基于渐进均匀化的力-电-热耦合光滑有限元法研究  

Research on thermo-electro-mechanical coupling smoothed finite element method based on asymptotic homogenization

作　　者：郑建校[1] 段志善[1] 周立明 ZHENG Jianxiao;DUAN Zhishan;ZHOU Liming(School of Mechanical and Electrical Engineering,Xi'an University of Architecture and Technology,Xi'an 710055,China;School of Mechanical and Aerospace Engineering,Jilin University,Changchun 130025,China)

机构地区：[1]西安建筑科技大学机电工程学院,陕西西安710055 [2]吉林大学机械与航空航天工程学院,吉林长春130025

出　　处：《中南大学学报（自然科学版）》2023年第4期1325-1335,共11页Journal of Central South University:Science and Technology

基　　金：陕西省自然科学基础研究计划-一般项目(面上)(2023-JC-YB-313);陕西省自然科学基础研究计划-青年项目(2020JQ-669);国家自然科学基金资助项目(52002309)。

摘　　要：针对基于微观结构的力-电-热多物理场耦合压电复合材料的力学特性分析问题,基于压电复合材料的基本方程和力-电-热多物理场耦合效应,结合渐进均匀化方法预测的压电复合材料有效性能参数,提出基于渐进均匀化的力-电-热耦合光滑有限元法;推导力-电-热耦合光滑有限元的动力学控制方程,并运用Wilson-θ法对压电复合材料结构动力学问题进行求解,研究温度变化对结构固有频率和动力学响应的影响,并将其结果与有限元法的求解结果进行对比,验证该方法的正确性和有效性。研究结果表明:本文方法所得结果与有限元法所得结果较一致,且具有较好的收敛性和较高的精度;该方法对分析压电复合材料元器件的多物理场耦合力学特性具有广阔的应用前景。Aiming at the mechanical property analysis problem of piezoelectric composite materials with microstructure-based thermo-electro-mechanical multi-physical-field coupling,the thermo-electro-mechanical coupling smoothed finite element method based on asymptotic homogenization was proposed.The theoretical basis of this method includes the basic equation,the thermo-electro-mechanical coupling effect and effective performance parameters of piezoelectric composite materials predicted by asymptotic homogenization.Thedynamic control equation of this method was deduced,and the structural dynamic problems of piezoelectric composite materials were solved by applying the Wilsonθmethod.The effects of temperature variation on the structure natural frequency and dynamic response were studied.The results of the proposed mechod were compared with those of the finite method to verify the correctness and validity of the proposed method.The results show that the proposed method produces consistent results with the finite element method,and has better convergence and higher precision,and thus this method has a broad application prospect for analyzing the multi field coupling mechanical properties of piezoelectric composite components.

关 键 词：固体力学 有限元法 力-电-热耦合 渐进理论 

分 类 号：TB115[理学—数学]