Coupled global-local and zigzag-local laminate theories for dynamic analysis of piezoelectric laminated plates

Abstract

Accurate prediction of interlaminar transverse stresses in smart piezolaminated structures through two-dimensional laminate theories that are efficient, directly from the constitutive equations, is a challenging task. In this study, we extend the 11 variable global-local theory (GLT) which was originally proposed for elastic laminated structures with this purpose, to the dynamic analysis of hybrid piezolaminated plates under electromechanical loading. The zigzag-local theory (ZLT), with nine primary displacement variables, which was recently developed for static analysis of hybrid plates and has the ability to calculate transverse shear stresses from constitutive equations, is also extended for dynamic analysis. A two-way electromechanical coupling is considered. A variational formulation is presented for the two theories by using the extended Hamiltons's principle, obtaining the governing dynamic field equations, and variationally consistent boundary conditions. The accuracy of the two theories are critically assessed in direct comparison with the exact 3D piezoelasticity solutions for static, free vibration and forced vibration response of hybrid plates for a variety of laminate configurations. It is revealed that the GLT, in spite of having higher number of primary variables, is unable to yield accurate prediction not only for the transverse shear stresses, but also for global responses like displacements under mechanical loading and natural frequencies. For the latter entities, the prediction is even worse than the five-variable zigzag theory. In contrast, the ZLT predicts with good accuracy all response entities including the transverse shear stresses for all laminates under mechanical as well as potential loading, and is superior to both GLT and the zigzag theory.