In this research, a computational technique is developed for determining effective in-plane properties of hexagonal core honeycombs utilizing homogenization multi-scale technique based on averaging theorems. Purposely associated with engineering constants, specialized unit cells under appropriate boundary conditions are elaborated for two well-known configurations of uniform cell wall thickness and doubled thickness vertical cell walls hexagonal honeycombs. Constant boundary element method (CBEM) are employed for discretizing the boundary integral form of equivalent stress and strain equations and avoiding dependency to the mesh density and elements type selection challenges at cell walls intersection. Comparing with available experimental data for uniform cell wall thickness hexagonal honeycombs, the proposed method validated for a wide range of relative densities. Then comparing with well-defined existing analytical methods which have been previously validated experimentally, the verification of proposed method is done for uniform cell wall thickness and double thickness vertical cell walls. The results show that the proposed methods can present a well approximation of in-plane engineering constants for relative densities lower than 0.3 and also can be applied to higher relative densities by defining proper unit cells where available analytical methods encounter with significant inability.

在这项研究中，开发了一种基于平均定理的均质化多尺度技术来确定六角芯蜂窝的有效面内特性的计算技术。故意与工程常数相关联，在适当的边界条件下，针对两个众所周知的均匀单元壁厚度和两倍厚度的垂直单元壁六边形蜂窝结构，详细阐述了特殊的单元单元。恒定边界元法（CBEM）用于离散等效应力和应变方程的边界积分形式，并避免依赖于单元格相交处的网格密度和单元类型选择挑战。与可用的实验数据进行比较，得出均匀的细胞壁厚度六角形蜂窝，所提出的方法可在较宽的相对密度范围内进行验证。然后，与定义明确的现有分析方法进行比较，这些分析方法先前已通过实验进行了验证，对均匀孔壁厚度和双层厚度垂直孔壁进行了所提出方法的验证。结果表明，所提出的方法可以为低于0.3的相对密度提供很好的平面内工程常数近似值，并且可以通过定义适当的晶胞来应用于更高的相对密度，而在可用的分析方法遇到严重缺陷的情况下。