含压电层复合材料结构的静力学行为分析

STATIC BEHAVIOR ANALYSIS OF COMPOSITE STRUCTURES WITH PIEZOELECTRIC LAYERS

为克服位移有限元法中求解单元节点应力时不方便引入应力边界条件的缺点,首先根据压电材料的广义最小势能原理,为压电材料结构的静力学分析提出了一种实用的8节点六面体非协调位移元。然后,基于广义H-R变分原理提出了一种计算含压电层复合材料结构广义应力的线性方程组方法,为广义应力边界条件的引入提供了条件,且保证了相邻单元同一节点上应力的连续性,为高精度的数值结果奠定了理论基础。数值结果表明,线性方程组方法得到的广义应力结果的精度高于高斯点应力外推法(Gauss-point Stress Extrapolation Method,GSEM)。

In order to overcome the disadvantage that it is inconvenient to introduce stress boundary conditions when solving the stress of element nodes in displacement finite element method,firstly,according to the generalized minimum potential energy principle of piezoelectric materials,a practical 8⁃node hexahedral nonconforming displacement element is proposed for the static analysis of piezoelectric structures.Then,based on the generalized H⁃R variational principle,a linear equations method for calculating the generalized stress of composite structures with piezoelectric layers is proposed.This method provides conditions for the introduction of generalized stress boundary conditions,and ensures the continuity of stress on the same node of adjacent elements,which lays a theoretical foundation for high⁃precision numerical results.Numerical results show that the accuracy of generalized stress results obtained by linear equations method is higher than that by Gauss⁃point stress extrapolation method(GSEM).