基于变分原理和一阶剪切理论 ,本文建立了一种新的机电耦合矩形有限单元 ,该单元具有四个节点 2 0个位移自由度 ,电自由度为单元中的压电铺层层数。通过静态控制方程推得的旋转位移表达式中含有横向位移的三次导数 ,从而该单元不仅能分析薄板的变形 ,而且还能分析中厚板在电载荷和外力载荷作用下的变形。然后 ,根据所建立的有限单元 ,结合相关方程 ,编写了有限元分析程序并对一些算例进行了数值模拟 ,通过将所得结果与有关文献的结果进行对比 ,验证了本文单元的有效性。最后对压电非均衡复合材料在电载荷作用下的变形进行了分析。结果表明 ,当复合材料中正的铺层角和对应的负铺层角的厚度比改变时 ,在相同电载荷作用下对结构的变形有较大的影响 Based on the principle of variational principle and the first-order shear theory, a new finite element of electromechanically coupled rectangular is established in this paper. The unit has 20 degrees of freedom of displacement of four nodes. The degree of electrical freedom is the number of piezoelectric layers . The rotational displacement expression derived from the static control equation contains the third derivative of the lateral displacement so that the unit can not only analyze the deformation of the sheet but also analyze the deformation of the plate under the action of electric and external loads. Then, based on the established finite element, combined with the relevant equations, the finite element analysis program is written and some numerical examples are simulated. The validity of the proposed method is verified by comparing the results with those of the related literatures. Finally, the deformation of the piezoelectric unbalanced composite under electric load is analyzed. The results show that when the thickness ratio of the positive ply angle and the corresponding negative ply angle in the composite material is changed, the deformation of the structure has a greater effect under the same electric load