A general algorithm for the numerical evaluation of nearly singular boundary integrals of various orders for two- and three-dimensional elasticity |
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Authors: | H Ma N Kamiya |
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Affiliation: | (1) Department of Mechanics, Shanghai Institute of Applied Mathematics and Mechanics, School of Sciences, Shanghai University, Shanghai 200436, PR China e-mail: hma@mail.shu.edu.cn, CN;(2) School of Informatics and Sciences, Nagoya University, 464-8601 Nagoya, Japan, JP |
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Abstract: | A general algorithm of the distance transformation type is presented in this paper for the accurate numerical evaluation
of nearly singular boundary integrals encountered in elasticity, which, next to the singular ones, has long been an issue
of major concern in computational mechanics with boundary element methods. The distance transformation is realized by making
use of the distance functions, defined in the local intrinsic coordinate systems, which plays the role of damping-out the
near singularity of integrands resulting from the very small distance between the source and the integration points. By taking
advantage of the divergence-free property of the integrals with the nearly hypersingular kernels in the 3D case, a technique
of geometric conversion over the auxiliary cone surfaces of the boundary element is designed, which is suitable also for the
numerical evaluation of the hypersingular boundary integrals. The effects of the distance transformations are studied and
compared numerically for different orders in the 2D case and in the different local systems in the 3D case using quadratic
boundary elements. It is shown that the proposed algorithm works very well, by using standard Gaussian quadrature formulae,
for both the 2D and 3D elastic problems.
Received: 20 November 2001 / Accepted: 4 June 2002
The work was supported by the Science Foundation of Shanghai Municipal Commission of Education. |
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Keywords: | Boundary element method Nearly singular integrals Elasticity Distance transformation Numerical integration |
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