双向荷载条件下八边形蜂窝结构因胞壁缺失所致应力集中分析

Stress concentration due to missing cell walls is an urgent problem to be solved in the additivemanufacturing process of cellular structures. The stress concentrations due to missing cell walls along one single row and multiple rows for octagonal honeycombs are studied in this paper. First, the defect region and the octagonal honeycomb are approximated by an elliptical hole and an infinite plate, respectively. The cell-wall stress close to the defect region is equivalent to tensile stress and bending stress. Based on the complex function method, the analytical formulas for tensile stress and the analytical method for the determination of bending stress are proposed. Stresses of the octagonal honeycombs with missing cell walls along one single row and multiple rows under the biaxial loading are calculated and compared with the FEM results, verifying the effectiveness of the proposed method. It is found that the analytical solutions of the tensile stress fit well with the FEM results, and an obvious linear relationship exists between the bending moment and the stress gradient. Moreover, both the analytical results and the FEM results show that the aspect ratio t/l has a negligible effect on tensile stress. Besides, the values of the tensile stress along one single row are almost unaffected by the loading coefficient λ, while those along multiple rows are considerably affected by the loading coefficient λ, the number of missing cell walls n and the number of rows m. Finally, the degree of stress concentration in terms of the size of defect region of the octagonal honeycomb is compared with that of the hexagonal honeycomb for different values of λ. The stress concentration effects of the octagonal honeycomb with defects spanning multiple rows in the cases of λ=0 and λ=1 are found lower, providing some theoretical guidance for the design of additive manufactured honeycombs.