Complex variable formulations for usual and hypersingular integral equations for potential problems???with applications to corners and cracks

Kolhe, R.; Ye, W.; Hui, Chung‐Yuen; Mukherjee, Sayandev

doi:10.1007/s004660050111

Cited by 4 publications

(9 citation statements)

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“…Note that the notations of f(t), g(t), h(t), F(z), G(z) and Hðz; zÞ used in Eqs. (10)- (12) have no relation with those mentioned in other places.…”

Section: Some Preliminary Knowledge In Complex Variable Methods Of Placontrasting

confidence: 61%

“…(31), letting t-t o (tAS + , t o AB ) and using the generalized Sokhotski-Plemelj formulae shown by Eqs. (10)- (12) and some results in Appendix B, yields…”

Section: Formulation Of Bie Using Real Variable or Complex Variablementioning

confidence: 94%

“…However, the property is obtained in a more explicit way in this paper, by using the generalized Sokhotski-Plemelj formulae shown by Eqs. (10)- (12) and some results in Appendix B. It is easy to prove that the complex BIE shown by (34) is equivalent to its counterpart in a real variable form shown by Eq.…”

Section: Formulation Of Bie Using Real Variable or Complex Variablementioning

confidence: 96%

“…Some researchers formulated the direct and indirect BIEs using complex variable [12][13][14][15][16][17]. Some researchers derived the complex BIE using the holomorphity theorem [16].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Formulation of indirect BIEs in plane elasticity using single or double layer potentials and complex variable

Chen

Lin

Wang

2010

Engineering Analysis with Boundary Elements

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“…Note that the notations of f(t), g(t), h(t), F(z), G(z) and Hðz; zÞ used in Eqs. (10)- (12) have no relation with those mentioned in other places.…”

Section: Some Preliminary Knowledge In Complex Variable Methods Of Placontrasting

confidence: 61%

“…(31), letting t-t o (tAS + , t o AB ) and using the generalized Sokhotski-Plemelj formulae shown by Eqs. (10)- (12) and some results in Appendix B, yields…”

Section: Formulation Of Bie Using Real Variable or Complex Variablementioning

confidence: 94%

Section: Formulation Of Bie Using Real Variable or Complex Variablementioning

confidence: 96%

“…Some researchers formulated the direct and indirect BIEs using complex variable [12][13][14][15][16][17]. Some researchers derived the complex BIE using the holomorphity theorem [16].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Formulation of indirect BIEs in plane elasticity using single or double layer potentials and complex variable

Chen

Lin

Wang

2010

Engineering Analysis with Boundary Elements

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“…Some relevant formulations based on complex variables can be referred to [11][12][13][14][15][16][17]. The suggested BIE is more straightforward, since all involved arguments are expressed in an explicit form.…”

Section: Complex Variable Boundary Integral Equations For Interior Rementioning

confidence: 99%

Numerical solution of elastic inclusion problem using complex variable boundary integral equation

Chen

2011

Acta Mech

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Based on a complex variable boundary integral equation (CVBIE) suggested previously, this paper provides a numerical solution for the elastic inclusion problem using CVBIE. A dissimilar elastic inclusion is embedded in the infinite matrix. The original problem is decomposed into two problems. One is an interior boundary value problem (BVP) for the elastic inclusion, while the other is an exterior BVP for the matrix with notch. Both problems are connected by conventional boundary integral equations (BIEs) in complex variables. After performing discretization for the coupled BIEs, the inverse matrix technique is suggested to solve the relevant algebraic equations. Based on the properties of some integral operators, three ways for the inverse matrix technique are suggested. Several numerical examples are carried out to prove the efficiency of the suggested method.

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A complex‐variable boundary element approach to fully developed flow and heat transfer in ducts of general cross‐section

Fisher

Torrance

1999

Int. J. Numer. Meth. Engng.

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SUMMARYThe complex-variable boundary element method (CVBEM) is used to analyse forced convection in cooling passages with general, convex cross-sections. Quadratic spline interpolation is employed for the modelling of coupled velocity and temperature ÿelds. The method is well-suited for ducts with curved surfaces and high geometric aspect ratios. The method is illustrated for ducts with rounded rectangular, elliptical and rounded diamond cross-sections. General correlations are presented for the fully developed Nusselt number and Moody friction factor, and the Hagenbach entrance region factor.

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Complex variable formulations for usual and hypersingular integral equations for potential problems???with applications to corners and cracks

Cited by 4 publications

References 0 publications

Formulation of indirect BIEs in plane elasticity using single or double layer potentials and complex variable

Formulation of indirect BIEs in plane elasticity using single or double layer potentials and complex variable

Numerical solution of elastic inclusion problem using complex variable boundary integral equation

A complex‐variable boundary element approach to fully developed flow and heat transfer in ducts of general cross‐section

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