A Generalized Solution Scheme Using an Implicit Time Integrator for Piecewise Linear and Nonlinear Systems

A generalized solution scheme using an implicit time integrator for piecewise linear and nonlinear systems is developed. The piecewise linear characteristic has been discussed in previous studies, which transform the problem into linear complementarity problems (LCPs) and solve the LCPs via the Lemke algorithm per step. In the proposed scheme, the projection function is used to describe the discontinuity in the dynamics equations, and the discrete nonlinear equation per step of the implicit integrator is solved by the semi-smooth Newton iteration. Compared with the LCP-based scheme, the new scheme is more general, since it allows other nonlinearities in the dynamics equations. Numerical results of illustrative examples indicate that the new scheme, where the generalized-α method is used as the implicit integrator, has obvious efficiency advantages over the LCP-based scheme for piecewise linear systems and can also present satisfactory numerical solutions for piecewise nonlinear systems.