Analysis of Rim Supports for Off‐Axis Inflatable Reflectors. I: Loads

A structural analysis is performed for the rim support of a pressurized off‐axis paraboloidal membrane, serving as a space‐based solar concentrator. The function of the rim support is to take up the tensile forces created by the stretched membrane. This paper deals with the load analysis. The tensile forces transmitted by the membrane to the rim support are calculated, and are proportional to pb, where p is the inflation pressure and b is one‐half the major axis of the elliptical rim. Next, the internal forces and moments generated in the rim support by the membrane forces are calculated. The compression forces are considerably larger, at any point, than the shear forces; both are proportional to ${\mathrm{pb}}^2\text{.}$ The bending moments are proportional to ${\mathrm{pb}}^3\text{.}$ The critical point is found to be at the top of the rim, where both the bending moment and compression force are at their maximum.