SIAM Journal on Control and Optimization, Volume 58, Issue 6, Page 3237-3261, January 2020.
In this article, the shape optimization of a linear elastic body subject to frictional (Tresca) contact is investigated. Due to the projection operators involved in the formulation of the contact problem, the solution is not shape differentiable in general. Moreover, shape optimization of the contact zone requires the computation of the gap between the bodies in contact, as well as its shape derivative. Working with directional derivatives, sufficient conditions for shape differentiability are derived. Then, some numerical results, obtained with a gradient descent algorithm based on those shape derivatives, are presented.

中文翻译：

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Tresca摩擦弹性接触问题的惩罚公式的形状导数

SIAM控制与优化杂志，第58卷，第6期，第3237-3261页，2020
年1月。在本文中，研究了受摩擦（Tresca）接触的线性弹性体的形状优化。由于涉及接触问题公式化的投影算子，该解决方案通常在形状上是不可微的。此外，接触区域的形状优化需要计算接触的物体之间的间隙及其形状导数。使用方向导数，可以得出形状微分的充分条件。然后，给出了基于这些形状导数的梯度下降算法获得的一些数值结果。