A generalized approach for implicit time integration of piecewise linear/nonlinear systems
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 t...
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| Published in | International journal of mechanical system dynamics Vol. 1; no. 1; pp. 108 - 120 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Nanjing
John Wiley & Sons, Inc
01.09.2021
Wiley |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2767-1402 2767-1399 2767-1402 |
| DOI | 10.1002/msd2.12007 |
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| 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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| AbstractList | 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. 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. |
| Author | Zhang, Huimin Masarati, Pierangelo Zhang, Runsen Zanoni, Andrea |
| Author_xml | – sequence: 1 givenname: Huimin orcidid: 0000-0003-3129-0170 surname: Zhang fullname: Zhang, Huimin email: huimin.zhang@polimi.it organization: Politecnico di Milano – sequence: 2 givenname: Runsen surname: Zhang fullname: Zhang, Runsen organization: Politecnico di Milano – sequence: 3 givenname: Andrea surname: Zanoni fullname: Zanoni, Andrea organization: Politecnico di Milano – sequence: 4 givenname: Pierangelo orcidid: 0000-0002-9347-7654 surname: Masarati fullname: Masarati, Pierangelo organization: Politecnico di Milano |
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| CitedBy_id | crossref_primary_10_1016_j_chaos_2022_112624 crossref_primary_10_1016_j_ijmecsci_2024_109578 crossref_primary_10_3390_ma15134414 crossref_primary_10_1002_eqe_4311 |
| Cites_doi | 10.1243/PIME_PROC_1994_208_148_02 10.1007/s11071-012-0676-8 10.1007/BF01581275 10.1016/j.compstruc.2018.11.001 10.1177/1077546304044795 10.1016/j.jsv.2015.01.038 10.1177/1077546314545098 10.1287/moor.1.2.97 10.1002/stc.215 10.1007/s11044-007-9084-0 10.1007/s11071-015-2212-0 10.1007/BFb0120782 10.1002/eqe.4290050306 10.1007/s11071-018-4475-8 10.1137/1.9780898719000 10.1177/0954406214543674 10.1002/nme.1620151011 10.1007/s11071-020-06020-8 10.1061/JMCEA3.0000098 10.1016/0022-460X(90)90585-N 10.1016/j.compstruc.2013.06.007 10.1016/j.ijmecsci.2017.06.040 10.1007/s11831-011-9060-y 10.1007/s11071-016-2825-y 10.1016/j.jsv.2004.07.026 10.1115/1.2900803 10.1002/nme.1620372303 10.1177/1687814017742313 10.1007/s11044-019-09713-0 10.1016/0045-7825(91)90022-X 10.1007/s12206-017-0302-2 10.1002/nme.4563 |
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| SubjectTerms | 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 |
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| Title | A generalized approach for implicit time integration of piecewise linear/nonlinear systems |
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