On a new integration rule with the Gegenbauer polynomials for singular integral equations used in the theory of elasticity

Ladopoulos, E. G.

doi:10.1007/bf00537198

Cited by 21 publications

(10 citation statements)

References 23 publications

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“…In The present numerical results agree with those given by Isida and Noguchi [7], and these also agree approximately with those given by Higasida and Kamada [2]. However, the values given by Ladopoulos [4] for h/a = 0.4 completely agree with those given by Erdogan [3]. For smaller values of h/a less than 0.1, we could not succeed when using the Schmidt method to satisfy (13), and then, the values of KI and Kn are not obtained.…”

Section: Numerical Examples and Resultssupporting

confidence: 81%

“…Recently, Ladopoulos has proposed a new technique for the numerical solution of Cauchytype singular integral equations [4], and has applied this method to the above problem treated in [3] and [2]. The numerical results for the stress intensity factors given by Ladopoulos are identical with Erdogan's.…”

Section: Introductionsupporting

confidence: 67%

“…As the h/a ratio decreases, it can be said that the boundary conditions inside the crack fail to be satisfied. For this reason, there may appear a disagreement between the values of the present numerical calculations and those given by Erdogan [3] and Ladopoulos [4].…”

Section: Numerical Examples and Resultscontrasting

confidence: 46%

“…[3] Ref. [4] 0 Tables 3 and 4. With use of the body force method, Isida and Noguchi solved the stress intensity factors for a crack placed arbitrarily in bonded dissimilar half-planes [7].…”

Section: Numerical Examples and Resultsmentioning

confidence: 99%

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Stress intensity factors around a crack parallel to a free surface of a half-plane

Itou

1994

Int J Fract

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In this paper, stress intensity factors for a crack in a half-plane are considered. The crack is parallel to the stress-free surface of the half-plane and subjected to internal gas pressure. By using Fourier transforms, the mixed boundary value problem is reduced to the solution of a pair of dual integral equations. To solve the equations, the crack surface displacements are expanded in a series of functions which are zero outside the crack. The unknown coefficients in that series are solved with the aid of the Schmidt method. The stress intensity factors are calculated numerically and the results are compared with those given in other papers.

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Section: Numerical Examples and Resultssupporting

confidence: 81%

Section: Introductionsupporting

confidence: 67%

Section: Numerical Examples and Resultscontrasting

confidence: 46%

Section: Numerical Examples and Resultsmentioning

confidence: 99%

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Stress intensity factors around a crack parallel to a free surface of a half-plane

Itou

1994

Int J Fract

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“…The problem of determining the stress distribution in the neighborhood of a crack parallel to the surface of a semi-infinite medium has been studied for tensile, compressive or concentrated force loadings [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. For a brief review, see [7].…”

Section: Introductionmentioning

confidence: 99%

Finite element analysis of a subsurface crack

Yang

Qian

1996

Int J Fract

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The problem of a subsurface crack parallel to the surface of a half space was studied by the finite element method. Without using the interface or gap elements over the crack faces, the crack faces would penetrate into each other for the traction-free boundary condition under shear loading, which is physically impossible. Using the gap elements, this problem was avoided, and a contact zone was observed near one crack tip. The size of the contact zone decreases but the maximum contact pressure at the closed crack tip increases as the crack approaches the surface. For tensile and shear loadings, both KI (mode I stress intensity factor) and KII (mode II stress intensity factor) increase as the crack approaches the surface. For shear loading there is no KI at the closed tip and the K~ and KIt at the open tip are comparable as the crack approaches the surface.

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Derivation of a new analytical solution for a general two‐dimensional finite‐part integral applicable in fracture mechanics

Mayrhofer

Fischer

1992

Numerical Meth Engineering

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An exact expression is derived for the general finite-part integral f a r -3 f dR over an inclined elliptical domain R. r denotes the distance of a point in R to the singular point (x, y).f= x b y i ,/Z(xo, yo) is a general function of the Cartesian co-ordinates xo,yo. The boundary of the region R represents the equation Z ( x o , y o ) = 0. These integrals appear during the numerical solution of plane crack problems in threedimensional elasticity where they are the dominant part of a hypersingular integral equation. The availability of exact expressions for the integrals with arbitrary integers i and j will increase the accuracy of the numerical results and, simultaneously, lead to quicker numerical results. The considered finite-part integral can be expressed in closed form as function of complete elliptical integrals or Gauss hypergeometric functions, respectively. Formulas for special cases and some i, j values and their numerical verification are given in Appendices I1 and 111. a/b 1 1 O.llOD+Ol 0.220D+Ol 0.3OOD+OO 0.400D+00 0.000D+00 0,50OD+00 Eq. (47) : a*Ell = -O.l7345678433062D+Ol Eq. (46) : a*EWll = -O.l7345678433062D+Ol Eq. (37) : a*E(i= l,j= 1) = -O.l7345678433062D+Ol Eq. (36) : a*EW(i= l,j= 1) = -O.l7345678433062D+Ol Eq. (27) : a*EW(i= l,j= 1) = -O.l7345678433062D+Ol Eq.(40): N = 2 a*EW(i= l,j= 1) = -O.l7345678433062D+Ol Eqs. (17,441:

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On a new integration rule with the Gegenbauer polynomials for singular integral equations used in the theory of elasticity

Cited by 21 publications

References 23 publications

Stress intensity factors around a crack parallel to a free surface of a half-plane

Stress intensity factors around a crack parallel to a free surface of a half-plane

Finite element analysis of a subsurface crack

Derivation of a new analytical solution for a general two‐dimensional finite‐part integral applicable in fracture mechanics

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