Sensitivity-analysis methods for nonsmooth multibody systems with contact and friction

A large number of collisions and frictions often occur in multibody systems. These nonsmooth events lead to discontinuous or piecewise-continuous dynamic equations of multibody systems, which brings great difficulties to the numerical solution. Accordingly, it is very difficult to calculate the dynamic sensitivity of nonsmooth multibody systems. In this paper, the analytical sensitivity formula of nonsmooth multibody systems with contact and friction is derived by the direct differentiation method. Also, a complete and unified mathematical framework for dynamic sensitivity analysis of nonsmooth multibody systems is given. On this basis, combined with the advantages of the finite-difference method, a semianalytical sensitivity-analysis method for nonsmooth multibody systems is further derived. For the dynamic equations in the form of differential–algebraic equations, the formulas of analytical and semianalytical sensitivity-analysis methods are given, including a global semianalytical method and a local semianalytical method. The correctness is verified by three numerical examples of nonsmooth multibody systems, and the results show that the semianalytical sensitivity-analysis method is effective and practical in engineering application.