We designed the laser beam director (LBD) with the radius of the primary mirror of 800mm, the focal length of 8,000 mm, and F-number of 10. To design the light weight primary mirror for the LBD system, we considered the primary mirror of double arch shape with parabolic contours, the maximum thickness of 120 mm, the outer edge mirror thickness of 15 mm. The considered axial support system was six equally spaced supports at 60 degrees and the radial support system was three equally spaced supports at 120 degrees. Considered material properties were the elastic modulus of 9.06x10(10)N/m the poisson's ratio of 0.24 and the weight density of 2.53 g/cm(3). A finite element model with 1,512 nodes was selected for structural analysis. In order to examine the validity of the closed-form solution for the primary mirror with a double arch shape, the primary mirrors of various contoured back shape equations with support ratio ranging from 0.5 to 0.8 were used. The considered support radii were 200, 240, 260, 270, 280, 290, 300, 310, and 320mm. We found that the deformation of the primary mirror for horizontal axis decreases, as the support ratio increases. The smallest deformation of primary mirror for zenith axis was given when the support ratio was 0.675. For this case, the P-V value was 27.810nm and the RMS wave error was 0.0160 lambda. We were also able to determine from the structural analysis that the optimum support ratio of the primary mirror for the LBD was 0.75.
