Asymptotical Modelling of Thermopiezoelastic Laminates

Abstract

A general anisotropic laminated plate model with thermal deformation and twoway coupled piezoelectric effect and pyroelectric effect is constructed using the variational asymptotic method, without any ad hoc assumptions. Total potential energy contains strain energy, electric potential energy and energy caused by temperature change. Three-dimensional strain field is built based on the concept of warping function and decomposition of the rotation tensor. The feature of small thickness and large in-plane dimension of plate structures helped to asymptotically simplify the three-dimensional analysis to a two-dimensional analysis on the reference surface and a one-dimensional analysis through the thickness. Several numerical examples are studied. The present model is validated by the excellent agreements between the results from 3D finite element analyses and the presented model.