Multi-Scale Modeling and Optimization of Single-Layer Reticulated Shell Structures Using Multi-Point Constraint and Variable Density Methods

Optimization methods tailored for practical engineering applications continue to evolve in order to realize lightweight single-layer reticulated shell structures and maximize node stiffness. This paper takes the minimum amount of steel as the objective function, and divides the rod types into three groups and three corresponding one-to-one optimization schemes. Considering the stress and stiffness of the rod and the displacement and stability constraints of the whole structure, the equal step search method combined with the criterion method is used to optimize the rod size. Then the multi-scale calculation model based on the multi-point constraint method is established. Through calculation and analysis, the boundary load condition of the target node is obtained as the boundary condition of node optimization. Finally, the variable density method is used to optimize the topology of the node domain, and the minimum member size is included in the constraint conditions to obtain the optimized node form that is conducive to additive manufacturing. The research shows that reasonable cross-section value and grouping of members can effectively reduce the steel consumption without compromising the overall stability performance. The amount of steel used in the three optimization plans was reduced by 12%, 23%, and 28%, respectively, compared to before the optimization. The multi-scale model not only takes into account the calculation accuracy, but also can effectively simulate the stress conditions in the node domain. The development of topology optimization and additive manufacturing technology broadens the space for optimization design, and provides new ideas for advanced design to integrate intelligent manufacturing.