Tresca摩擦接触问题罚函数形式的形状导数
Shape derivatives for the penalty formulation of contact problems with Tresca friction
摘要：
本文研究了摩擦接触下线弹性体的形状优化问题。由于接触问题的公式化涉及到投影算子，所以一般情况下，该解不是形状可微的。此外，接触区的形状优化需要计算接触体之间的间隙及其形状导数。利用方向导数，得到了形状可微的充分条件。%这个问题是在两个具有光滑边界的机构的一般框架中解决的。然后，给出了基于这些形状导数的梯度下降算法的数值结果。
英文摘要：
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. %The problem is addressed in the general framework of two bodies with smooth boundaries. Then, some numerical results, obtained with a gradient descent algorithm based on those shape derivatives, are presented.
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