Multimaterial homologous topology optimization of large telescope structure under multiple elevation conditions

This paper describes a novel numerical design method for homologous deformation problems in large telescope structural design using density-based multimaterial topology optimization. The Large Submillimeter Telescope (LST), which is a new 50-m-class single-dish telescope, is planned to be constructed. From the view of the structural design of the LST, the weight of the lattice backup structure (BUS) of the primary reflector must be reduced and self-weight deformation must be controlled by considering the usage of multiple materials under different evaluation angles. Moreover, the telescope shape must be kept paraboloid after deformation for the surface accuracy of the primary reflector. In this paper, multimaterial homologous topology optimization was formulated and applied to the BUS structure to optimize both its topology and materials. The artificial density of the lattice structure of the BUS was chosen as the design variable. The main problem was defined as a linear elastic problem of the lattice structure under the self-weight load of different elevation angles of the telescope. The weighted sum of homologous deformation in different conditions of the elevation angles was used as an objective cost function. The volume of the lattice structure and usage ratio of materials were chosen as constraint cost functions. For the material interpolation scheme with respect to the artificial density, the rational approximation of material properties was introduced and generalized for the arbitrary number of materials. Then, practical examples of the lattice structure of the LST model were demonstrated to show the effectiveness of the proposed solution.