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引用次数: 0
摘要
本文涉及线性弹性中峰值应力的最小化。我们建议尽量减小弹性体的最大 von Mises 应力。这将导致一个非光滑的形状函数。我们推导出形状导数,并将其与克拉克子导数联系起来。我们使用最陡峭下降算法进行了数值模拟。我们将结果与通常的[公式:见正文]正则化进行了比较,结果表明我们的算法在测试中表现更好。
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 [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'.
期刊介绍:
Continuing its long history of influential scientific publishing, Philosophical Transactions A publishes high-quality theme issues on topics of current importance and general interest within the physical, mathematical and engineering sciences, guest-edited by leading authorities and comprising new research, reviews and opinions from prominent researchers.