Thorsten Schindler

Shahed Rezaei, Thorsten Schindler

This work deals with the integration of nonsmooth flexible multibody systems with impacts and dry friction. We develop a framework which improves a non-impulsive trajectory of state variables by impulsive correction after each time-step if necessary. This correction is automatic and is evaluated on the same kinematic level as the piecewise non-impulsive trajectory. The resulting overall mixed timestepping scheme is consistent with respect to impacts and friction as well as benefits from advantages of the base integration schemes used to calculate the approximation inside the time-step. Therefore, we compare the generalized-$α$ method, the Bathe method and the ED-$α$ method.

Svenja Schoeder, Heinz Ulbrich, Thorsten Schindler

In multibody simulation, the Gear-Gupta-Leimkuhler method for only persistent contacts enforces constraints on position and velocity level at the same time. It yields a robust numerical discretization of differential algebraic equations avoiding the drift-off effect. In this work, we carry over these benefits to impacting mechanical systems with unilateral constraints. For this kind of a mechanical system, adding the position level constraint to a timestepping scheme on velocity level even maintains physical consistency of the impulsive discretization. Hence, we propose a timestepping scheme based on Moreau's midpoint rule which enables to achieve not only compliance of the impact law but also of the non-penetration constraint. The choice of a decoupled and consecutive evaluation of the respective constraints can be interpreted as a not energy-consistent projection to the non-penetration constraint at the end of each time step. It is the implicit coupling of position and velocity level which yields satisfactory results. An implicit evaluation of the right hand side improves stability properties without additional cost. With the prox function formulation, the overall set of nonsmooth equations is solved by a Newton scheme. Results from simulations of a slider-crank mechanism with unilateral constraints demonstrate the capability of our approach.