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Structure de la semi-dérivée eulérienne dans le cas de domaines fissurés et quelques applications

Abstract : In the general theory of shape optimization, the regularity conditions imposed on the boundaries of geometrical domains in R[exponent N], N = 2, 3, are relatively restrictive. Usually, the domain is supposed to be C2 , or at least Lipschitz for an application of boundary variations technique in order to derive the first order optimality conditions. On the other hand, there are many partial results on shape sensitivity analysis in domains with cracks. In particular such results concern the so-called Griffith criteria in damage rnechanics. In the work the unified approach is proposed for shape sensitivity analysis in the presence of cracks. We restrict ourselves to the 2D case, however the method is general and can be applied as well as to the 3D problems. Using the speed method of shape optimization, the structure of the Eulerian semiderivative of differentiable shape functionals is established in non smooth domains. The result is applied to several examples including energy functionals, Signorini problem, control problems and eigenvalues of Laplacian.
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Submitted on : Thursday, March 29, 2018 - 10:42:25 AM
Last modification on : Saturday, October 16, 2021 - 11:18:03 AM

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  • HAL Id : tel-01746671, version 1



Gilles Fremiot. Structure de la semi-dérivée eulérienne dans le cas de domaines fissurés et quelques applications. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2000. Français. ⟨NNT : 2000NAN10188⟩. ⟨tel-01746671⟩



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