On topological derivatives for contact problems in elasticity

0443130 - MÚ 2016 RIV US eng J - Journal Article
Giusti, S.M. - Sokolowski, S. - Stebel, Jan
On topological derivatives for contact problems in elasticity.
Journal of Optimization Theory and Applications. Roč. 165, č. 1 (2015), s. 279-294. ISSN 0022-3239. E-ISSN 1573-2878
R&D Projects: GA ČR GA201/09/0917
Institutional support: RVO:67985840
Keywords : topological derivative * static frictionless contact problem * asymptotic analysis
Subject RIV: BA - General Mathematics
Impact factor: 1.160, year: 2015
http://link.springer.com/article/10.1007%2Fs10957-014-0594-7

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. The differentiability of the energy with respect to the nonsmooth perturbation is established, and the topological derivative is presented in the closed form.
Permanent Link: http://hdl.handle.net/11104/0245885