Size effects of basic cell in static analysis of sandwich beams
Size effects of basic cell in static analysis of sandwich beams
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DOI：
10.1016/j.ijsolstr.2007.12.007
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发表时间：
2008-05
影响因子：
3.6
通讯作者：
Gaoming Dai;Weihong Zhang
中科院分区：
文献类型：
--
作者：
Gaoming Dai;Weihong Zhang
本文考虑了多层夹层梁结构。在此类轻量化功能结构的静力分析和刚度设计范围内，首次系统地从理论上和数值上研究了基本单元的尺寸效应。本文对直接有限元离散化方法、均匀化方法和经典梁理论进行了系统的检验，一方面揭示了尺寸效应的存在，另一方面揭示了每种方法捕捉尺寸效应对静应力分布和结构挠度的影响的能力。特别是，澄清了均匀化方法的局限性，尽管后者目前广泛应用于夹层结构细胞材料的等效建模和拓扑设计。通过上述方法，对多层梁和蜂窝芯夹层的弯曲问题进行了求解，以说明挠度、应力的变化以及计算精度随基本单元尺寸的变化。结果表明，当基本单元相对于结构尺寸具有相当大的尺寸时，尺寸效应是重要的，并且这种效应随着基本单元尺寸的减小而迅速减小。理论上，均质化的结果对应于基胞尺寸趋于无穷小时的极限解。
In this paper, multilayered sandwich beam structures are considered. Within the scope of static analyses and stiffness design of such type of lightweight and functional structures, size effects of the basic cell are studied both theoretically and numerically in a systematic way for the first time. The direct FE discretization method, the homogenization method and the classical beam theory are examined systematically to reveal, on one hand, the existence of the size effect, and on the other hand, the ability of each method in capturing the size effect upon the static stress distribution and structural deflection. Particularly, limitations of the homogenization method are clarified although the latter is widely applied today in the equivalent modeling and topology design of cellular materials of sandwich structures. By means of the above methods, bending problems of multilayered beams and cellular core sandwiches are solved to illustrate variations of the deflection, stress as well as the computing accuracies in terms of the size of the basic cell. It is shown that the size effect is important when the basic cell has a considerable dimension relative to the structural size and that this effect decreases rapidly with the size reduction of the basic cell. Theoretically, the homogenized result corresponds to the limit solution when the size of the basic cell tends to be infinitely small.