A multiscale eigenelement method and its application to periodical composite structures
A multiscale eigenelement method and its application to periodical composite structures
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DOI：
10.1016/j.compstruct.2009.08.006
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发表时间：
2010-08
影响因子：
6.3
通讯作者：
Y. Xing;Ying Yang;Xiaodong Wang
中科院分区：
文献类型：
--
作者：
Y. Xing;Ying Yang;Xiaodong Wang
本文提出了一种基于多级子结构技术的多尺度特征元方法，用于周期性复合材料结构的多尺度分析，并从用户角度对数学均匀化方法、非均匀多尺度方法、多尺度有限元方法和广义有限元方法等多尺度方法进行了比较研究，重点介绍了它们的思想、实现方法，适应性和相似性。结果表明，新发展的特征元法满足两个基本的均匀化条件，一个是应变能等效，这是至关重要的低阶频率，另一个是变形相似，这是至关重要的局部或微观应力。数值实验验证了该方法的有效性。
This paper develops a multiscale eigenelement method based on multilevel substructure technology for the multiscale analysis of periodical composite structures, and provides a comparison study with user point of view for the multiscale methods including the mathematical homogenization method, the heterogeneous multiscale method, the multiscale finite element method and the generalized finite element method, laying emphasis on their ideas, implementations, adaptabilities and similarities. It is shown that the newly developed eigenelement method satisfies the two essential homogenization conditions, one is the strain energy equivalence which is crucial to the lower order frequencies, and the other is the deformation similarity which is crucial to the local or micro stresses. Numerical experiments validate the present method.