Equilibrium Shapes for Pressurized Fiberglas Domes

The netting concept is used to analyse filament wound shells of revolution. First the fiber tensions are resolved parallel and perpendicular to the meridian. These components of the fiber tensions give the meridional and hoop forces in the dome. A comparison of these forces is made with the forces calculated from membrane theory. It is shown that the shell will be unstable unless the forces calculated from the fiber tensions are equal to the membrane forces computed from membrane theory. A dome with a polar opening is examined to see if a shape can be found which will make the dome stable. It is shown that for stability, two separate differential equations must be satisfied by the dome curve. The two equations are found to be dependent, and thus both are satisfied by the same curve. The equation for a stable dome is presented in terms of a nondimensional integral.