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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.12978 |
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| _version_ | 1866910337434910720 |
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| author | Baumann, Phillip Sturm, Kevin |
| author_facet | Baumann, Phillip Sturm, Kevin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12978 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimisation of peak stresses with the shape derivative Baumann, Phillip Sturm, Kevin Optimization and Control 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. |
| title | Minimisation of peak stresses with the shape derivative |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2402.12978 |