Stability of Submerged Cylindrical Shells with Deformable Ring Stiffeners
Authors: Goldberg John E. , Pathak Dvaker V. , Setlur Achyut V. 
Published: October 2008

Abstract
A computer procedure is presented or determining the critical combinations of longitudinal loading and external, pressure for ring-stiffened cylindrical shells. Such shells have various applications in offshore technology, the most important of these perhaps being the supports for offshore platforms. Other possible applications might include under water chambers, underwater storage and submerged pipelines.
In the present paper, the longitudinal loading and the lateral pressure may vary arbitrarily with the distance along the axis of the shell. The thickness of the shell, the thickness, spacing and form of the ring stiffeners may also vary along the shell. This is a typical situation associated with the design of offshore platform supports which stand in an essentially vertical position and are subjected to varying hydrostatic pressure and varying axial loading due to gravity.

Introduction
Many applications of ring-stiffened cylindrical shells exist in offshore technology. The most apparent and important of these applications perhaps is their use as supports for offshore platforms; but ring- stiffened cylindrical shells also have been used as submerged containers and storage vessels, pipelines, research stations and submarine vehicles, and conceivably may have other applications in production, transport, exploration and research.
Since these cylinders operate in a submerged or partially submerged state, they are subjected to external hydrostatic pressures, frequently in combination with superimposed axial compressive loads. Consequently, these cylinders are exposed to the possibility of buckling under operating conditions or during installation, and their design must be such as to preclude buckling under these circumstances. The purpose of the present Raper is to describe a computer method for calculating critical combinations of external pressure and axial load on cylindrical shells having deformable ring stiffeners.
An extensive literature exists on buckling of stiffened cylinders. The present paper makes no effort to review the existing literature but merely mentions that the majority of the publications have dealt with cases in which the stiffeners have compact cross sections that may be assumed to be undeformable, and with cases in which the loadings are constant or uniformly distributed.
In actual practice, structural efficiency tends to dictate that the ring stiffeners should have thin-walled sections, often in the shape of an I, L, T or J. The thickness of the stiffening rings are comparable to the thickness of the shell and the cross sections of the stiffeners must therefore be considered as deformable during buckling.
The procedure described in the present paper uses the numerical integration technique developed originally by Goldberg and Bogdanoff [1,2,3,4]. In this procedure, the complete set of governing equations is written, in the case of thin shells, as a system of eight first-order differential equations in the complete set of dependent variables that are exposed at the boundaries.