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A method for direct evaluation of singular integral in direct boundary element method
Author(s) -
Liao Heshan,
Xu Zhixin
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620350706
Subject(s) - cauchy principal value , mathematics , singular integral , principal value , mathematical analysis , cauchy distribution , cauchy's integral formula , singular boundary method , boundary element method , quadrature (astronomy) , gaussian quadrature , transformation (genetics) , boundary value problem , integral equation , nyström method , finite element method , cauchy problem , mixed boundary condition , initial value problem , cauchy boundary condition , physics , biochemistry , chemistry , gene , optics , thermodynamics
A new method is presented for evaluating the Cauchy principal value integral and the free term in the three‐dimensional elastic boundary element method. This method expresses the singular integral as the sum of a weakly singular integral and an integrable Cauchy principal value integral. The former can be computed by means of the usual standard Gaussian quadrature after a transformation suggested by Lachat and Watson, 10 who correctly limited its use only to weakly singular integral. The latter can be calculated by direct integration in the Cauchy principal value sense. This paper also points out some limitations in the use of triangle polar co‐ordinate suggested by Li et al . 11 and later extended by Zhang and Xu. 16 The general expression of the free term for a boundary point with arbitrary characteristic surface is also presented. Simple numerical examples which verify the efficiency and accuracy of the present method are given.