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.
Convergence of penalty Robin-Robin domain decomposition methods for unilateral multibody contact problems of elasticity
Ivan Franko National University of Lviv（伊万·弗兰科大学）；Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine（乌克兰国家科学院皮德斯特雷哈赫应用力学与数学问题研究所）
