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首页> 外文期刊>Engineering analysis with boundary elements >A new dual reciprocity hybrid boundary node method based on Shepard and Taylor interpolation method and Chebyshev polynomials
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A new dual reciprocity hybrid boundary node method based on Shepard and Taylor interpolation method and Chebyshev polynomials

机译：基于Shepard和Taylor插值方法以及Chebyshev多项式的新的双互易混合边界节点方法

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摘要

A new dual reciprocity hybrid boundary node method (DHBNM) is proposed in this paper, in which the Shepard and Taylor interpolation method (STIM) and Chebyshev polynomials interpolation are proposed. Firstly, the Shepard interpolation is used to construct zero level shape function, and the high-power shape functions are constructed through the Taylor expansion, and through those two methods, no inversion is needed in the whole process of the shape function construction. Besides, Chebyshev polynomials are used as the basis functions for particular solution interpolation instead of the conical function, radial basis functions, and the analytical solutions of the basic form of particular solutions related to Chebyshev polynomials for elasticity are obtained, by means of this method, no internal node is needed, and interpolation coefficients can be given as explicit functions, so no inversion is needed for particular solution interpolation, which costs a large amount of computational expense for the traditional method. Based on those two methods, a new dual reciprocity hybrid boundary node method is developed, compared to the traditional DHBNM, no inversion is needed for both shape function construction and particular solution interpolation, which greatly improves the computational efficiency, and no internal node is needed for particular solution interpolation. Numerical examples are given to illustrate that the present method is accurate and effective.
机译：提出了一种新的对等混合边界节点方法（DHBNM），提出了Shepard和Taylor插值方法（STIM）以及Chebyshev多项式插值方法。首先，使用Shepard插值构造零级形状函数，通过泰勒展开构造高功率形状函数，通过这两种方法，在形状函数构造的整个过程中不需要求逆。此外，将切比雪夫多项式用作特定解插值的基础函数，而不是圆锥函数，径向基函数，并通过此方法获得与切比雪夫多项式有关的弹性的特定解的基本形式的解析解，不需要内部节点，并且可以将插值系数作为显式函数给出，因此对于特定的解决方案插值不需要进行求逆，这为传统方法带来了大量的计算费用。在这两种方法的基础上，开发了一种新的双互易混合边界节点方法，与传统的DHBNM相比，形状函数构造和特定解插值均不需要反演，大大提高了计算效率，并且不需要内部节点用于特定的解决方案插值。数值例子说明了该方法的准确性和有效性。

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  • 来源
    《Engineering analysis with boundary elements》 |2016年第12期|61-68|共8页
  • 作者

    Fei Yan; Xia-Ting Feng; Jia-He Lv; Peng-Zhi Pan; Shao-Jun Li;

  • 作者单位

    State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China;

    State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China;

    State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China;

    State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China;

    State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, 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

    Meshless method; Shepard and Taylor interpolation method; Dual reciprocity hybrid boundary node method; Dual reciprocity method; Chebyshev polynomials;

    机译：无网格方法;Shepard和Taylor插值法;双互易混合边界节点方法;双重互惠法;切比雪夫多项式;

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