Progress in the use of boundary integral equations, illustrated by examples

Lachat, Jacob; Watson, J. O.

doi:10.1016/0045-7825(77)90073-1

Cited by 79 publications

(5 citation statements)

References 6 publications

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“…The details of this procedure [26][27][28] are summarised here for later reference. The details of this procedure [26][27][28] are summarised here for later reference.…”

Section: Review Of the Bie Methodsmentioning

confidence: 99%

Stress intensity factors for semi-elliptical surface cracks in pressurised cylinders using the boundary integral equation method

Tan

Fenner

1980

Int J Fract

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Three dimensional linear elastic fracture mechanics analyses of the problem of an internally pressurised thick-walled cylinder with a semi-elliptical surface crack are carried out using the Boundary Integral Equation method. The cases treated are for ratios of external to internal cylinder radii of 2 and 3, with maximum crack depths ranging from 20% to 80% of the wall thickness. For a typical crack, the predicted value of stress intensity factor decreases slightly along the crack front moving away from the point of deepest penetration, reaching a minimum before increasing rapidly as the free internal surface of the cylinder is approached. The results, presented will be of considerable use in the prediction of residual or safe life of, for example, chemical reactor tubes known to be cracked to a certain depth.

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“…The details of this procedure [26][27][28] are summarised here for later reference. The details of this procedure [26][27][28] are summarised here for later reference.…”

Section: Review Of the Bie Methodsmentioning

confidence: 99%

Stress intensity factors for semi-elliptical surface cracks in pressurised cylinders using the boundary integral equation method

Tan

Fenner

1980

Int J Fract

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“…It should be mentioned that the elastic domain may also be divided into several sub-regions if required [9], such as when treating problems made up of, piecewise, several different materials, or when treating crack problems using the multi-region modelling approach [15], [18]- [21]. Equations (10) and (21) may then be written for each of the subregions in turn, with the appropriate displacement and traction compatibility conditions applied at the common subregion boundaries. Equation (21), or the modified form for multi-regions, represents a set of linear algebraic equations for the unknown nodal values of displacements and tractions at the boundary S of the numerical solution domain.…”

Section: A22mentioning

confidence: 99%

“…Normalised stress intensity factors, K* = K~/ao~L, for an edge crack in a long orthotropic strip with IlL =0 10. …”

mentioning

confidence: 99%

Boundary integral equation fracture mechanics analysis of plane orthotropic bodies

Tan

Gao

1992

Int J Fract

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In this paper, a quick and efficient means of determining stress intensity factors, K~ and Kn, for cracks in generally orthotropic elastic bodies is presented using the numerical boundary integral equation (BIE) method. It is based on the use of quarter-point singular crack-tip elements in the quadratic isoparametric element formulation, similar to those commonly employed in the BIE fracture mechanics studies in isotropic elasticity. Analytical expressions which enable K~ and K u to be obtained directly from the BIE computed crack-tip nodal traction, or from the computed nodal displacements, of these elements are derived. Numerical results for a number of test problems are compared with those established in the literature. They are accurate even when only a very modest number of boundary elements are used.

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“…The method was generalized to elastodynamic analysis by Cruse and Rizzo [10,11]. Its significant advances in elastostatics applications were made by Lachat and Watson [12][13][14]. Rizzo & Shippy [15] developed the first BEM procedure and presented numerical results for three-dimensional linear homogeneous isotropic and steady-state thermoelasticity.…”

Section: Introductionmentioning

confidence: 99%

Boundary integral equation formulation for coupled thermoelasticity with three phase-lags

Prasad

Das

Mukhopadhyay

2012

Mathematics and Mechanics of Solids

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The present paper is aimed at formulating the boundary integral equations for the solution of equations in three-dimensional Euclidian space under coupled thermoelasticity with three phase-lags. We consider the initial mixed boundary value problem in the present context and obtain the fundamental solutions of corresponding differential equations in the Laplace transform domain by employing the treatment of scalar and vector potential theory. On the basis of these fundamental solutions we formulate the boundary integral equations by using a reciprocal relation of Betti type for coupled thermoelasticity with three phase-lags. The implementation of the boundary element method is also outlined for the solution of the derived boundary equations with an example.

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Progress in the use of boundary integral equations, illustrated by examples

Cited by 79 publications

References 6 publications

Stress intensity factors for semi-elliptical surface cracks in pressurised cylinders using the boundary integral equation method

Stress intensity factors for semi-elliptical surface cracks in pressurised cylinders using the boundary integral equation method

Boundary integral equation fracture mechanics analysis of plane orthotropic bodies

Boundary integral equation formulation for coupled thermoelasticity with three phase-lags

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