Assessment of computational models for thermoelectroelastic multilayered plates

Abstract

A study is made of the accuracy of the steady-state (static) thermoelectroelastic response of multilayered hybrid composite plates predicted by five modeling approaches, based on two-dimensional plate theories. The plates consist of a combination of fibre-reinforced and piezothermoelastic layers. The standard of comparison is taken to be the exact three-dimensional thermoelectroelastic solutions, and the quantities compared include gross response characteristics (e.g. strain energy components, and average through-the-thickness displacements); detailed, through-the-thickness distributions of displacements and stresses; and sensitivity coefficients of the response quantities (derivatives of the response quantities with respect to material parameters of the plate). The modeling approaches considered include first-order theory; third-order theory; discrete-layer theory (with piecewise linear variation of the in-plane displacements, temperature and electric potential, in the thickness direction); and two predictor-corrector procedures. Both procedures use first-order theory in the predictor phase, but differ in the elements of the computational model being adjusted in the corrector phase. The first procedure adjusts the transverse shear stiffnesses of the plate and the second procedure corrects the functional dependence of the displacements on the thickness coordinate. The corrected quantities are then used in conjunction with the three-dimensional equations to obtain better estimates for the different response quantities and their sensitivity coefficients. Numerical results are presented for nine-layer plates consisting of eight graphiteepoxy layers and one piezothermoelastic layer, subjected to transverse mechanical loading, temperature change and electric potential. Based on the numerical studies conducted, the second predictor-corrector approach appears to be the most accurate among the five modeling approaches considered. For multilayered hybrid composite plates, the detailed response quantities, and sensitivity coefficients obtained by this approach are shown to be in close agreement with the exact three-dimensional thermoelectroelastic solutions for a wide range of the thickness parameter.