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Optimization techniques are powerful tools for producing lightweight structures with the maximum structural stiffness. They allow an optimized design to be produced directly for a given structure and, in this way, save considerable time in the design phase of a structure by avoiding multiple iterations between the definition of the design under computer-aided design (CAD) and the verification of the performance under finite-element (FE) analysis. There are three classes of optimization: size optimization, shape optimization and topology optimization. The topology optimization technique aims to find an optimal distribution of material given boundary conditions, i.e. the fixing points and the external loads. It starts from an initial volume representing a blank of the structure and removes the most unused material to meet the objective of mass reduction. In optomechanical engineering, this technique is met in the design of lightweight mirrors and especially in the design of their core-cell shapes. To provide reliable and useable results, this technique requires a fine and regular mesh of the mirror as well as a postprocessing of the results by the mechanical engineers. These constraints, combined with the necessity of using 3-D models, contribute an increase in the computation time and complicate the meshing. We propose here an innovative approach to this design problem by using topography optimization instead of topology optimization. Topography optimization, also named bead optimization, is a branch of the shape optimization and consists in introducing beads to a surface in order to increase its structural stiffness. The main advantage of this technique is that shell models can be used instead of solid models, easing the meshing operation and decreasing the number of degrees of freedom in the FE model, and thereby reducing computation cost. This paper presents an example of the application of this technique to the design of the primary mirror panel of the GCT (Gamma-ray Cherenkov Telescope), a dual-mirror 4-meter telescope proposed for the future Cherenkov Telescope Array. FE models and optimizations are made with MD.Patran and MD.Nastran respectively.
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