Optimal Design of Flat Carbon Fiber Composite Mirror

This study aims to achieve the optimal design of a carbon fiber composite mirror, focusing on minimizing mass and wavefront error (WFE). To achieve this, central composite design (CCD) was employed as the method of design of experiments (DOE) for sampling. Mass and displacement were calculated using finite-element analysis (FEA), and the WFE was determined using Zernike polynomials based on the displacement data. Metamodels using the response surface method (RSM) were created to predict the effects of design variables on mass and WFE. The results of the metamodels demonstrated high accuracy, with R2 values of 0.9978 for mass and 0.9561 for WFE. Multiobjective optimization was performed using the nondominated sorting genetic algorithm II (NSGA-II). To validate the RSM-based model, a comparative analysis was conducted with an equation-based model using flexural rigidity and mass as the objective functions. Flexural rigidity was selected due to its inverse correlation with surface deformations. The comparison of design variables between the RSM-based model and the equation-based model showed equal values for the thickness of the mirror panel, the thickness of the grid, and the height of the grid, except for a difference of 1.5 mm in the inscribed circle diameter of the grid. This result confirms the robustness of the RSM approach. When comparing the FEA results derived from the RSM-based model with those from the equation-based model, the mass showed a difference of 0.0057 kg, and the WFE showed a difference of 0.67 nm. Although the equation-based model showed slightly lower values, the differences were not significant. Additionally, comparing NSGA-II and FEA within the RSM-based optimal model, the error rates for mass and WFE were within 8%. The close similarity in these results validates the RSM-based model, suggesting its effectiveness in designing high-performance carbon fiber composite mirrors for aerospace applications.