非均质压电结构动力学问题的多尺度有限元法研究  

Multi-scale finite element method for dynamic analysis of heterogeneous piezoelectric structures

作　　者：李霄琳[1] 夏世显 李新玥 郭庆 苑晓青[1] 高欣[1] LI Xiaolin;XIA Shixian;LI Xinyue;GUO Qing;YUAN Xiaoqing;GAO Xin(College of Construction Engineering,Jilin University,Changchun 130026,China)

机构地区：[1]吉林大学建设工程学院,长春130026

出　　处：《重庆理工大学学报（自然科学）》2023年第12期155-162,共8页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金项目(42102346,42172301)。

摘　　要：基于多尺度有限元法,通过构造位移多尺度基函数和电势多尺度基函数将细观非均质信息引入到宏观响应中,同时引入耦合附加项考虑各坐标方向位移场间的耦合作用。所构造的多尺度基函数可以直接高效地双向传递粗尺度与细尺度之间的信息,使问题在宏观尺度上求解,降低计算消耗。数值模拟结果表明,与传统有限元法相比,采用多尺度有限元法求解非均质压电结构的动力学问题,在保证计算精度的同时,还具有较高的计算效率,为非均质压电结构动力学问题的数值模拟提供了一种有效手段。In this paper,based on the multi-scale finite element method,the meso-heterogeneous information is introduced into the macroscopic response by constructing the displacement multi-scale basis functions and the potential multi-scale basis functions.Coupling additional terms are also incorporated for the coupling between the displacement fields in each coordinate direction.The constructed multi-scale basis functions can directly and efficiently transfer the information between coarse scale and fine-scale,addressing problems on the macro scale and reducing the computational costs.The numerical simulation results show the multi-scale finite element method not only guarantees calculation accuracy but also achieves higher computational efficiency compared with the traditional finite element method,and thus it provides an effective means for the numerical simulation of the dynamic problems of heterogeneous piezoelectric structures.

关 键 词：多尺度有限元法 压电结构 力电耦合 基函数 动力响应 

分 类 号：TB115[理学—数学]