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Minimisation of peak stresses with the shape derivative
Published 20 Feb 2024 in math.OC | (2402.12978v1)
Abstract: This paper is concerned with the minimisation of peak stresses occurring in linear elasticity. We propose to minimise the maximal von Mises stress of the elastic body. This leads to a nonsmooth 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 regularisation and show that our algorithm performs better in the presented tests.
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