Sensitivity Analysis for Unilateral Contact Problems: "Boundary" Variational Formulations and B.E.M. Discretisations

A great interest has been recently devoted to the sensitivity analysis of structures in the presence of unilateral constraints and to its mathematical foundations. The problem has been usually tackled by using classical domain variational formulations, such as the ones based on the total potential energy, and its discretisation has been always performed with Finite Element models. On the contrary, this paper aims at proposing a sensitivity analysis based on boundary variational formulations and such as to retain most of the mathematical results obtained until now. It allows to take advantage of a discretisation carried out with Boundary Element Methods which appear to be more suitable than Finite Element models for this class of problems.