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

IF 3.4 Q1 ENGINEERING, MECHANICAL 国际机械系统动力学学报(英文) Pub Date : 2021-11-29 DOI:10.1002/msd2.12007
Huimin Zhang, Runsen Zhang, Andrea Zanoni, Pierangelo Masarati
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引用次数: 3

Abstract

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.

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分段线性/非线性系统隐式时间积分的一种广义方法
提出了一种利用隐式时间积分器求解分段线性和非线性系统的广义解法。在以往的研究中,对分段线性特性进行了充分的讨论,将原问题转化为线性互补问题,然后通过Lemke算法对每个时间步进行求解。该方案采用投影函数来描述动力学方程的不连续,并采用半光滑牛顿迭代法对隐式积分器得到的非线性方程进行求解。与基于lcp的方案相比,新方案允许控制方程中存在其他非线性,从而提供了更普遍的选择。为了评估其性能,求解了几个说明性实例。数值解表明,新格式不仅能对分段非线性系统给出满意的预测结果,而且在分段线性系统中也比基于lcp的格式具有显著的效率优势。
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