一种压电复合材料层合板机电耦合有限单元

Finite Element for Composite Piezoelectric Laminate

基于压电复合材料层合板经典理论，建立了一种四边形机电耦合有限单元．所建单元具有ｍ个电自由度，可直接模拟单元中的电压作用和检测电压输出；单元每一节点具有５个位移自由度，可计及复合材料层合板的拉弯耦合变形．给出了各类刚度矩阵的形式，简述了利用Ｈａｍｉｌｔｏｎ原理推导出机电耦合基本运动方程的过程，并根据所推导的有限元素和基本方程编制了程序并进行了计算，所得结果与文献中的计算和试验结果相吻合．

The purpose of the research is to develop a more efficient finite element code for laminated piezoelectric composite plates, which contain one or more piezoelectric layers as actuators or sensors subjected to mechanical and electrical loads. Each piezoelectric layer may be attached to or embedded in the laminate and may have a different voltage applied. Therefore a new FEA element which has twenty displacement degrees of freedom and has m (the number of piezoelectric material layers) electrical degrees of freedom is built. And the explicit forms of derived electromechanical matrices are also presented. This element will be more realistic and efficient in simulating applied voltages on piezoelectric material layers and detecting output voltages. The derivation of motion equations is stated briefly. Then a FEA code is implemented and the computational results agree well with the referents.