# A Fluid-Structure Coupling Analysis of a Far-Field Flat Mirror for AliCPT-1 Telescope Calibration
## 4 Structural Analysis  
### FEA Model  
The finite element method was chosen for FFF structural analysis [24]. In finite element analysis, the matrix expression for the control equations by  
\[[\mathrm{K}]\{\mathrm{x}\}=\{\mathrm{F}\} \tag{5}\]  
where \(\{\mathrm{K}\}\) is the stiffness coefficient matrix, \(\{\mathrm{x}\}\) is the displacement vector, and \(\{\mathrm{F}\}\) is the force vector. In static structural analysis, assuming \(\{\mathrm{F}\}\) to be a constant matrix and continuous, materials should adhere to elastic, small deformation theory. Nonlinear boundary conditions may be applied, and \(\{\mathrm{F}\}\) represents the static loads applied to the model, which is independent of time variation and inertial forces [24].  
We employed a static strength analysis in ANSYS Workbench to analyze the deformation of the reflection mirror under maximum wind pressure and simultaneously evaluate the stability of the support rod structure.  
Figure 11: Pressure distribution maps on the reflective mirror surface after applying pressure: (**a**) Pressure contour plot for wind from the front. (**b**) Pressure contour plot for wind from the back.  
Firstly, simplify the model. Reduce the number of mesh subdivisions by removing bolts, small holes, and threads from the model to minimize the amount of numerical calculations and save time. The structural outline was effectively captured through mesh refinement in finite element analysis, and additional nodes are available for displacement and stress calculation. Localized refinement to the connection between the support structure of the FFF mirror and the base plate to ensure the accuracy of critical structures and to mitigate potential stress concentration points. For optimal computational performance and practical conditions, tetrahedral elements with a size of 10 mm were chosen, with denser meshing at complex connection points. The final model encompasses approximately 9 million elements and 12 million nodes, as depicted in Figure 12.  
Almost all structures within FFF are composed of aluminum alloy 6061 (6061 for short), which exhibits fine corrosion resistance, mechanical properties, formability, weldability, and machinability; additionally, the superior specific strength is the most crucial factor for the lightweight design of FFF. The key parameter of which is detailed in Table 1.  
Analyze the FFF deformation and stress with forward and backward wind load, assuming the baseplate is fixed, as depicted in Figure 13. The figure shows that the surface of the FFF mirror experiences the highest pressure with the supporting bracket. This uneven pressure distribution can cause a decrease in the accuracy of the mirror's shape. Additionally, stress concentration may occur in the supporting bracket.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Material Properties** & **Material Parameters** \\ \hline Density (t/mm\({}^{3}\)) & 2.77 \(\times\) 10\({}^{-9}\) \\ Young’s Modulus (MPa) & 71,000 \\ Poisson’s Ratio & 0.33 \\ Tensile Yield Strength (MPa) & 280 \\ Tensile Ultimate Strength & 310 \\ \hline \hline \end{tabular}
\end{table}
Table 1: AL6061 material properties.  
Figure 12: Mesh model.