Limit Loads of Cylindrical Shells under Hydrostatic Pressure

Abstract

The limit analysis of circular cylindrical shells under hydrostatic pressure is formulated as a mathematical programming problem using the static theorem of plasticity. The governing differential equilibrium equations and force boundary conditions are linearized through a finite difference scheme. This discretization is combined with a piecewise linearization of the nonlinear yield curve to convert the formulation into a conventional linear programming exercise. This approach is shown to be superior to the more commonly used analytical techniques. In particular, it is general, systematic, and does not require prior knowledge of the stress field or collapse mechanism. In spite of the fact that a lower‐bound solution is not guaranteed due to possible yield violation at unchecked points in the structure, very accurate solutions can be obtained by suitably refining the finite difference mesh and, if necessary, the yield polygon. Examples of reported cases are solved to illustrate ease of application of the method, its flexibility, and accuracy.