Topological sensitivity of a shape functional defined from a solution of a high order PDE
Résumé
The topological gradient is defined as the leading term in the asymptotic expansion of a shape functional with respect to the size of a local perturbation. Introduced by Sokolowski [15] and Masmoudi [12], this notion has been intensively developed in recent years. There are many applications such as in mechanics of structures [3], in damage evolution modelling [2] and in image processing [6, 10, 5, 8]. This paper deals with the topological sensitivity of a cost function of the form j(Ω) = Ω |∇ m u Ω | 2 where u Ω solves a PDE of order 2m defined from the m-th Laplacian with Neumann boundary conditions. We place us in 2D and we consider a domain perturbed by a small crack.
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