Buckling of Compound Spherical-Toroidal Shells under External Pressure

Buckling of shallow spherical shells made from composites, and subjected to external pressure, can be a design limitation in a number of applications, e.g., in pressure safety devices, shallow mirrors, energy concentrators/inflatable space antenna. The magnitude of buckling pressure in shallow spherical caps is strongly dependant on the boundary conditions applied at the cap's outer edge. The current paper examines the use of toroidal shells with closed, circular and non-circular cross-sections, as means of supporting/constraining the outer edge of the cap. This implicitly aims at preventing buckling of the cap or at increasing the cap's buckling load. The toroids can also be internally pressurized, differently laminated, etc. Additionally the point of cap's attachment can be chosen in such a way that buckling load is as large as possible. The effect of some of these parameters on the buckling pressures of spherical caps is quantified. This is an entirely numerical study.