Shape optimisation with the level set method for contact problems in linearised elasticity

Maury, Aymeric; Allaire, Grégoire; Jouve, François

The SMAI Journal of computational mathematics, Tome 3 (2017), pp. 249-292.

This article is devoted to shape optimisation of contact problems in linearised elasticity, thanks to the level set method. We circumvent the shape non-differentiability, due to the contact boundary conditions, by using penalised and regularised versions of the mechanical problem. This approach is applied to five different contact models: the frictionless model, the Tresca model, the Coulomb model, the normal compliance model and the Norton-Hoff model. We consider two types of optimisation problems in our applications: first, we minimise volume under a compliance constraint, second, we optimise the normal force, with a volume constraint, which is useful to design compliant mechanisms. To illustrate the validity of the method, 2D and 3D examples are performed, the 3D examples being computed with an industrial software.

Classification : 74P05, 75P10, 74P15, 74M10, 74M15, 49Q10, 49Q12, 35J85
Mots clés : Shape and topology Optimisation; Level set method; Unilateral contact problems; Frictional contact; Penalisation and Regularisation

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