论文标题
形状衍生物，用于与TRESCA摩擦的接触问题的罚款表述
Shape derivatives for the penalty formulation of contact problems with Tresca friction
论文作者
论文摘要
在本文中，研究了受摩擦（TRESCA）接触的线性弹性体的形状优化。由于参与接触问题制定的投影算子，该解决方案通常不可分割。此外，接触区的形状优化需要计算接触中的身体之间的间隙及其形状导数。使用定向衍生物，得出了足够的形状不同条件。 ％的问题在两个具有光滑边界的物体的一般框架中解决。然后，提出了一些基于这些形状衍生物的梯度下降算法获得的数值结果。
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.
