Non-FEM analysis and modeling in opto-structural mechanics

Abstract

In spite of the widespread and mushrooming use of FEM (Finite Element Method) based modeling and analysis by the optical community in recent years, other methods of analysis and modeling are still viable, useful, cost-effective and sometimes necessary in some areas of opto-structural mechanics. This paper provides a review of some of this writer’s applications using closed-form solutions and mathematical modeling based on the equations of elasto-mechanics to three topics in opto-structural mechanics; namely, (1) the distortion of circular mirrors under operational and environmental loads, (2) design/analysis of deformable mirrors and related performance prediction, and (3) polishing of optical surfaces (analysis/design of flexible polishing laps, material wear rate and smoothing). Solutions of Kirchoffs flat plate equation and E.Reissner's spherical shell equation were derived and used for the first two topics of application. A modified flat plate equation, which included, besides bending, the transverse shear and lap compressibility, was solved for the flexible lap pressure distribution. Using this, Preston’s wear rate equation was solved for material wear and smoothing during optical polishing. Where available, comparative data are presented in this paper for finite element analyses and test measurements corresponding to the closed-form solutions. Excellent correlation is observed among the three. The paper also includes reviews of (1) the flexural rigidity characteristics of open and closed back light weighted mirrors, (2) the meshing characteristics of curved deformable mirrors, and (3) related publications of other writers in the field of opto-structural mechanics.