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Generalization of the multi-scale finite element method to plane elasticity problems

机译：多尺度有限元方法对平面弹性问题的推广

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摘要

In this paper, according to the governing differential equations of problem, the theory to construct the shape functions in the multi-scale finite element method is established for plane elasticity problems. An approach is then suggested to numerically solve the shape functions via the corresponding homogeneous governing equations on an element level. The linear, quadratic and cubic shape functions are finally obtained by prescribing the appropriate boundary conditions. Typical numerical experiments are conducted, including bending of a homogeneous beam, bending of a beam with voids, as well as bending of a beam with a random material distribution and with an oscillatory material property. The current work shows that the multi-scale finite element method has a prominent advantage in solution efficiency even for classic problems, and therefore can be implemented on a considerably coarse mesh for problems with complex microstructures, as well as for large scale problems to effectively save the solution cost.
机译：本文根据控制问题的微分方程，建立了平面弹性问题多尺度有限元方法中构造形状函数的理论。然后建议一种方法，通过元素级别上的相应齐次控制方程对形状函数进行数值求解。通过规定适当的边界条件，最终获得线性，二次和三次形状函数。进行了典型的数值实验，包括均匀光束的弯曲，带有空隙的光束的弯曲以及具有随机材料分布和具有振荡材料特性的光束的弯曲。当前工作表明，即使对于经典问题，多尺度有限元方法在求解效率上也具有显着优势，因此可以在相当粗糙的网格上实现，以解决复杂的微观结构问题以及大规模问题，从而有效地节省成本。解决方案成本。

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  • 来源
    《Applied Mathematical Modelling》 |2015年第2期|642-653|共12页
  • 作者

    L.X. Li; Y.L. Chen; Z.C. Lu;

  • 作者单位

    State Key Laboratory for Strength and Vibration of Mechanical Structures, Department of Engineering Mechanics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, PR China;

    State Key Laboratory for Strength and Vibration of Mechanical Structures, Department of Engineering Mechanics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, PR China;

    State Key Laboratory for Strength and Vibration of Mechanical Structures, Department of Engineering Mechanics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, PR 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

    Plane elasticity; Multi-scale finite element method (MsFEM); Shape functions; Accuracy and efficiency;

    机译：平面弹性;多尺度有限元方法（MsFEM）;形状函数;准确性和效率;

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