【摘要】 在线弹性范围内,根据均匀化理论,并结合有限元方法推导出适用于二维周期性结构的均匀化的有限元格式（Homo FEM）,计算出不同相对密度下的规则蜂窝结构的等效弹性模量Ee和泊松比νe.同时,利用蜂窝结构的代表胞元模型,用常规的有限元方法（FEM）模拟计算出相应的等效弹性参数.最后将两种数值计算结果与己有的理论公式进行了比较和分析讨论.结果表明:在考察的相对密度全场范围内（0～0.4）,HOmO FEM得到的蜂窝结构的 Ee和νe 与 FEM使用平面实体单元模拟计算得到的结果一致吻合,反映出 Homo FEM数值方法的客观准确性和可行性.而 Gibson公式和 W-K得到的等效弹性模量值 Ee只是在较小相对密度的情况下（小于0.15）与数值计算结果吻合.当结构的相对密度较大时,必须考虑胞棱附近区域由应力集中导致的复杂的应力和应变分布的影响.更多还原

【Abstract】 In this paper the equivalent in-plane elastic moduli of two-dimensional honeycomb structures are evaluated. Starting from the weak form of virtual displacement equations, the homogenization method is introduced for linear elastic problems. Then a homogenization finite element method （Homo FEM） is developed for the 2-D periodic structures and applied to the calculation of the equivalent elastic constants Es and?_s of a regular honeycomb structure with various relative densities. Simultaneously, we use the model of representative unit cell （RUC） to simulate the equivalent mechanical properties of the honeycomb by conventional finite element method （FEM）. The numerical results of Es and vs obtained by both Homo FEM and conventional FEM are then compared with some of the existing analytical results. It transpires that the Homo FEM technique works well on the honeycomb structures. Within the range of the relative densities considered （0⁰.4）, the calculated values of Es and vs by Homo FEM coincide well with those by conventional FEM using plane solid elements, indicating the feasibility and accuracy of the new method. On the other hand, only at low relative density of less than 0.15 did earlier theoretical analyses give the same results of honeycomb’s equivalent elastic constants as those obtained by the present methods. When the relative density is higher than 0.25, obvious deviation between the theoretical prediction and the numerical results is found. When the relative density is large, the honeycomb’s equivalent mechanical properties are affected significantly by the complicated distribution of stresses and strains in the solid areas neighboring the cell edges due to the stress concentration, which was ignored in the theoretical model.更多还原