Micromechanical analysis of grid-reinforced thin composite generally orthotropic shells

This paper develops a comprehensive micromechanical model for the analysis of periodic thin composite shells with an embedded grid of generally orthotropic reinforcements. The use of generally orthotropic constituents renders the analysis more complicated than with simply isotropic reinforcements, but significantly enhances the applicability of the model. The model is derived on the basis of asymptotic homogenization and allows the determination of the effective elastic stiffnesses (coefficients) of the composite shells. These effective coefficients are only dependent on the structural make-up of the pertinent periodicity unit (referred to as unit cell) of the composite shell, and are completely independent of the global formulation of the problem. As such, they are universal in nature and can be used to study a wide variety of boundary-value problems. In the limiting case in which the shell reduces to a thin flat plate with periodicity in the two in-plane orthogonal directions, the derived model converges to that of previously obtained models. The model is illustrated by means of several examples of practical importance including cylindrical-reinforced shells, multi-layer shells, grid-reinforced plates and single-walled carbon nanotubes.