一种基于Layerwise理论的压电复合材料层合圆柱壳机电耦合有限单元  

A coupled finite element method for composite laminated cylindrical shells with piezoelectric layers using Layerwise theory

作　　者：李伟[1] 蔺越国[1] 陈昱晨 LI Wei;LIN Yueguo;CHEN Yuchen(College of Aeronautical Engineering,Civil Aviation University of China,Tianjin 300300,China;College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)

机构地区：[1]中国民航大学航空工程学院,天津300300 [2]南京航空航天大学航空学院,南京210016

出　　处：《复合材料学报》2020年第2期366-375,共10页Acta Materiae Compositae Sinica

基　　金：江苏省研究生科研创新计划项目(KYCX17_0248)

摘　　要：基于Reddy的Layerwise理论,对含压电铺层的复合材料层合壳的静力响应特性进行了理论研究。基于Layerwise理论,推导了含压电层的复合材料层合壳的应变分量与电场强度表达式。利用Hamilton原理和变分法,推导了压电智能层合壳的欧拉-拉格朗日方程,并采用有限元解法,建立了相应的有限元控制方程及其机电耦合刚度矩阵。通过算例结果与文献中的精确解和试验值进行了对比,表明相较于传统的经典层合板壳理论,本文理论方法的有效性和优势性;并分析了径厚比等参量对两端简支压电智能层合壳静力响应值的影响规律。A piezoelectric-mechanical coupled finite element model of composite laminated shells with piezoelectric layers was presented. The Reddy’s layerwise laminate theory was used to derive the according expressions of strains and electric field, the Euler-Lagrange equations were obtained by employing Hamilton’s principle and variational method, and then a finite element model and the according piezoelectric-mechanical coupled stiffness were formulated based on the developed layerwise mechanics. Numerical examples were implemented to evaluate the efficiency and accuracy of the present method by comparing with the results obtained with classical laminated plate theory. The effects of radius to thickness ratio of a simply-supported laminated piezoelectric composite shell for static response were also investigated in the end.

关 键 词：复合材料 压电材料 层合壳 有限元 Layerwise理论 机电耦合 

分 类 号：O343.8[理学—固体力学]