The analysis of geometrically nonlinear behavior of SMAs using RKPM

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-12-28 DOI:10.1016/j.cnsns.2024.108581

Yijie Zhang , Gaofeng Wei , Tengda Liu , Fengfeng Hua , Shasha Zhou

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Abstract

As the temperature surpasses the threshold for the completion of austenitic transformation, shape memory alloys (SMAs) necessitate a substantial external force to trigger internal phase transformation. Given the substantial deformation induced by the external force on SMAs, the application of geometrically nonlinear analysis becomes essential. In this paper, reproducing kernel particle method (RKPM) is employed to investigate the geometrically nonlinear behavior of SMAs. The penalty function method is applied to impose the displacement boundary conditions. The study utilizes the Galerkin weak form with total Lagrangian (TL) framework to develop geometrically nonlinear SMAs equations, solved via Newton-Raphson (N-R) iteration. The effects of varying penalty factor and radius control parameter of the influence domain on error and computational stability are investigated. Ultimately, the suitability of applying RKPM for exploring the geometrically nonlinearity behavior of SMAs is demonstrated via numerical examples.

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基于RKPM的sma几何非线性行为分析

当温度超过完成奥氏体相变的阈值时，形状记忆合金（sma）需要一个巨大的外力来触发内部相变。考虑到SMAs在外力作用下产生的大量变形，应用几何非线性分析变得至关重要。本文采用再现核粒子法（RKPM）研究了sma的几何非线性行为。采用罚函数法施加位移边界条件。该研究利用Galerkin弱形式和全拉格朗日（TL）框架建立几何非线性sma方程，通过牛顿-拉夫森（N-R）迭代求解。研究了影响域的不同惩罚因子和半径控制参数对误差和计算稳定性的影响。最后，通过数值算例证明了应用RKPM分析sma几何非线性行为的适用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.