The analysis of geometrically nonlinear behavior of SMAs using RKPM

作     者：Zhang, Yijie Wei, Gaofeng Liu, Tengda Hua, Fengfeng Zhou, Shasha 

作者机构：Qilu Univ Technol Shandong Acad Sci Sch Mech Engn Jinan 250353 Shandong Peoples R China Shandong Inst Mech Design & Res Jinan 250353 Shandong Peoples R China SDEE Hitachi High Voltage Switchgear Co Ltd Jinan Peoples R China 

出 版 物：《COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION》 (Comm. Nonlinear Sci. Numer. Simul.)

年 卷 期：2025年第142卷

核心收录：

学科分类：07[理学] 0701[理学-数学] 0702[理学-物理学] 0801[工学-力学（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：Natural Science Foundation of Shandong Province [ZR2020MA059  ZR2022QA044] 

主　　题：Phase transformation Shape memory alloys Geometrically nonlinear behavior Reproducing kernel particle method Numerical analysis 

摘      要：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.