Series solution for a cylindrical composite shell subject to axisymmetric loadings.

Abstract

The elasticity equations have been solved to an arbitrary degree of precision for a thick-walled orthotropic cylinder, subject to axisymmetric loading. The theory is directly applicable to a layered composite material where each layer is orthotropic in character. The solution proceeds by representing the deformations of the cylinder wall as a power series in a non-dimensional radial parameter. By introducing a generalized stress resultant and a generalized stiffness for the material, a series of coupled second order differential equations in the coefficients of the deformation series results. These have been solved using a generalized eigenvalue technique for an infinitely long cylinder, a simply held cylinder, and a rigidly clamped cylinder. The solution has been shown to reduce to standard shell solutions for thin cylinders. A thick-walled filament wound test specimen is also detailed that when fabricated and pressurized, would experimentally verify the refined theory developed.