https://univ-pau.hal.science/hal-04046683Jacob de Cordemoy, AymericAymericJacob de CordemoyLMAP - Laboratoire de MathÃ©matiques et de leurs Applications [Pau] - UPPA - UniversitÃ© de Pau et des Pays de l'Adour - CNRS - Centre National de la Recherche ScientifiqueShape optimization for contact problem involving Signorini unilateral conditionsHAL CCSD2023Shape optimizationShape sensitivity analysisShape derivativeSignorini unilateral conditionsVariational inequalitiesProximal operatorTwice epi-differentiability[MATH] Mathematics [math]Jacob de Cordemoy, Aymeric2023-03-26 16:51:452023-03-28 03:51:172023-03-27 12:08:54enPreprints, Working Papers, ...application/pdf1This paper investigates a shape optimization problem involving the Signorini unilateral conditions in a linear elastic model, without any penalization procedure. The shape sensitivity analysis is performed using tools from convex and variational analysis such as proximal operators and the notion of twice epi-differentiability. We prove that the solution to the Signorini problem admits a directional derivative with respect to the shape, and we characterize it as the solution to another Signorini problem. Then, the shape gradient of the corresponding energy functional is explicitly characterized which allows us to perform numerical simulations to illustrate this methodology.