Analysis Of Piezoelectric Laminated Plate Based On The Hybrid Isoparametric Element

Due to its structural characteristics, smart composite material has obtained a wide range of applications and great development in the field of aviation. Piezoelectric material is now the most widely used type of smart composite material. Its unique property of electromechanical coupling, as well as the anisotropy of piezoelectric phenomena, makes the analysis of piezoelectric problem complicated. In this paper, a hybrid finite element theory and the isoparametric element were employed to study the static problems of piezoelectric laminated plates with complex boundary conditions. The research contents are as follows:A new stress mode based on differentiation for general composite materials was derived directly from the stress-strain relation. Then based on the basic equations of elasticity and the modified Hellinger-Reissner(H-R) mixed variation principle, the hybrid isoparametric finite element formulation under the Cartesian coordinate system was established for general composite materials. Numerical examples of laminated composite plates were analyzed through programming with the Mathematica language. Comparing with the results of Abaqus analysis, the results for each statics quantity obtained from this method were closer to their exact solutions, and higher accuracy was obtained with less meshing.Based on the modified Hellinger-Reissner(H-R) mixed variation principle and the constitutive relation of orthotropic piezoelectric elastic bodies, the hybrid isoparametric finite element formulation for piezoelectric composite materials was established under the Cartesian coordinate system. And then by using the iso-function method and according to the constitutive relation of piezoelectric elastic bodies a new stress mode based on differentiation was derived for the 3D eight-node element of piezoelectric composite materials. Several numerical examples were analyzed using Mathematica as the programming language to explore the electromechanical coupling characteristics of piezoelectric material laminated plates with various complex boundary conditions. The analysis showed that the present method is easy to be realized on computer and its accumulated data error is small, therefore it improves the calculation accuracy. What's more, this method is insensitive to the cell division, that is to say, high accuracy can be obtained even with few meshes and mesh encryption has little effect on the accuracy. Therefore this method provides a new idea for the static analysis of piezoelectric laminated plates.