{"title":"基于RKPM的sma几何非线性行为分析","authors":"Yijie Zhang , Gaofeng Wei , Tengda Liu , Fengfeng Hua , Shasha Zhou","doi":"10.1016/j.cnsns.2024.108581","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"142 ","pages":"Article 108581"},"PeriodicalIF":3.4000,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The analysis of geometrically nonlinear behavior of SMAs using RKPM\",\"authors\":\"Yijie Zhang , Gaofeng Wei , Tengda Liu , Fengfeng Hua , Shasha Zhou\",\"doi\":\"10.1016/j.cnsns.2024.108581\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>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.</div></div>\",\"PeriodicalId\":50658,\"journal\":{\"name\":\"Communications in Nonlinear Science and Numerical Simulation\",\"volume\":\"142 \",\"pages\":\"Article 108581\"},\"PeriodicalIF\":3.4000,\"publicationDate\":\"2024-12-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Nonlinear Science and Numerical Simulation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1007570424007664\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570424007664","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
The analysis of geometrically nonlinear behavior of SMAs using RKPM
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.
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.
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