An eigenelement method of periodical composite structures
An eigenelement method of periodical composite structures
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DOI：
10.1016/j.compstruct.2010.08.029
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发表时间：
2011
影响因子：
6.3
通讯作者：
Y. Xing;Ying Yang
中科院分区：
文献类型：
--
作者：
Y. Xing;Ying Yang
特征元法是一种基于特征向量展开的有限元方法，是作者提出的一种计算复杂复合材料宏观力学行为的方法。为了提高经典本征元法（CEEM）的宏观精度，提出了一种在一定程度上考虑复合材料不同相的几何和弹性性质的偶发本征元法（SEEM）。给出了多尺度特征元法（MEM）的形函数及其构造方法，并将SEEM和MEM的结果与CEEM和数学均匀化法（MHM）的结果进行了比较，首次揭示了MHM的物理解释。结果表明，MEM是最精确的特征元，SEEM比CEEM更精确，MEM满足两个基本的均匀化条件：应变能等效和变形相似。对应力、位移和频率进行了广泛的数值比较。
Eigenelement method is an eigenvector expansion based finite element method, which was proposed by the authors to solve the macro behaviors of composites with less computational cost. To improve the macroscopic accuracy of the classical eigenelement method (CEEM), a serendipity eigenelement method (SEEM) is proposed, which takes the geometry and elastic properties of different phases of composites into account to some extent. Moreover, the shape function and its construction method of a multiscale eigenelement method (MEM) are presented, and the results of SEEM and MEM are compared with that of CEEM and the mathematical homogenization method (MHM) whose physical interpretation is revealed for the first time. It is shown that MEM is the most accurate eigenelement, SEEM is more accurate than CEEM, and MEM satisfies the two essential homogenization conditions: the strain energy equivalence and the deformation similarity. The extensive numerical comparison is given for stresses, displacements and frequencies.