Topology optimization of elastic contact problems with maximum contact pressure constraint

In this work, we develop a topology optimization method for linear elastic contact problems with maximum contact pressure constraint. First, the Kreisselmeier–Steinhauser (KS) function is adopted as an aggregated measure of the maximum contact pressure over specific contact regions. Then, the maximum contact pressure constraint is introduced into the standard volume-constrained compliance minimization problem and formulated in the framework of B-spline parameterization method. Two geometric constraints are further extended to suppress the intermediate densities and control minimum length scale. The adjoint method is employed for deriving design sensitivities analytically. Finally, both frictionless and frictional problems are tested to demonstrate the effectiveness of the proposed method. It is shown that the maximum contact pressure can be effectively controlled using the contact pressure constraint and thus avoiding the concentration of contact pressure. The influence of maximum contact pressure constraint on the optimization result is discussed in comparison with the standard maximum stiffness design. Effects of friction behavior upon optimized results and contact pressure are also highlighted. It concludes that the maximum contact pressure can be reduced at the cost of the structural stiffness.