A generalized approach for implicit time integration of piecewise linear/nonlinear systems

• Published in: International journal of mechanical system dynamics Vol. 1; no. 1; pp. 108 - 120
• Main Authors: Zhang, Huimin, Zhang, Runsen, Zanoni, Andrea, Masarati, Pierangelo
• Format: Journal Article
• Language: English
• Published: Nanjing John Wiley & Sons, Inc 01.09.2021; Wiley
• Subjects: Algorithms; implicit time integrator; Integrators; Linear systems; Methods; Nonlinear dynamics; Nonlinear equations; Nonlinear systems; Nonlinearity; piecewise linear and nonlinear systems; projection function; Time integration; Variables
• ISSN: 2767-1402; 2767-1399; 2767-1402
• DOI: 10.1002/msd2.12007

A generalized solution scheme using implicit time integrators for piecewise linear and nonlinear systems is developed. The piecewise linear characteristic has been well‐discussed in previous studies, in which the original problem has been transformed into linear complementarity problems (LCPs) and then solved via the Lemke algorithm for each time step. The proposed scheme, instead, uses the projection function to describe the discontinuity in the dynamics equations, and solves for each step the nonlinear equations obtained from the implicit integrator by the semismooth Newton iteration. Compared with the LCP‐based scheme, the new scheme offers a more general choice by allowing other nonlinearities in the governing equations. To assess its performances, several illustrative examples are solved. The numerical solutions demonstrate that the new scheme can not only predict satisfactory results for piecewise nonlinear systems, but also exhibits substantial efficiency advantages over the LCP‐based scheme when applied to piecewise linear systems.