the authors in many papers requires knowledge of point-wise values of solutions to partial differential equations or variational equalities. However, the contact or unilateral problems are studied in the energy space setting, wsznumer2005here point-wise values are not defined. The authors proposed the approach based on domain decomposition...
We introduce the Griffith shape functional as the distributed shape derivative of the elastic energy evaluated in a domain with a crack, with respect to the crack length. We are interested in the dependence of this functional on domain perturbations far from the crack. As a result, the directional shape and topological derivatives of the nonsmooth Griffith shape functional are obtained with respect...
Formulae for the first order expansions of the Steklov-Poincaré operators in the case of the Laplace operator and of the elasticity boundary value problems in singularly perturbed domains in ℝ3 are presented. Such expansions are required for the evaluation of topological derivatives of the energy shape functionals.
We consider an elastic body with a rigid inclusion and a crack located at the boundary of the inclusion. It is assumed that non-penetration conditions are imposed at the crack faces which do not allow the opposite crack faces to penetrate each other. The differentiability of the elastic energy with respect to the crack length, for the crack located at the boundary of rigid inclusion, is established.
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