Multi‐objective stiffness and mass optimization of bio‐inspired hierarchical grid‐honeycomb sandwich structures with cutouts considering buckling constraints

Abstract The engineering structures with cutouts should consider both buckling and stiffness. Inspired by the multi‐level leaf veins, in this paper, the skeleton of the grid‐honeycomb sandwich structure was designed in the hierarchical form, and combined with the cutout characteristics of the side walls of the railway vehicle body, the multi‐objective stiffness and mass optimization of the skeleton layout under buckling constraints was achieved. The cutout honeycomb sandwich structure was designed with orthogonal grids in the stiffness design area and curved grids based on the quadratic polynomial in the buckling design area. The optimization model also included the linear angle hierarchical grid, the constant angle hierarchical grid, and the single‐level orthogonal grid. The multi‐objective optimization framework based on the Radial Basis Function (RBF) surrogate model and the Non‐dominated Sorting Genetic Algorithm (NSGA‐II) was developed. The optimization results indicated that the hierarchical grid provided the more extensive design space. The optimal solution of the quadratic polynomial hierarchical grid had the highest stiffness and stiffness per unit mass compared to the rest of the grid layouts, which were 23.28% and 30.47% higher than the single‐level orthogonal grid, respectively. Finally, the multi‐order eigenvalue buckling was analyzed based on the optimal structure. Highlights Layout of hierarchical grids proposed inspired by multi‐level leaf veins. Orthogonal grids ensure stiffness and curved grids inhibit buckling at cutouts. Apply the hierarchical grids as skeletons to honeycomb sandwich structures. Stiffness and mass optimization subject to buckling constraints is performed.