Back Frame Section Size Optimization of Large Aperture Telescope

The back frame structure of a large radio telescope is an important component supporting the reflecting surface, which is directly related to the surface precision. Its optimal design is of key significance for ensuring the surface precision and reducing structural weight. Two methods are constructed to optimize the cross-section size of the telescope back frame in this paper, the criterion method and the first-order optimization method. The criterion method is based on the Lagrangian multiplier method and Kuhn-Tucker condition. This method first establishes the mathematical model by taking the inner and outer radiuses of the back frame beams as the design variables, the structural weight as the constraint condition, and the structural compliance as the objective function, then derives the optimization criterion. The first-order optimization method takes the inner and outer radiuses of the beams as the design variables, the back frame RMS as the objective function, and the structural weight as the constraint condition. Comparison of RMS, structural stress uniformity and optimization efficiency shows that both algorithms can effectively reduce structural deformation and improve RMS, but the criterion method has relatively better result than the first-order method.