A simple thermopiezoelastic model for smart composite plates with accurate stress recovery**Presented at the 44th Structures, Structural Dynamics and Materials Conference, Norfolk,VA, 7–10 April 2003.

Abstract

A Reissner–Mindlin model for analyzing laminated composite plates including piezoelectriclayers under mechanical, thermal and electric loads has been constructed using thevariational-asymptotic method. The present work formulates the original nonlinear,three-dimensional, one-way coupled, thermopiezoelasticity problem allowing for arbitrarydeformation of the normal line and using a set of intrinsic variables defined on the referenceplane. The variational-asymptotic method is used to rigorously split the three-dimensionalproblem into two problems: a nonlinear, two-dimensional, plate analysis over the referenceplane to obtain the global deformation, and a linear analysis through the thickness toprovide both the two-dimensional generalized constitutive model and recovery relations toapproximate the original three-dimensional results. The obtained asymptoticallycorrect second-order electric enthalpy is cast into the form of the commonly usedReissner–Mindlin model to account for transverse shear deformation. The present theory isimplemented into the computer program VAPAS (variational-asymptotic plate and shellanalysis). Results for several cases obtained from VAPAS are compared with theexact thermopiezoelasticity solutions, classical lamination theory and first-ordershear–deformation theory for the purpose of demonstrating the advantages of the presenttheory and the use of VAPAS. The proposed theory can achieve an accuracy comparableto higher-order layerwise theories at the cost of a first-order shear–deformationtheory.