Limit Analysis of Cylindrical Shells

The load carrying capacity of circular cylindrical shells simply supported at both ends and subjected to axisymmetric hydrostatic load is examined. The shell material is assumed to obey an inscribing hexagonal approximation to the Tresca yield curve for axisymmetrical bending of cylindrical shells with zero end load. The results of this analysis, together with those obtained on the assumption that the shell material obeys a circumscribing square approximation to the Tresca yield curve, bound the limit loads associated with the Tresca yield conditions. The values of the limit loads are plotted against a wide range of the shell parameter. For long shells, it is demonstrated that the curve is asymptotic to the limit load given by the membrane analysis. The stress profiles, as well as the corresponding statically admissible stress fields and kinematically admissible velocity fields, are also demonstrated for particular values of the shell parameter.