A generalized approach for implicit time integration of piecewise linear/nonlinear 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 (LC...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-09-01
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| Series: | International Journal of Mechanical System Dynamics |
| Subjects: | |
| Online Access: | https://doi.org/10.1002/msd2.12007 |
| _version_ | 1828774301721952256 |
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| author | Huimin Zhang Runsen Zhang Andrea Zanoni Pierangelo Masarati |
| author_facet | Huimin Zhang Runsen Zhang Andrea Zanoni Pierangelo Masarati |
| author_sort | Huimin Zhang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T15:18:47Z |
| format | Article |
| id | doaj.art-3e4534c8af6f4be8a971a9b000d53cf3 |
| institution | Directory Open Access Journal |
| issn | 2767-1402 |
| language | English |
| last_indexed | 2024-12-11T15:18:47Z |
| publishDate | 2021-09-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mechanical System Dynamics |
| spelling | doaj.art-3e4534c8af6f4be8a971a9b000d53cf32022-12-22T01:00:27ZengWileyInternational Journal of Mechanical System Dynamics2767-14022021-09-011110812010.1002/msd2.12007A generalized approach for implicit time integration of piecewise linear/nonlinear systemsHuimin Zhang0Runsen Zhang1Andrea Zanoni2Pierangelo Masarati3School of Aeronautic Science and Engineering Beihang University Beijing ChinaSchool of Aeronautic Science and Engineering Beihang University Beijing ChinaDipartimento di Scienze e Tecnologie Aerospaziali Politecnico di Milano Milano ItalyDipartimento di Scienze e Tecnologie Aerospaziali Politecnico di Milano Milano ItalyAbstract 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.https://doi.org/10.1002/msd2.12007implicit time integratorpiecewise linear and nonlinear systemsprojection function |
| spellingShingle | Huimin Zhang Runsen Zhang Andrea Zanoni Pierangelo Masarati A generalized approach for implicit time integration of piecewise linear/nonlinear systems International Journal of Mechanical System Dynamics implicit time integrator piecewise linear and nonlinear systems projection function |
| title | A generalized approach for implicit time integration of piecewise linear/nonlinear systems |
| title_full | A generalized approach for implicit time integration of piecewise linear/nonlinear systems |
| title_fullStr | A generalized approach for implicit time integration of piecewise linear/nonlinear systems |
| title_full_unstemmed | A generalized approach for implicit time integration of piecewise linear/nonlinear systems |
| title_short | A generalized approach for implicit time integration of piecewise linear/nonlinear systems |
| title_sort | generalized approach for implicit time integration of piecewise linear nonlinear systems |
| topic | implicit time integrator piecewise linear and nonlinear systems projection function |
| url | https://doi.org/10.1002/msd2.12007 |
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