On the Self-weight Sag of Arch-like Structures in the Context of Light-weight Mirror Design

Guided by the concept of arch-like structures for optimum design, self-weight deflections are obtained for various structural configurations constructed within the envelope of a solid disc. This is achieved through a finite element formulation for the axi-symmetric system. The superiority of arch-type designs over solid discs with respect to deflection and weight is established. The theoretical predictions of reduction in the weight to stiffness ratio for mirror structures by removing materials in an arch-like manner is substantiated by the use of silicone rubber models.