Integration of singular Galerkin-type boundary element integrals for 3D elasticity problems |
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Authors: | H Andrä E Schnack |
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Institution: | (1) Institute of Solid Mechanics, Karlsruhe University, P. O. Box 6980, D-76128 Karlsruhe, Germany; heiko@imfsun2.mach.uni-karlsruhe.de, DE |
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Abstract: | Summary. A Galerkin approximation of both strongly and hypersingular boundary integral equation (BIE) is considered for the solution
of a mixed boundary value problem in 3D elasticity leading to a symmetric system of linear equations. The evaluation of Cauchy
principal values (v. p.) and finite parts (p. f.) of double integrals is one of the most difficult parts within the implementation
of such boundary element methods (BEMs). A new integration method, which is strictly derived for the cases of coincident elements
as well as edge-adjacent and vertex-adjacent elements, leads to explicitly given regular integrand functions which can be
integrated by the standard Gauss-Legendre and Gauss-Jacobi quadrature rules. Problems of a wide range of integral kernels
on curved surfaces can be treated by this integration method. We give estimates of the quadrature errors of the singular four-dimensional
integrals.
Received June 25, 1995 / Revised version received January 29, 1996 |
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Keywords: | Mathematics Subject Classification (1991): 65N38 65D30 65R20 65N30 |
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