A linear relaxation model for shape optimization of constrained contact force problem

This paper is devoted to shape optimization of constrained contact force problem. A linear relaxation model of contact force-clearance relation is developed. It is shown that such relaxation is essential to avoid zero sensitivity values of zero contact force with respect to design variables and to drive the satisfaction of contact force constraint at the specific contact region. In this work, both frictionless and frictional contact optimization problems are investigated by means of a gradient-based optimization algorithm. The optimization procedure including sensitivity analysis with relaxation model is implemented outside the structural contact analysis software to deal with non-smooth contact problems. The procedure is firstly validated by simple examples with analytical solutions and is finally applied to the design of an assembled aero-engine structure for leakproofness.