This paper presents a rigorous elasticity solution for filament wound
composite laminated cylindrical shells subjected to out-of-plane bendi
ng. The material of the shell is assumed to be cylindrically anisotrop
ic. Based on the theory of cylindrically anisotropic elasticity, coupl
ed partial differential governing equations are developed using Lekhni
tskii's stress functions. Homogeneous solutions are obtained using sep
aration of variables and polynomial forms are used for particular solu
tions. To illustrate the fundamental nature of the problem, an example
of off-axis composite shells is presented. Complex three-dimensional
stress states, large stress gradients through the thickness and strong
effect of fiber orientations are reported. Detailed stress distributi
ons of two laminated shells [45/-45]s, [45/-45] are examined.