Reinforcement minimization of cylindrical shells

In the search for the absolute minimum amount of reinforcement to be provided in a structure to support predefined loading, most attention has been given to problems for which the relationship between unit cost of material and stress relationships is simple—usually linear. Such an assumption is convenient and reasonably realistic when reinforcement percentages are low. However, for higher reinforcement percentages, and when, as in the case of cylindrical shells, there occur axial as well as radial loads, a more refined analysis procedure is desirable. This paper considers the optimal (absolute minimum reinforcement) strength design of closed cylindrical shells subject to uniform pressure and having rigid ends. Two cases are considered: the shell wall rigidly connected to the ends, and the shell wall hinged at the ends. For convenience, only internal pressure loading is considered in detail, although, using the theory given, results for external pressure cases can readily be obtained. It is assumed that buckling is not a critical factor in the design and that serviceability criteria can be met independently.