Modeling and simulation of a planar rigid multibody system with multiple revolute clearance joints based on variational inequality

Song, Ningning; Peng, Haijun; Xu, Xiaoming; Wang, Gang

doi:10.1016/j.mechmachtheory.2020.104053

Cited by 38 publications

(8 citation statements)

References 58 publications

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“…In an attempt to obtain an increasing rate of convergence, several iterative schemes have been investigated and tested. A such attempt was made to enhance the convergence rate by adding inertial term, see, [29,34,45,46,49]. It was Polyak [43] who originated the inertial term to investigate an optimization problem.…”

Section: Introductionmentioning

confidence: 99%

Approximation of an Inertial Iteration Method for a Set-Valued Quasi Variational Inequality

Mohammad Akram

2024

Iraqi Journal For Computer Science and Mathematics

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In this article, a projection type two step inertial iterative scheme for investigating set-valued quasivariational inequality in real Banach spaces is designed. We manifest the existence result and verified by an illustrativeexample. Also, we estimate the approximate solution of a set-valued quasi variational inequality by analyzing theconvergence of the proposed inertial iterative algorithm. Further, an extended Weiner-Hopf equation is consideredand substantiated that it is analogous to the extended set-valued quasi variational inequality. Finally, we investigatethe extended Weiner-Hopf equation by analyzing the convergence of the composed iterative scheme.

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Section: Introductionmentioning

confidence: 99%

Approximation of an Inertial Iteration Method for a Set-Valued Quasi Variational Inequality

Mohammad Akram

2024

Iraqi Journal For Computer Science and Mathematics

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“…Following the "effective rod length theory," Lee and Gilmore [8] established a reliability analysis model for discontinuous-contact revolute pairs, laying a solid foundation for research on the reliability of mechanisms with kinematic pair clearance. Song et al [9] used variational inequality to analyze the planar rigid multibody systems with multiple revolute clearance joints motion mechanism, and for this systems provide a nonsmooth strategy. Li et al [10] used the reliability analysis model established by Lee and Gilmore to conduct a reliability-based virtual experimental study analyzing the mechanism's motion precision.…”

Section: Introductionmentioning

confidence: 99%

Time-Variant Reliability Analysis Method for Uncertain Motion Mechanisms Based on Stochastic Process Discretization

et al. 2022

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The reliability of a motion mechanism is affected by corrosion, wear, aging and other components' performance degradations with the extension of service time. This paper tackles this problem by proposing a time-varying reliability analysis method for uncertain motion mechanisms. First, a model of motion mechanism error is constructed by assessing the difference between actual and expected motion. A time-varying reliability analysis method for a motion mechanism is proposed. The time-varying performance function is discretized into several static performance functions, which are further approximated with several normal variables. Then, the correlation coefficient matrix and probability density function of these normal variables are calculated, and the time-varying reliability of a motion mechanism is obtained via high-dimensional Gaussian integration. The study demonstrates that the proposed method successfully transforms the time-varying reliability problem into several time-invariant reliability problems for analysis, and handles the time-varying reliability problem of a nonlinear motion mechanism involving random variables and stochastic processes, and significantly increases the computational efficiency. Finally, the proposed method's effectiveness is verified by two numerical examples and one practical engineering problem.

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“…It is well documented that the study of variational inequality, which was initiated by Stampacchia [1] becomes a very productive and fruitful tool to examine several problems arising in the natural sciences. Due to an application oriented nature, this field of research has been expanded and generalized in several directions, see [2][3][4][5][6][7][8]. One of the pronounced generalizations of variational inequality is quasi-variational inequality (QVI) which is to find p * ∈ K(p * ), such that:…”

Section: Introductionmentioning

confidence: 99%

A Unified Inertial Iterative Approach for General Quasi Variational Inequality with Application

Akram

Dilshad

2022

Fractal Fract

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In this paper, we design two inertial iterative methods involving one and two inertial steps for investigating a general quasi-variational inequality in a real Hilbert space. We establish an existence result and a non-trivial example is furnished to substantiate our theoretical findings. We discuss the convergence of the inertial iterative algorithms to approximate the solution of a general quasi-variational inequality. Finally, we apply an inertial iterative scheme with two inertial steps to investigate a delay differential equation. The results presented herein can be seen as substantial generalizations of some known results.

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Modeling and simulation of a planar rigid multibody system with multiple revolute clearance joints based on variational inequality

Cited by 38 publications

References 58 publications

Approximation of an Inertial Iteration Method for a Set-Valued Quasi Variational Inequality

Approximation of an Inertial Iteration Method for a Set-Valued Quasi Variational Inequality

Time-Variant Reliability Analysis Method for Uncertain Motion Mechanisms Based on Stochastic Process Discretization

A Unified Inertial Iterative Approach for General Quasi Variational Inequality with Application

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