带有接触力学应用的半变分不等式数值方法综述
A survey of numerical methods for hemivariational inequalities with applications to Contact Mechanics
AI总结：
本文研究半变分不等式的数值方法，提出抽象非光滑优化问题并展示数值求解方案，将其应用于弹性体摩擦接触问题，最后比较三种计算方法。
摘要：
本文提出了一个抽象的非光滑优化问题，并回顾了其存在性与唯一性结果。我们展示了一种数值方案来近似其解。随后将该理论应用于一个静态接触问题样本，描述弹性体与基础之间的摩擦接触。该问题导出一个半变分不等式，我们对其进行了数值求解。最后，我们比较了求解接触力学问题的三种计算方法：直接优化法、增广Lagrangian法及原始-对偶活动集策略。
英文摘要：
In this paper we present an abstract nonsmooth optimization problem for which we recall existence and uniqueness results. We show a numerical scheme to approximate its solution. The theory is later applied to a sample static contact problem describing an elastic body in frictional contact with a foundation. This problem leads to a hemivariational inequality which we solve numerically. Finally, we compare three computational methods of solving contact mechanical problems: direct optimization method, augmented Lagrangian method and primal-dual active set strategy.
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