Abstract The one-dimensional dynamic contact problem describing a rigid obstacle collided by an elastic bar is considered in gravitational field. The collision problem is non-smooth with respect to velocity and axial strain, and formulated as a variational inequality. For the corresponding wave equation subject to complementary conditions which are imposed at the contact boundary, its nonlinear solution is expressed with the help of Fourier Series representing longitudinal vibrations. Moreover, before the bar rebound, an analytical solution comprising piece-wise quadratic function is constructed on a partition of the rectangular space-time domain along characteristics. The analytical benchmark is implemented for low initial speeds in numerical experiments solving the variational inequality over uniform space-time triangulation with the Space-Time Primal-Dual Active Set method of semi-smooth Newton type.
Victor A. Kovtunenko (Tue,) studied this question.