Meshless shape design sensitivity analysis and optimization for contact problem with friction (Q1570300)

There is a huge literature on the numerical treatment of contact problems for elastic bodies. The present paper considers the contact between a rigid and a deformable body, taking friction into account when, during progressive penetration, interfacial slip occurs between surface elements at contact. The original constrained minimization problem is converted into a free minimum problem by adding a penalty term to the functional representing the total potential energy. The process of minimization is done step by step by considering the geometric changes of the deformable body at the end of each step. A numerical example, the penetration of a rigid door into a seal of rubber, illustrates the procedure. The authors, however, do not prove the convergence of the contact set to a well-defined region, since the shape of this contact set is, in general, unstable in problems posed in terms of variational inequalities.