基于直接多层有限元模拟的二维压电材料的力电性能研究  

Electro-mechanical performance of 2D piezoelectric material based on direct multi-layer finite element simulation

作　　者：陈磊磊 王佳晨 李帅[3] 陈攀 CHEN Leilei;WANG Jiachen;LI Shuai;CHEN Pan(Henan International Joint Laboratory of Structural Mechanics and Computational Simulation,College of Architecture and Civil Engineering,Huanghuai University,Zhumadian 463000,China;College of Architecture and Civil Engineering,Xinyang Normal University,Xinyang 464000,China;College of Civil Engineering and Architecture,Dalian University,Dalian 116622,China)

机构地区：[1]黄淮学院建筑工程学院河南省结构力学与仿真计算国际联合实验室,河南驻马店463000 [2]信阳师范大学建筑工程学院,河南信阳464000 [3]大连大学建筑与工程学院,辽宁大连116622

出　　处：《振动与冲击》2024年第21期46-54,88,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(11702238);河南省高等学校重点科研项目(20A560018)。

摘　　要：该文采用直接多层有限元模拟(Direct multi-layer finite element,Direct FE^(2))方法,模拟非均质材料的力-电耦合问题。该方法突破了传统并发多尺度分析方法必须依赖控制脚本进行宏-微观跨尺度信息传递的固有框架。首先,通过有限元的控制方程和并发多尺度分析所需的Hill-Mandel均质化条件,推导出可直接实现宏观与微观信息实时传递的多节点约束方程。其次,将并发多尺度分析所需的宏观结构模型和代表体积单元模型合并为一个有限元模型,避免了在两个尺度之间的重复数据传输。最后,通过算例验证该文算法的正确性和有效性。Here,the Direct multi-layer finite element(FE^(2))method was adopted to simulate electric-mechanical coupled problems of heterogeneous materials.This method could break through the inherent framework of traditional concurrent multiscale analysis methods relying on control scripts for macro-micro cross-scale information transmission.Firstly,by using governing equations of FE method and Hill-Mandel homogenization conditions required for concurrent multiscale analysis,multi-point constraints(MPCs)equations being able to directly realize real-time transmission of macroscopic information and microscopic information were derived.Secondly,macroscopic structural model and representative volume element(RVE)model required for concurrent multiscale analysis were merged into a FE model to avoid repetitive data transmission between 2 scales.Finally,the correctness and effectiveness of the proposed algorithm were verified with numerical examples.

关 键 词：直接多层有限元模拟(Direct FE^(2)) 均匀化计算 压电结构 多点约束 

分 类 号：O343.2[理学—固体力学]