Design for Buckle-Free Shapes in Pressure Vessels

There are many applications of thin-walled axisymmetric structures as pressure vessels in which buckle-free in-service behavior can only be guaranteed by reinforcements, such as stringers and girths, which not only raise the weight of the structure but also increase its cost. Buckle-free behavior, however, can also be assured by “correcting” the shape of the pressure vessel by a small amount in the area of impending instability. This paper proposes the use of the theory of inflatable membranes to obtain the shape of a pressure vessel subjected to tension only stress state, whereby the possibility of buckling is excluded. Such a shape will be referred to as the “buckle-free” shape. A set of nonlinear differential equations are derived which are valid for any axisymmetric pressure vessel subjected to axisymmetric loadings. The shape obtained from the solution of the equations is an “extremum” to possible stable shapes under the given loading conditions; i.e., there are other stable shapes, for which the circumferential compressive stiffness of the structure has to be relied upon. A closed-form solution for the set of equations was obtained for the constant pressure loading case. For hydrostatic pressure a numerical procedure is applied. Results on “buckle-free” shapes for typical pressure vessel strucures for these two loading conditions are presented. It is established that the deviation of such shapes from the shapes obtained by present design methods and code specifications is small so that this proposed method and the resulting “corrections’ leading to “buckle-free” inservice behavior should not present an aesthetic problem in design.