A Simple Thermopiezoelastic Model for Composite Shells with Accurate Stress Recovery

Abstract

Georgia Institute of Technology, Atlanta, Georgia 30332-0150 A simple model for analyzing composite shells with embedded piezoelectric materials under mechanical, thermal and electrical 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 transverse normal and using a set of intrinsic variables defined on the reference surface. The variational-asymptotic method is used to mathematically split the three-dimensional problem into two problems: a nonlinear, two-dimensional, shell analysis over the reference surface to obtain the global deformation, and a linear analysis through the thickness to provide both the generalized two-dimensional constitutive model and recovery relations to approximate the original three-dimensional fields. The asymptotically correct electric enthalpy obtained herein is cast into the form of the Reissner-Mindlin model to account for transverse shear deformation including geometric refinement due to initial curvatures. Recovery relations have been provided to obtain accurate stress distribution through the thickness. The present model is implemented into the computer program VAPAS (variational-asymptotic plate and shell analysis). Results for several cases obtained from VAPAS are compared with exact thermopiezoelasticity solutions, classical lamination theory, and first-order shear-deformation theory. Results demonstrate that an excellent compromise between efficiency and accuracy for analyzing piezoelectric composite shells has been achieved.