The Branched Multi-point Approximation (BMA) method holds immense potential in tackling topology optimization challenges involving discrete variables. This research focuses on enhancing the adaptability, approximation efficiency and engineering application of the method. Four key advancements are presented below. Firstly, an adjusted BMA function is introduced, which comprehensively incorporates the topologies of known and current points, utilizing topological difference between them as the foundation for function segmentation. This function further mitigates singularities as continuous variables approach zero, and is verified for its approximation capability through randomized numerical simulations. Secondly, the concept of adjacent individuals is proposed to ensure that the topological disparities between the current point and current optimal solution remain within manageable limits. This approach prevents approximation failures while maintaining the diversity of the population generated by genetic algorithm. Thirdly, for optimizing continuous variable in complex problems, an improved separable-variable approximation is formulated to ensure strong duality validity. Finally, an adaptive technique for move limit of the retained continuous variables is established. Benchmark examples demonstrate the effectiveness of the improved method in iterations and optimal results. Optimization systems capable of performing topology optimization for spacecraft such as stiffened satellite and carrier rocket have been rare in prior research.

This study suggests the development program of a sleeve type spiral deployment coiled mast using the combination of threaded cylinder and straight guide cylinder, with the goal of designing the sleeve type spiral deployment coiled mast and addressing the crucial issue of whether the mast can be smoothly retracted. In order to predict the overall performance of the ground prototype, this paper adopts the virtual prototype technology, based on ADAMS software, establishes the dynamic simulation model of the sleeve type spiral deployment coiled mast, simulates the retraction and extension process of the mast, and analyzes the deformation characteristics of the crossbar in the transition zone in the post-flexion state. Finally, the ground test of the mast retraction and extension was carried out by the assembled ground prototype. The destabilizing deformation of the triangular cross frame during the mast's deformation process was used to determine the working principle of the mast using elemental instability. The simulation results were compared with the experimentally obtained relationship curves between the change in the mast's length with the chassis angle during the retraction and extension process and the change in the mast's coiled radius in the transition zone, confirming that the simulation model was in the post-flexion state. Comparison is made with the simulation results to verify the correctness of the simulation model and the feasibility of the design scheme.