This article proposes a boundary element method for the dynamic contact between a linearly elastic body and a rigid obstacle. The Signorini contact problem is formulated as a variational inequality for the Poincar\'{e}-Steklov operator for the elastodynamic equations on the boundary, which is solved in a mixed formulation using boundary elements in the time domain. We obtain an a priori estimate for the resulting Galerkin approximations. Numerical experiments confirm the stability and convergence of the proposed method for the contact problem in flat and curved two-dimensional geometries, as well as for moving obstacles.

翻译：本文提出了一种用于线弹性体与刚性障碍物之间动态接触的边界元方法。该Signorini接触问题被表述为边界上弹性动力学方程的Poincaré-Steklov算子的变分不等式，并通过时域边界元在混合公式中进行求解。我们获得了所得Galerkin逼近的先验估计。数值实验验证了所提方法在平面和弯曲二维几何以及移动障碍物接触问题中的稳定性和收敛性。