Membrane caps under hydrostatic pressure

It is shown that the exact nonlinear theory for a rotationally symmetric membrane cap deformed by hydrostatic pressure is statically determinant. A small strain theory is obtained without any assumptions on the relative magnitudes of the displacements. This small strain theory can be reduced to a single second-order ordinary differential equation for the determination of the radial stress. A linear shallow cap theory is obtained and solved explicitly for the case of the shallow spherical cap.