Coupled finite element for the nonlinear dynamic response of active piezoelectric plates under thermoelectromechanical loads

Abstract

A theoretical framework is presented for analyzing the coupled nonlinear dynamic behavior of laminated piezoelectric composite plates subject to high thermoelectromechanical loadings. It incorporates coupling between mechanical, electric, and thermal governing equations and encompass geometric non-linearity effects due to large displacements and rotations. The mixed-field shear-layerwise plate laminate theory formulation is considered, thus degenerating the 3D electromechanical field to 2D nodal variables, and an eight-node coupled nonlinear plate element is developed. The discrete coupled nonlinear dynamic equations of motion are formulated, linearized, and numerically solved at each time step using the implicit Newmark scheme with a Newton-Raphson technique. Validation and evaluation cases on active laminated beams demonstrate the accuracy of the method and its robust capability to effectively predict the nonlinear dynamic response under time-dependent combined mechanical, thermal, and piezoelectric actuator loads. The results illustrate the capability of the method to simulate large amplitude vibrations and dynamic buckling phenomena in active piezocomposite plates. The influence of loading rates on the nonlinear dynamic structural response is also quantified. Additional numerical cases demonstrate the complex dynamic interactions between electrical, mechanical, and thermal buckling loads.