Thermally nonlinear non-Fourier piezoelectric thermoelasticity problems with temperature-dependent elastic constants and thermal conductivity and nonlinear finite element analysis

Abstract

In non-isothermal conditions, numerous experimental and theoretical investigations reveal that the elastic constants and thermal conductivity in piezoelectric solids depend on temperature distribution. This work aims to investigate thermally nonlinear non-Fourier piezoelectric thermoelasticity problems with temperature-dependent elastic constants and thermal conductivity. The nonlinear time-domain finite element method is developed to directly solve nonlinear finite element governing equations, which maximally avoids the precision losses within the applications of the integrated transformation method. As a numerical example, the developed method is applied to analyze nonlinear transient thermo-electromechanical responses of a two-dimensional orthotropic piezoelectric plate of crystal class mm2. The achieved results reveal that temperature-dependent thermal conductivity and elastic constants remarkably affect the structural dynamic responses, whilst thermal wave or elastic wave will travel faster and the electrical energy harvesting ability is significantly elevated.