In this article, the existing nonsmooth generalized-$\alpha$ method for the simulation of mechanical systems with frictionless contacts, modeled as unilateral constraints, is extended to systems with frictional contacts. On that account, we complement the unilateral constraints with set-valued Coulomb-type friction laws. Moreover, we devise a set of benchmark systems, which can be used to validate numerical schemes for mechanical systems with frictional contacts. Finally, this set of benchmarks is used to numerically assert the properties striven for during the derivation of the presented scheme. Specifically, we show that the presented scheme can reproduce the dynamics of the frictional contact adequately and no numerical penetration of the contacting bodies arises—a big issue for most popular time-stepping schemes such as the one of Moreau. Moreover, we demonstrate that the presented scheme performs well for multibody systems containing flexible parts and that it allows general parametrizations such as the use of unit quaternions for the rotation of rigid bodies.

中文翻译：

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摩擦接触机械系统的一种非光滑广义α方法

在本文中，现有的非光滑广义-$\alpha$用于模拟具有无摩擦接触的机械系统的方法，建模为单边约束，扩展到具有摩擦接触的系统。因此，我们用定值库仑型摩擦定律补充了单边约束。此外，我们设计了一组基准系统，可用于验证具有摩擦接触的机械系统的数值方案。最后，这组基准用于在数值上断言在所提出方案的推导过程中力求的属性。具体来说，我们表明所提出的方案可以充分再现摩擦接触的动力学，并且不会出现接触体的数值渗透——这对于大多数流行的时间步长方案（例如 Moreau 方案）来说是一个大问题。而且，