Asymptotic homogenization modeling and analysis of effective properties of smart composite reinforced and sandwich shells

Abstract

General micromechanical models for smart composite shells with periodically arranged actuators and varying thickness are developed using the asymptotic homogenization techniques. The models make it possible to determine both local fields, i.e., stresses, strains and displacements, and effective elastic and piezoelectric coefficients of the smart composite shells. It is shown that the original boundary value problem decouples into a set of simpler problems, known as unit cell problems. In particular, it is the solution of these unit cell problems that yields the aforesaid effective coefficients. These coefficients are universal in nature and may be used to study a wide variety of boundary value problems associated with a given smart composite structure. The derived models and the expressions for the effective coefficients are illustrated by means of four examples pertaining to hexagonal honeycomb sandwich structures and rectangular-reinforced, diagonally restrained and triangular-reinforced smart wafer shells. These structures are endowed with piezoelectric carrier layers made of orthotropic material and isotropic core or wafer. It is shown that the derived models can be used to tailor the effective properties of such smart composite structures to meet the requirements of particular applications of interest.