On the Statics of Supports and the Geometry of Wrinkling of Large Spherical Pressure Vessels

Thin-walled spherical pressure vessels, the bending and compressive stiffnesses of which are small in comparison with their tensile stiffness, are discussed using membrane theory. In the first part of the paper linear membrane theory is used to analyze the statics of supports for large spherical pressure vessels. The reactions from such supports which are tangential or almost tangential to the pressure vessel surface, require reinforcements so as to distribute the reactions into the wall without causing undue stress concentrations and/or wrinkling. The size and contour of such reinforcing elements depend, of course, on the magnitude of the reactions as well as the internal pressure. In the second part of the paper, nonlinear membrane theory is used to analyze the geometry of wrinkled domains in such membrane pressure vessels. Using an Eulerian formulation, the parameters of the first and second fundamental forms of the surface are treated as key variables and are determined from the analysis as functions of the curvilinear coordinates referred to the current deformed configuration. The solution technique is applied to a simple example.