General micromechanical modeling of smart composite shells with application to smart honeycomb sandwich structures

Analytical solutions for the static deformations of piezoelectric composite shells with a periodic structure are developed and effective elastic and piezoelectric coefficients are determined. The derived model also allows the determination of the displacement, strain and stress fields. The underlying mathematical framework is that of asymptotic homogenization. It is shown that the original boundary value problem decouples into a set of four simpler problems called local or unit cell problems. It is precisely these unit cell problems that determine the effective elastic and piezoelectric coefficients. These coefficients are universal in nature and can be used to study a wide variety of boundary value problems. The model is applied to the practically important case of a hexagonal honeycomb-type sandwich structure composed of an isotropic core and orthotropic carrier faces that also exhibit piezoelectric behavior.