Summary
A principal value definition of the basic hypersingular integral in the fundamental integral equation for two-dimensional cracks in three-dimensional isotropic elasticity is proposed. As is the case with the corresponding definitions of Cauchy-type one-dimensional and two-dimensional principal value singular integrals, as well as Mangler-type one-dimensional principal value hypersingular integrals, the present definition is based on the special consideration of an appropriate region around the singular point. The cases of circular, square and equilateral triangular regions are considered in some detail.
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References
Muskhelishvili, N. I.: Some basic problems of the mathematical theory of elasticity, 1st english ed. Groningen: P. Noordhoff 1963.
Parton, V. Z., Perlin, P. I.: Mathematical methods of the theory of elasticity, Vol. 1, 1st english ed. Moscow: Mir Publishers 1984.
Ashley, H., Landahl, M.: Aerodynamics of wings and bodies, 1st ed. New York: Dover 1985. (Original edition: Reading, Mass.: Addison-Wesley 1965).
Ioakimidis, N. I.: Application of finite-part integrals to the singular integral equations of crack problems in plane and three-dimensional elasticity. Acta Mechanica45, 31–47 (1982).
Ioakimidis, N. I.: A natural approach to the introduction of finite-part integrals into crack problems of three-dimensional elasticity. Engng. Fracture Mech.16, 669–673 (1982).
Ioakimidis, N. I.: On the boundary integral equation method for the problem of a plane crack inside a three-dimensional elastic medium. Rev. Roumaine Sci. Tech. Sér. Méc. Appl.31, 533 to 538 (1986).
Ioakimidis, N. I.: Application of Betti's reciprocal work theorem to the construction of the hyper-singular integral equation of a plane crack in three-dimensional elasticity. J. Elasticity18, 165–171 (1987).
Ioakimidis, N. I.: Exact expression for a two-dimensional finite-part integral appearing during the numerical solution of crack problems in three-dimensional elasticity. Comm. Appl. Numer. Meth.1, 183–189 (1985).
Ioakimidis, N. I.: Mangler-type principal value integrals in hypersingular integral equations for crack problems in plane elasticity. Engng. Fracture Mech.31, 895–898 (1988).
Kutt, H. R.: On the numerical evaluation of finite-part integrals involving an algebraic singularity. CSIR Special Report WISK 179. Pretoria: National Research Institute for Mathematical Sciences 1975.
Rong, E.-Q.: A new solution for the space crack problem from hypersingular integral equation. Applic. Anal.31, 91–102 (1988).
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Ioakimidis, N.I. Two-dimensional principal value hypersingular integrals for crack problems in three-dimensional elasticity. Acta Mechanica 82, 129–134 (1990). https://doi.org/10.1007/BF01173742
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DOI: https://doi.org/10.1007/BF01173742