Global optimization of the hexagonal segmented ultra-lightweight design and 27-point Whiffletree support distribution in segmented telescopes

To address the requirements for lightweight design and high surface accuracy in large-aperture segmented mirrors and to address issues such as the significant impact of support point locations on the mirror’s back surface on surface accuracy, the tendency of previous studies on support point optimization to fall into local optima, and the empirical grouping of stiffeners. We propose a global optimization strategy that coordinates the support layout and structural parameters of a hexagonal segmented mirror. First, an adaptive simulated annealing algorithm was employed to perform global optimization of the 27-point Whiffletree support positions, and support pad dimensions were selected to satisfy weight and performance requirements. Second, based on the results of topological optimization, the load-bearing contributions of the ribs were quantified, and a scientific method for classifying their functions was established. Finally, a multi-objective genetic algorithm was used to perform multicondition collaborative optimization of 17 fully parameterized dimensions. The results show that after achieving a 50.6% weight reduction through initial lightweighting, full-parameter optimization further reduced the mass to 117.34 kg, with a lightweighting rate of 69.3%; the RMS values of the body shape under the three gravitational loading conditions improved by 2.69%, 49.22%, and 48.42%, respectively, verifying the effectiveness and broad engineering applicability of the proposed method in comprehensively suppressing gravitational deformation under multiple loading conditions while achieving significant weight reduction.