Numerical problems in modelling of collision in sliding systems subjected to seismic excitations

Abstract

The study addresses collision in sliding systems subjected to seismic excitations. The collision is modelled according to the impact laws of the mechanics of particles using coefficient of restitution to account for energy losses (Newton's hypothesis). An analytical solution in a small time interval after the collision is constructed viewing the sliding velocity. When constructing numerical solutions, it is assumed that the friction force does not change its sign within one step of integration. If at end of the time step, velocity with an opposite sign is calculated, the obtained solution is incorrect, because the result contradicts the accepted constant sign of the friction force during the time step. To avoid these problems expressions are derived for the magnitude of the time step in which a mathematically correct solution will have place. Recommendations are formulated for numerical simulation of collision in sliding systems subjected to seismic excitations. The obtained correct numerical solutions using the Coulomb model are compared with numerical results from the velocity model of friction forces. It is shown that the velocity model provides the possibility to avoid automatically the above numerical problems by use of its correctness condition.