LAUSR

The non-smooth dynamic model can effectively handle unilateral constraints in multi-body systems, but its complex mathematical definition is difficult to be applied in engineering applications. To reduce the difficulty of this model’s application and to improve its calculation accuracy, an implicit integration algorithm is proposed in this paper to solve non-smooth dynamic models more effectively. Using velocity and impulse as independent variables, the linear complementary form of non-smooth dynamic equations, which are expressed as a set of differential–algebraic equations (DAEs), is derived based on the complementary contact law. By constructing an approximate velocity of a system at the next point in time, the proposed algorithm obtains the displacement in the next time step by weighting the approximate velocity constructed before and the real velocity at current point in time, and then updates the other state variables of the next time step. The accuracy of the proposed algorithm and the stability of the improved time-stepping method are verified by three numerical experiments. The results show that the time-stepping method based on the proposed implicit integration algorithm has higher accuracy and less time cost than Moreau’s midpoint method for solving linear complementarity based non-smooth dynamic models. The third study case examines the computational ability of the algorithm proposed in this paper for contact phenomena with friction. The algorithm proposed in this paper can be applied in engineering applications that require an accurate solution of contact force.