Baumann Phillip, Sturm Kevin
Institut für Analysis und Scientific Computing Wiedner Hauptstraße 8-10, Wien 1040, Austria.
Philos Trans A Math Phys Eng Sci. 2024 Aug 23;382(2277):20230309. doi: 10.1098/rsta.2023.0309. Epub 2024 Jul 15.
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 [Formula: see text]-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'.
本文关注线性弹性中出现的峰值应力的最小化问题。我们提议将弹性体的最大冯·米塞斯应力最小化。这导致了一个非光滑的形状泛函。我们推导了形状导数并将其与克拉克次微分联系起来。使用最速下降算法，我们进行了数值模拟。我们将我们的结果与通常的[公式：见正文] - 范数正则化进行比较，并表明我们的算法在所呈现的测试中表现更好。本文是主题为“力学中的非光滑变分问题及其应用”的一部分。
