A simple thermopiezoelastic model for smart composite plates with accurate stress recovery

摘要

A Reissner-Mindlin model for analyzing laminated composite plates including piezoelectric layers under mechanical, thermal and electric loads has been constructed using the variational-asymptotic method. The present work formulates the original nonlinear, three-dimensional, one-way coupled, thermopiezoelasticity problem allowing for arbitrary deformation of the normal line and using a set of intrinsic variables defined on the reference plane. The variational-asymptotic method is used to rigorously split the three-dimensional problem into two problems: a nonlinear, two-dimensional, plate analysis over the reference plane to obtain the global deformation, and a linear analysis through the thickness to provide both the two-dimensional generalized constitutive model and recovery relations to approximate the original three-dimensional results. The obtained asymptotically correct second-order electric enthalpy is cast into the form of the commonly used Reissner-Mindlin model to account for transverse shear deformation. The present theory is implemented into the computer program VAPAS (variational-asymptotic plate and shell analysis). Results for several cases obtained from VAPAS are compared with the exact thermopiezoelasticity solutions, classical lamination theory and first-order shear-deformation theory for the purpose of demonstrating the advantages of the present theory and the use of VAPAS. The proposed theory can achieve an accuracy comparable to higher-order layerwise theories at the cost of a first-order shear-deformation theory.