Modelling and Numerical Shape and Topology Optimization for a Hemivariational Inequality in Stokes Flows with Slip Boundary Conditions

This paper focuses on modelling and numerical shape and topology optimization for a nonlinear hemivariational inequality in a Stokes flow with contact and frictional conditions. For the energy functional to be minimized subject to geometric volume constraint, we present shape sensitivity analysis and propose a volume preserving gradient-type method for shape optimization. Moreover, we build a relaxed topology optimization model for the hemivariational inequality in a Stokes fluid and solve it by a level set method. Numerical examples are presented to verify effectiveness of the shape and topology optimization algorithms.