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

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.