Minimisation of peak stresses with the shape derivative

2024/02/20 by Phillip Baumann, Baumann, Phillip, Kevin Sturm +1
Computer Science · Engineering · #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Metallurgy and Material Forming #Optimization and Control (math.OC) #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.2402.12978

openalex publication_date 2024/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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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