The paper proposes an approach for the efficient model order reduction of dynamic contact problems in linear elasticity. Instead of the augmented Lagrangian method that is widely used for mechanical contact problems, we prefer here the Linear Complementarity Programming (LCP) method as basic methodology. It has the advantage of resulting in the much smaller dual problem that is associated with the governing variational principle and that turns out to be beneficial for the model order reduction. Since the shape of the contact zone depends strongly on the acting outer forces, the LCP for the Lagrange multipliers has to be solved in each time step. The model order reduction scheme, on the other hand, is applied to the large linear system for the displacements and computed in advance by means of an Arnoldi process. In terms of computational effort the reduction scheme is very appealing because the contact constraints are fully satisfied while the reduction acts only on the displacements. As an extension of our approach, we furthermore take up the idea of the Craig-Bampton method in order to distinguish between interior nodes and the nodes in the contact zone. A careful performance analysis closes the paper.
翻译:本文提出了在线性弹性方面有效减少动态接触问题示范命令的方法。我们不赞成广泛用于机械接触问题的扩大拉格朗加方法,而是倾向于将线性互补规划方法作为基本方法,其优点是造成与管理差异原则有关的、对减少模式订单有利的两个小得多的问题。由于接触区的形状在很大程度上取决于外力,因此,必须在每个时间步骤中解决拉格朗格乘数的LCP。另一方面,对迁移的大型线性系统适用示范命令削减计划,并预先用Arnoldi进程计算。在计算工作中,削减计划非常有吸引力,因为接触限制已完全得到满足,而减少作用仅对迁移产生影响。作为我们方法的延伸,我们进一步采用Craig-Bamptonbon方法的想法,以便区分接触区的内节点和节点。仔细的绩效分析将文件关闭。