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首页> 外文期刊>International Journal for Multiscale Computational Engineering >EXTENDED MULTISCALE FINITE ELEMENT METHOD FOR MECHANICAL ANALYSIS OF PERIODIC LATTICE TRUSS MATERIALS
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EXTENDED MULTISCALE FINITE ELEMENT METHOD FOR MECHANICAL ANALYSIS OF PERIODIC LATTICE TRUSS MATERIALS

机译：周期性格子桁架材料力学分析的扩展多尺度有限元法。

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摘要

An extended multiscale finite element method (EMsFEM) is developed to study the equivalent mechanical properties of periodic lattice truss materials. The underlying idea is to construct the numerical multiscale base functions to reflect the heterogeneity of the unit cell of periodic truss materials. To consider the coupled effect among different directions in the multidimensional problems, the coupled additional terms of base functions for the interpolation of the vector fields are introduced. Numerical results show that the base functions constructed by linear boundary conditions will induce nonequilibrium of the boundary nodal forces and thus lead to a strong scale effect of the unit cell in the multiscale computation. Thus, more reasonable oscillatory boundary conditions are introduced by using the oversampling technique in the construction of the multiscale base functions of the unit cell. A special algorithm is introduced to improve the properties of the equivalent stiffness matrix of the unit cell to make the numerical results more accurate. The advantage of the developed method is that the downscaling computation could be realized easily and the stress and strain in the unit cell can be obtained simultaneously in the multiscale computation. Therefore, the developed method has great potential for strength analysis of heterogeneous materials.
机译：为了研究周期性晶格桁架材料的等效力学性能，开发了一种扩展的多尺度有限元方法（EMsFEM）。基本思想是构造数值多尺度基函数，以反映周期性桁架材料的晶胞的异质性。为了考虑多维问题中不同方向之间的耦合效应，引入了用于矢量场插值的基本函数的耦合附加项。数值结果表明，由线性边界条件构造的基函数将引起边界节点力的不平衡，从而在多尺度计算中引起单位单元的强尺度效应。因此，在构造晶胞的多尺度基函数时，通过使用过采样技术引入了更合理的振荡边界条件。引入了一种特殊的算法来改善单位单元的等效刚度矩阵的属性，以使数值结果更加准确。该方法的优点是可以容易地实现按比例缩小计算，并且在多尺度计算中可以同时获得晶胞中的应力和应变。因此，所开发的方法对于异质材料的强度分析具有很大的潜力。

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  • 作者

    H. W. Zhang; J. K. Wu; Z. D. Fu;

  • 作者单位

    State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineer- ing Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, China;

    rnState Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineer- ing Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, China;

    rnState Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineer- ing Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, China;

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  • 正文语种 eng
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  • 关键词

    multiscale finite element method; truss material; homogenization method; downscaling computation; base function;

    机译：多尺度有限元法桁架材料均质化方法缩减计算;基本功能;

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