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首页> 外文期刊>Journal of Elasticity >Mechanical Quadrature Methods and Extrapolation Algorithms for Boundary Integral Equations with Linear Boundary Conditions in Elasticity
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Mechanical Quadrature Methods and Extrapolation Algorithms for Boundary Integral Equations with Linear Boundary Conditions in Elasticity

机译：具有弹性线性边界条件的边界积分方程的机械正交方法和外推算法

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摘要

By potential theory, elastic problems with linear boundary conditions are converted into boundary integral equations (BIEs) with logarithmic and Cauchy singularity. In this paper, a mechanical quadrature method (MQMs) is presented to deal with the logarithmic and the Cauchy singularity simultaneously for solving the boundary integral equations. The convergence and stability are proved based on Anselone’s collective compact and asymptotical compact theory. Furthermore, an asymptotic expansion with odd powers of errors is presented, which possesses high accuracy order O(h 3). Using h 3−Richardson extrapolation algorithms (EAs), the accuracy order of the approximation can be greatly improved to O(h 5), and an a posteriori error estimate can be obtained for constructing a self-adaptive algorithm. The efficiency of the algorithm is illustrated by examples.
机译：通过势能理论，将具有线性边界条件的弹性问题转换为具有对数和柯西奇异性的边界积分方程（BIE）。本文提出了一种机械正交方法（MQMs）来同时处理对数和柯西奇异性，以解决边界积分方程。基于Anselone的集体紧致和渐近紧致理论证明了收敛性和稳定性。此外，提出了具有奇数次幂误差的渐近展开式，它具有高精度的阶数O（h 3 ）。使用h 3 -Richardson外推算法（EAs），可以将近似的精度阶数提高到O（h 5 ），并且可以得到后验误差估计以构造自自适应算法。实例说明了该算法的效率。

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  • 来源
    《Journal of Elasticity》 |2012年第2期|p.193-207|共15页
  • 作者

    Pan Cheng; Xin Luo; Zhu Wang; Jin Huang;

  • 作者单位

    School of Science, Chongqing Jiaotong University, Chongqing, 400074, P.R. China;

    School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, P.R. China;

    School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, P.R. China;

    School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, P.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

    Mechanical quadrature method; Asymptotic expansion; Extrapolation algorithm; A posteriori error estimate; Elasticity; 65N25; 65N38;

    机译：机械正交法渐近展开外推算法后验误差估计弹性65N25 65N38;

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