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 in Octagonal Honeycombs due to Missing Cell Walls Subjected to the Biaxial Loading

因胞壁缺失引起的应力集中问题是蜂窝结构增材制造过程中亟待解决的问题.通过将胞壁缺失所致的缺陷等效成椭圆,基于复变函数方法得到了预测拉伸应力的解析公式和预测弯矩应力的分析方法,进而得到八边形蜂窝结构在双向荷载条件下缺失单行和多行胞壁产生的应力组合值.与有限元结果的对比分析验证了所提理论解析公式的有效性;同时得出距离缺陷最近胞壁上的拉伸应力理论结果与有限元结果吻合良好,弯矩应力的有限元结果与胞壁上的应力梯度呈明显的线性关系.与规则六边形蜂窝在多行缺陷条件下的应力集中问题进行对比,得出八边形蜂窝结构在荷载系数λ=0和λ=1时应力集中程度小于规则六边形蜂窝结构,从而为蜂窝结构增材制造设计提供理论指导.

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 coefficientλ,while those along multiple rows are considerably affected by the loading coefficientλ,the number of missing cell walls nand 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 ofλ.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.