The treatment of singularities in the calculation of stress intensity factors using the boundary integral equation method

Xanthis, Leonidas S.; Bernal, M. J. M.; Atkinson, C.

doi:10.1016/0045-7825(81)90118-3

Cited by 54 publications

(12 citation statements)

References 9 publications

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“…To take into account the form of the singularity more e ectively and achieve better accuracy and faster convergence, special methods are often required which incorporate the form of the singularity in the numerical scheme, which is, in general, more e ective than mesh reÿnement (see References [2][3][4] and references therein). We should also add here the early works of Symm [5] Papamichael and Symm [6] and Xanthis et al [7] who developed singular boundary integral methods. Two notable alternatives to singular methods are the hp version of the ÿnite element method with geometrically graded meshes [8; 9], and a recently proposed multigrid ÿnite element method on quasi-uniform meshes [10].…”

Section: Introductionmentioning

confidence: 97%

The solution of Laplacian problems over L‐shaped domains with a singular function boundary integral method

Elliotis¹,

Georgiou²,

Xenophontos³

2002

Commun. Numer. Meth. Engng.

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SUMMARYThe singular function boundary integral method is applied for the solution of a Laplace equation problem over an L-shaped domain. The solution is approximated by the leading terms of the local asymptotic solution expansion, while the Dirichlet boundary conditions are weakly enforced by means of Lagrange multipliers. Estimates of great accuracy are obtained for the leading singular coe cients, as well as for the Lagrange multipliers. Comparisons are made with recent numerical results in the literature.

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Section: Introductionmentioning

confidence: 97%

The solution of Laplacian problems over L‐shaped domains with a singular function boundary integral method

Elliotis¹,

Georgiou²,

Xenophontos³

2002

Commun. Numer. Meth. Engng.

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“…Engng, 14, 289±304 (1998) without calculating the other coecients in the polynomial approximation (13). To compare our enhancement procedure to one of those existing in the literature, namely Aitken's d 2 technique used successfully in the SIF determination by Sinclair et al 24 or Xanthis et al, 22 we summarize it in the present Section. Aitken's d 2 technique consists in assuming that the SIF in mode J is related to grid size h by the following expression: where c and a are arbitrary constants and J belongs to {I, II, III}.…”

Section: Stress Intensity Factors Determination By Richardson's Extramentioning

confidence: 97%

“…18 Our technique derives from the new approach, using the PII, studied in References 19 and 20. For antiplane problems, we use one of the PII introduced by Eshelby and Knowles 21,22 and for plane problems we base our technique on that exhibited by Stern et al in Reference 13 to distinguish contributions due to crack opening and those due to shear in the mixed mode.…”

Section: Introductionmentioning

confidence: 99%

Improvement of stress intensity factors computed from path‐independent integrals by Richardson's extrapolation

Kpegba

Ottavy

Souchet

1998

Commun. Numer. Meth. Engng.

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SUMMARYA new method for improving the approximations of stress intensity factors computed from pathindependent integrals is developed. The method uses Richardson's extrapolation. Numerical results are given to show the eciency and the stability of the present method. # 1998 John Wiley & Sons, Ltd.KEY WORDS stress intensity factors (SIF); ®nite element method (FEM); reciprocal work contour integral (RWCI); path-independent integrals (PII); displacement correlation technique (DCT); quarter-point displacement technique (QPDT)

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“…In Table 2 we compare the results computed by using formula (34) with results obtained by several other methods [18,27,37].…”

Section: The Motz' Anti-plane Crack Problemmentioning

confidence: 99%

COMPUTATION of generalized stress intensity factors for bonded elastic structures

Bochniak

Sändig

1999

ESAIM: M2AN

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Abstract. We consider coupled structures consisting of two different linear elastic materials bonded along an interface. The material discontinuities combined with geometrical peculiarities of the outer boundary lead to unbounded stresses. The mathematical analysis of the singular behaviour of the elastic fields, especially near points where the interface meets the outer boundary, can be performed by means of asymptotic expansions with respect to the distance from the geometrical and structural singularities. The coefficients in the asymptotics, which are called generalized stress intensity factors, play an important role in classical fracture criteria. In this paper we present several formulas for the generalized stress intensity factors for 2D and 3D coupled elastic structures. The formulas have the form of scalar products or convolution integrals of the given data or the unknown displacement field and the so-called weight functions, similar to Maz'ya/Plamenevsky functionals introduced in [19] for elliptic boundary value problems. The weight functions are non-energetic elastic fields, which admit a decomposition into a known singular part and a more regular one, which is computed by boundary element domain decomposition methods. Numerical experiments for two-dimensional problems illustrate the theoretical results.

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The treatment of singularities in the calculation of stress intensity factors using the boundary integral equation method

Cited by 54 publications

References 9 publications

The solution of Laplacian problems over L‐shaped domains with a singular function boundary integral method

The solution of Laplacian problems over L‐shaped domains with a singular function boundary integral method

Improvement of stress intensity factors computed from path‐independent integrals by Richardson's extrapolation

COMPUTATION of generalized stress intensity factors for bonded elastic structures

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