×

zbMATH — the first resource for mathematics

The use of simple solutions in the regularization of hypersingular boundary integral equations. (English) Zbl 0728.73081
This paper presents the regularization of hypersingular integral equations which are derived from the strongly singular integral representation of the normal derivative of the potential field by approaching the internal point to the boundary and interpreting the strongly singular integrals in the sense of Hadamard finite part. The elimination of the strongly singular integrals is based on the superposition of the potential field considered and the linearly distributed field. Nonconforming linear elements are employed for the numerical implementation. The method can be extended also to elasticity problems. No confrontation is made with another known regularization technique leaving direct evaluation of the strong singularities, too.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
65R20 Numerical methods for integral equations
45E05 Integral equations with kernels of Cauchy type
74R99 Fracture and damage
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ioakimidis, N.I., A natural approach to the introduction of finite-part integrals into crack problems of three-dimensional elasticity, Engineering fracture mechanics, 16, 5, 669-673, (1982)
[2] Mangler, K.W., Improper integrals in theoretical aerodynamics, Royal aircraft establishment, ministry of supply, aeronautical research council, (1952), London, Current Papers No. 94
[3] Kaya, A.C.; Erdogan, F., On the solution of equations with strongly singular integrals, Quarterly of applied mathematics, XLV, 1, 105-122, (1987) · Zbl 0631.65139
[4] Brandao, M.P., Improper integrals in theoretical aerodynamics: the problem revisited, AIAA journal, 25, 9, 1258-1260, (1987)
[5] Rudolphi, T.J.; Krishnasamy, G.; Schmerr, L.W.; Rizzo, F.J., On the use of strongly singular integral equations for crack problems, (), 249-263 · Zbl 0729.73251
[6] G. Krishnasamy, L.W. Schmerr, T.J. Rudolpi and F.J. Rizzo, Hypersingular boundary integral equations: some applications in acoustics and elastic wave scattering, submitted to Journal of Applied Mechanics. · Zbl 0729.73251
[7] P.A. Martin, F.J. Rizzo and I.R. Gonsalves, On hypersingular boundary integral equations for certain problems in mechanics, Mechanics Research Communications (to appear). · Zbl 0687.76081
[8] Hadamard, J., Lectures on Cauchy’s problem in linear partial differential equations, (1952), Dover Publications · Zbl 0049.34805
[9] Forsythe, G.E.; Malcolm, M.A.; Moler, C.B., Computer methods for mathematical computation, (1977), Prentice Hall · Zbl 0361.65002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.