Analysis of Rim Supports for Off‐Axis Inflatable Reflectors. II: Deformations

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 analyzes the deformations in the rim support, based on an earlier evaluation of the internal forces and moments resulting from the load applied by the membrane. The deformations are calculated in the x‐ and y‐directions at all points along the rim. They are shown to depend on the rim geometry, the applied loads, and a dimensionless rigidity parameter comprising the inflation pressure, the major axis of the elliptical rim, the modulus of elasticity of the rim support material, and its moment of inertia. The angular deformation at each point is also evaluated. A simplified solution for small deformations shows them to be approximately proportional to the rigidity parameter.