蜂窝夹层结构等效弹性常数的多步三维均匀化数值计算分析

Numerical Computation of Effective Elastic Constants of the Honeycomb Sandwich Panel with the 3-D Multi-Step Homogenization

基于三维均匀化方法并结合有限元技术,计算三维蜂窝夹层板的等效弹性常数。首先把三维蜂窝夹芯看成由实体与空洞两相材料组成的复合材料结构,建立单胞有限元模型,计算宏观等效弹性常数,通过与其它计算方法相比较,验证了三维均匀化方法的有效性;在此基础上考虑上下面板,运用直接、二次及多步均匀化方法计算三维蜂窝夹层板的整体等效弹性常数,并与工程计算方法比较,结果表明三维均匀化方法的可靠性。

Using the 3-D homogenization method and the finite element technique, we evaluate the effective elastic constants of the 3-D honeycomb sandwich panel. Like Hassani, we consider the 3-D honeycomb core as a two-phase composite and model it with the finite element techniques we take Hassani＇s 2-D homogenization method and extend it to become a 3-D one. We validate our 3-D homogenization method through comparing the results obtained with 3-D homogenization method with those obtained with the methods of Fu et al and Hassani; the comparison can be seen in Table 2 of the full paper. We use three variations of our 3-D homogenization method （one-step, two-step, and multi-step ones explained in the full paper with the aid of Fig. 3） to evaluate the overall effective elastic constants of the 3-D honeycomb sandwich with upper and lower skins;the evaluation results are given in Table 3 of the full paper. We use one-step, two-step, multi-step homogenization methods and the engineering empirical method of Ref. 1 to calculate three kinds of effective elastic moduli of 3-D honeycomb sandwich panels the computed results, given in Table 4 of the full paper, of the one-step, two-step, and multi-step homogenization methods are in fairly good agreement with those of the engineering empirical method of Ref. 1.