Minimization of peak stresses with the shape derivative

This article is concerned with the minimization of peak stresses occurring in linear elasticity. We propose to minimize the maximal von Mises stress of the elastic body. This leads to a non-smooth shape functional. We derive the shape derivative and associate it with the Clarke sub-differential. Using a steepest descent algorithm, we present numerical simulations. We compare our results to the usual p -norm regularization and show that our algorithm performs better in the presented tests. This article is part of the theme issue ‘Non-smooth variational problems with applications in mechanics’.