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The multiscale eigenelement method in dynamic analyses of periodical composite structures

机译：周期复合结构动力分析中的多尺度特征化方法

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摘要

Multiscale eigenelement method (MEM), which was presented by the author and co-authors, is based on the idea of eigenvector expansion, and the shape functions in MEM bridge the information between macro and micro scales. In previous works, the shape functions in the classical MEM are solved from the self-equilibrium equation of unit cell, while in the improved MEM they are from the self equilibrium equation as well as the eigenvalue problem of clamped unit cell. In this work, MEM is compared with substructure method for static problem, two effective correction terms are suggested to improve accuracy if necessary. Another contribution of the present work is, the dynamic governing differential equation of MEM is derived for periodical composite structures according to the generalized Hamilton variational principle, and the details about efficient and accurate use of mode superposition method and Newmark integration method are presented. The numerical comparisons with the standard FEM using fine meshes are conducted for free and forced vibration analyses of one-dimensional and two-dimensional problems. And it is concluded that the improved MEM is suitable for the analyses of both static and dynamic problems, and the classical MEM is suitable for the static problems, especially the one with correction term. (C) 2017 Elsevier Ltd. All rights reserved.
机译：作者和合著者提出的多尺度本征化方法（MEM）基于本征向量展开的思想，MEM中的形状函数在宏观和微观尺度之间架起了桥梁。在以前的工作中，经典MEM中的形状函数是通过晶胞的自平衡方程求解的，而在改进的MEM中，形状函数是从自平衡方程以及夹紧的晶胞的特征值问题求解的。在这项工作中，将MEM与静态问题的子结构方法进行比较，必要时建议使用两个有效的校正项以提高准确性。本工作的另一个贡献是，根据广义汉密尔顿变分原理推导了周期复合结构的MEM动态控制微分方程，并详细介绍了模式叠加方法和Newmark积分方法的有效和精确使用。与标准FEM使用细网格进行了数值比较，以对一维和二维问题进行自由振动和强制振动分析。得出的结论是，改进的MEM适用于静态和动态问题的分析，经典MEM适用于静态问题，尤其是带有校正项的问题。 （C）2017 Elsevier Ltd.保留所有权利。

著录项

  • 来源
    《Composite Structures》 |2017年第7期|330-338|共9页
  • 作者

    Xing Y. F.; Gao Y. H.; Li M.;

  • 作者单位

    Beihang Univ BUAA, Inst Solid Mech, Beijing 100191, Peoples R China;

    Beihang Univ BUAA, Inst Solid Mech, Beijing 100191, Peoples R China;

    Beihang Univ BUAA, Inst Solid Mech, Beijing 100191, Peoples R China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Periodical composite; Multiscale; Eigenelement; Dynamic analysis;

    机译：期刊复合;多尺度;本征化;动态分析;

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