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总览 评价 朱国庆 * （ 数学与统计学院,北京理工大学,北京,100081； ） 摘要： 本文中,针对三维周期构型的复合材料板结构的弯曲问题,二阶双尺度分析方法以构造的形式给出.此方法可以捕捉由三维微结构带来的三维微观力学行为.首先,由三维弹性复合材料板结构的
朱国庆*
（
数学与统计学院,北京理工大学,北京,100081； ）
摘要：
本文中,针对三维周期构型的复合材料板结构的弯曲问题,二阶双尺度分析方法以构造的形式给出.此方法可以捕捉由三维微结构带来的三维微观力学行为.首先,由三维弹性复合材料板结构的力学模型出发,三个单胞给出新的构造,相应的三组单胞函数也给出重新定义.接下来,复合材料有效参数由三组单胞函数计算,可以得出二维的板模型.求解即可得到均匀化解.最后二阶双尺度渐近展开式由微单胞函数和均匀化解构造.
关键词：
计算数学;双尺度方法;复合材料板
ZHU Guoqing*
（
School of Mathematics and Statistics,Beijing Institute of Technology,Beijing,100081； ）
Abstract：
In this paper, the second-order two-scale analysis method for bending behaviors of the plate made from composites with 3-D periodic configuration is presented by means of construction way. It can capture the microscopic 3-D mechanics behaviors caused from 3-D micro-structures. First, directly starting from the 3-D elastic plate model of composite materials with 3-D periodic configuration, three cell models are defined, and correspondingly the three classes of cell functions only defined on 3 normalized cells are constructed. And then, the effective homogenization parameters of composites are calculated from those local functions, it leads to a 2-D homogenized laminar plate problem. Next, to solve it the homogenization solution is obtained. Finally, the second-order two-scale solution is constructed from the micro-cell functions and the homogenization solution.
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