Mathematical construction of an engineering thermopiezoelastic model for smart composite shells

摘要

An engineering model for composite piezoelectric shells under mechanical, thermal, and electrical loads has been constructed mathematically using the variational-asymptotic method. This work presents a unique formulation of the nonlinear, three-dimensional, one-way coupled, thermopiezoelasticity problem having the combined merits of both mathematical rigor and engineering simplicity. The variational-asymptotic method is used to rigorously split the three-dimensional problem into two problems: a nonlinear, two-dimensional, shell analysis over the reference surface to obtain the global response, and a linear analysis through the thickness to provide both the generalized shell constitutive model and recovery relations to approximate the original three-dimensional fields. The asymptotically correct electric enthalpy obtained herein is cast into the Reissner-Mindlin form to account for transverse shear deformation including the geometrical 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. Results for several cases obtained from VAPAS are compared with exact thermopiezoelasticity solutions, classical lamination theory, and first-order shear-deformation theory. An excellent compromise between efficiency and accuracy for analyzing piezoelectric composite shells has been achieved.