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 引用本文: 杨勇林, 张亚莉, 马海亮, 丁生虎, 李星, 汪文帅. 受载空心柱下多孔半空间的接触分析. 力学学报, 2024, 56(8): 2338-2350.
Yang Yonglin, Zhang Yali, Ma Hailiang, Ding Shenghu, Li Xing, Wang Wenshuai. Contact analysis of porous half-space under hollow column loading. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(8): 2338-2350.
 Citation: Yang Yonglin, Zhang Yali, Ma Hailiang, Ding Shenghu, Li Xing, Wang Wenshuai. Contact analysis of porous half-space under hollow column loading. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(8): 2338-2350.

## 受载空心柱下多孔半空间的接触分析

• 摘要: 多孔结构具有诸多优良特性被广泛应用于航空航天、生物医疗以及各种工程装备中, 而空心柱具有独特的结构常被用于承担结构载荷. 因此, 研究空心柱与多孔半空间的接触问题显得尤为重要. 文章运用Hankel变换将轴对称接触问题转化为积分方程的求解问题, 推导出表面接触应力和位移的精确表达式. 发展了高斯-切比雪夫结合乘积型Bessel函数的无穷积分的数值求解方法, 并退化对比验证了方法的正确性, 结果表明该方法在奇异值处的计算精度和效果更佳. 数值分析了表面接触应力随泊松比、孔隙率、力载荷、内径、壁厚(空心圆柱)和半径(碗形抛物柱)的变化情况, 并给出了位移随孔隙率、内径、壁厚、半径及深度的变化情况. 研究结果表明基体的接触区域中心产生明显的叠加变形, 并且接触区域外侧的奇异性要高于内侧, 所以外侧更有可能是裂纹的起始位置. 此外, 在较小的内径下, 当空心柱壁厚与实心柱半径一致时, 空心柱比实心柱所导致的基体接触区域外边缘的应力奇异性小1倍以上, 并且随着孔隙率的增大该比值降低; 当空心柱外径与实心柱半径一致时, 空心柱比实心柱所导致的基体接触区域外边缘的应力奇异性大1倍以上, 并且在大孔隙下该比值更大. 研究结果对多孔材料的设计和应用具有重要的指导意义.

Abstract: Porous structures, owing to their excellent characteristics, are widely used in aerospace, biomedical, and various engineering applications. Hollow columns, due to their unique structure, are extensively employed to bear structural loads. Therefore, the study of the axisymmetric contact problem between hollow columns and porous half space is particularly important. In this paper, the Hankel transform is used to transform the contact problem into the problem of solving an integral equation, and exact expressions for surface contact stress and displacement are derived. The Gauss-Chebyshev method coupled with the infinite integration of product-type Bessel functions for solving integral equations is developed, and degradation comparisons are carried out to verify the correctness of the method. The results indicate that the method has better computational accuracy and performance at singular points. The numerical results show the variations of surface contact stress with respect to Poisson's ratio, porosity, mechanical loading, inner diameter, wall thickness (hollow cylinder), and radius (bowl shaped parabolic column). The study additionally provides insights into the displacement variation concerning porosity, inner diameter, wall thickness, radius, and depth. The results further indicate that the center of the contact region of the substrate has obvious superimposed deformation, and the singularity of the outer side of the contact region is higher than that of the inner side. Therefore, it is more likely that the outer side is the initial position for cracks. Furthermore, for a smaller inner diameter, when the wall thickness of the hollow column matches the radius of the solid column, the stress singularity at the outer edge of the contact area of the substrate caused by the hollow column is more than 1 times smaller compared to that caused by the solid column, and this ratio decreases as the porosity increases. On the other hand, when the outer diameter of the hollow column matches the radius of the solid column, the stress singularity at the outer edge of the contact area of the substrate caused by the hollow column is more than 1 times larger compared to that caused by the solid column, and this ratio increases with an increase in the porosity. The research results have important guiding significance in the design and application of porous materials.

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