Semiexplicit numerical integration by splitting with application to dynamic multibody problems with contacts

whereA is significantly more expensive to evaluate than B , and B is stiff (highly oscillatory) in comparison with A. Examples of such problem are multibody problem with contact forces acting between bodies, and constraints formulated as penalty forces. Based on the splitting A+B of the acceleration field, a numerical integration algorithm, which is explicit in the A–part and implicit in the B–part, is suggested. Consistency and linear stability analysis of the proposed method is carried out. Numerical examples with the proposed method is carried out for two simple test problems, and for a complex multibody model of a rotating ball bearing. Comparison with conventional implicit methods is given for each example. The results indicate that the proposed method is more efficient, in terms of number of evaluations of A, at the same accuracy level.