On Topological Derivatives for Contact Problems in Elasticity
In this article, a general method for shape-topology sensitivity analysis of contact problems is proposed. The method uses domain decomposition combined with specific properties of minimizers for the energy functional. The method is applied to the static problem of an elastic body in frictionless contact with a rigid foundation. The contact model allows a small interpenetration of the bodies in the contact region. This interpenetration is modeled by means of a scalar function that depends on the normal component of the displacement field on the potential contact zone. We present the asymptotic behavior of the energy shape functional when a spheroidal void is introduced at an arbitrary point of the elastic body. For the asymptotic analysis, we use a nonoverlapping domain decomposition technique and the associated SteklovPoincar pseudodifferential operator. The differentiability of the energy with respect to the nonsmooth perturbation is established, and the topological derivative is presented in the closed form.
topological derivative domain decomposition asymptotic analysis static frictionless contact problem steklovpoincar operator 41a60 49j52 49q10 35j50 35q93