Topology optimization for compliance and contact pressure distribution in structural problems with friction

Abstract

This paper concerns density-based topology optimization of linear elastic contact problems, aiming to present robust and practically realizable designs for different objective functions. First we revisit a compliance minimization with frictionless contact problem from the literature and present crisp solid–void designs, based on the so-called modified robust topology optimization formulation. An adaptation of this problem to frictional contact is then solved for various friction coefficients and it is checked that the optimization algorithm indeed exploits the presence of friction for lowering the objective further. Secondly, we propose and demonstrate the use of a p-norm based objective function to control the distribution and variation of contact pressure, on an a priori unknown area of contact, between a body of unknown topology and an obstacle. To have control over the contact pressure, a Lagrange multiplier based contact formulation is used within a coupled Newton solution, for imposing impenetrability, friction, and the corresponding complementarity conditions. The adjoint method is employed for deriving consistent design sensitivities for the mixed formulation involving both displacements and contact Lagrange multipliers. Through a series of numerical examples, it is demonstrated how an even distribution of contact pressure and crisp solid–void designs can be obtained for problems with and without friction.