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Direct evaluation of singular integrals in elastoplastic analysis by the boundary element method
Author(s) -
Lu Shan,
Ye T. Q.
Publication year - 1991
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.1620320205
Subject(s) - mathematics , singularity , cauchy principal value , singular integral , boundary element method , mathematical analysis , quadratic equation , gaussian quadrature , quadrature (astronomy) , singular boundary method , principal value , cauchy distribution , boundary value problem , polar coordinate system , finite element method , geometry , nyström method , mixed boundary condition , integral equation , physics , cauchy boundary condition , optics , thermodynamics
This paper presents a new method for the direct and accurate evaluation of strongly singular integrals in the sense of Cauchy principal values and weakly singular integrals over quadratic boundary elements in three‐dimensional stress analysis and quadratic internal cells in two‐dimensional elastoplastic analysis by the boundary element method. A quadratic triangle polar co‐ordinate transformation technique is applied to reduce the order of singularity of the singular integrals. Next, a form of Stokes' theorem is introduced in order to remove the singularity in the Cauchy principal value integrals; therefore, the evaluation of these integrals can be carried out by standard Gaussian quadrature. Numerical examples of 2‐D elastoplastic problems and a 3‐D elastic problem show the effectiveness and efficiency of the method.