A boundary element sensitivity formulation for contact problems using the implicit differentiation method

In this paper a sensitivity formulation using the boundary element method (BEM), for problems involving contact is presented. The proposed formulation is based on the implicit differentiation method (IDM), where the boundary integral equations are differentiated analytically with respect to the design variables. In the proposed formulation the design variables are defined in terms of the normal gap between the contact bodies. The analysis demonstrates that the proposed method is accurate and robust, as it does not resolve the whole system. The proposed method can be used for evaluating the sensitivities in any shape-optimisation problem involving contact.