Qin Tai-yan, Tang Ren-ji. Finite-Part Integral and Boundary Element Method to Solve Flat Crack Problems[J]. Applied Mathematics and Mechanics, 1992, 13(12): 1045-1051.
 Citation: Qin Tai-yan, Tang Ren-ji. Finite-Part Integral and Boundary Element Method to Solve Flat Crack Problems[J]. Applied Mathematics and Mechanics, 1992, 13(12): 1045-1051.

# Finite-Part Integral and Boundary Element Method to Solve Flat Crack Problems

• Publish Date: 1992-12-15
• Using the Somigliana formula and the concepts of finite-part integral,a set of hypersingular integral equations to solve the arbitrary flat crack in three-dimensional elasticity is derived and its numerical method is then proposed by combining the finite-part integral method with boundary element method.In order to verify the method,several numerical examples are carried out.The results of the displacement discontinuities of the crack surface and the stress intensity factors at the crack front are in good agrement with the theoretical solutions.
•  [1] Ioakimidis,N.I.,Application of finite-part integrals to the singular integral equations of crack problems in plane and three-dimensional elasticity,Acta Mechanica,45(1982),31-47. [2] Bui,H.D.,An integral equations method for solving the problems of a plane crack of arbitrary shape,J.Mech.Phys.Solids,25(1977),29. [3] Weaver,J.,Three-dimensional crack analysis,Internat.J.Solids and Structures,13(1977),321. [4] Ioakimidis,N.I.,Remarks on the Gaussian quadrature rule for finite-part integrals with a second order singularity,Comput.Metheds.Appl.Mech.Engrg.,69(1988),325. [5] Tsamasphyros,G.and G.Dimou,Gauss quadrature rule for finite part integrals,Internat.J.Numer.Methods.Engrg.,30(1990),13-26. [6] Kaya,A.C.and F.Erdogan,On the solution of singular integral equations with strongly singular kernels,Quart.Appl.Math.,415,1(1987),105. [7] Sohn,G.H.and C.S.Hong,Application of singular integral equations to embedded planar crack problems in finite body,Boundary Element,C.A.Brebbia and G.Maier,Ed.,2(1985),8-57. [8] 汤任基,断裂力学中的两类奇异积分方程,上海交通大学学报,24(5-6)(1990),36. [9] Kutt,H.R.,The numerical evaluation of principal value integrals by finite-part integration,Numer.Math.,24(1975),205. [10] Zienkiewicz,O.C.,The Finite Element in Engineering Science,McGraw-Hill(1971). [11] Sneddon,I.N.and M.Lowengrub,Crack Problems in the Classical Theory of Elasticity,New York(1969).

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