An efficient method for simulating the dynamic behavior of periodic structures with piecewise linearity

He, Dongdong; Gao, Qiang; Zhong, Wanxie

doi:10.1007/s11071-018-4475-8

Cited by 4 publications

(1 citation statement)

References 32 publications

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“…They use the Bozzak–Newmark method 25 as the implicit integrator in the schemes. A similar idea was employed by He et al, 26 based on the precise integration method (PIM) 27 and the Lemke algorithm. These methods, referred to as the LCP‐based schemes, are applicable only when the piecewise linear characteristic is the only nonlinearity in the dynamics equations.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

Zanoni

et al. 2021

Int Journal of Mech Sys Dyn

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A generalized solution scheme using implicit time integrators for piecewise linear and nonlinear systems is developed. The piecewise linear characteristic has been welldiscussed 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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Section: Introductionmentioning

confidence: 99%

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

Zhang

Zanoni

et al. 2021

Int Journal of Mech Sys Dyn

View full text Add to dashboard Cite

show abstract

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

Zhang

Zanoni

et al. 2021

NODYCON Conference Proceedings Series

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Exact Analytical Periodic Solutions in Special Cases and Numerical Analysis of a Half-Undamped 1-DOF Piecewise-Linear Vibratory System

Nguyen-Thai

2021

Advances in Asian Mechanism and Machine Science

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An efficient method for simulating the dynamic behavior of periodic structures with piecewise linearity

Cited by 4 publications

References 32 publications

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

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

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

Exact Analytical Periodic Solutions in Special Cases and Numerical Analysis of a Half-Undamped 1-DOF Piecewise-Linear Vibratory System

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