ANALYSIS OF SLIGHTLY ANISOTROPIC SHELLS

Abstract

A perturbation method of solution for the governing system of differential equations for laminated anisotropic shells is presented. These shells may be composed of an arbitrary num- ber of bonded layers, each with a different thickness, different orientation, and different aniso- tropic elastic properties. Such a construction can appropriately describe filament-wound pressure vessels. By the perturbation scheme it is possible to reduce the system of anisotropic ' shell equations to successive systems of orthotropic shell equations. Thus, the complete solution consists of a series of solutions of equivalent orthotropic shells. The general per- turbation system of equations is then specialized for cylindrical shells using the well-known Donnell approximations. The particular case of uniform pressurization and axial force is solved in detail. F ILAMENT-WOUND pressure vessels are prominent in the aerospace industry because their improved strength- to-weight ratio permits the design of more efficient rocket motor cases. The construction and material properties of these pressure vessels are such that they can be appropriately characterized as laminated anisotropic shells. A theory governing the behavior of laminated anisotropic shells has recently been presented in Refs. 1 and 2. The mathe- matical model employed in the theory represents a shell structure composed of an arbitrary number of bonded layers with different thicknesses, orientations of elastic axes, and anisotropic elastic properties. A new feature arising from such a construction technique is the appearance of a coupled system of differential equations. This coupling reflects the simultaneous response of extensional and flexural deforma- tions for a single load component (either an in-plane force or a bending moment).% As a consequence of this coupling and the general difficulty of solving anisotropic problems, very few solutions have appeared in the literature. In Refs. 3 and 4 a perturbation scheme was employed to uncouple the governing system of equations. This method of analysis reduces the original system of equations to suc- cessive systems of homogeneous anisotropic shell equations. As a result, solutions from homogeneous shell theory can be used. In this paper the perturbation scheme is used to re- duce general anisotropic shell equations to successive systems of orthotropic shell equations, provided that the degree of anisotropy is small.§ The final systems of equations are in a form used for analysis of nonhomogeneou s, orthotropic shells with additional terms to account for anisotropy. The general system of equations is then specialized for circular cylindrical shells. The case of uniform pressurization of a semi-infinite cylindrical shell is presented as an illustration of practical application.