A remark on the numerical solution of singular integral equations and the determination of stress-intensity factors

Theocaris, PS; Ioakimidis, NI

dc.contributor.author	Theocaris, PS	en
dc.contributor.author	Ioakimidis, NI	en
dc.date.accessioned	2014-03-01T01:05:44Z
dc.date.available	2014-03-01T01:05:44Z
dc.date.issued	1979	en
dc.identifier.issn	00220833	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/8949
dc.subject	Hermite Interpolation	en
dc.subject	Integral Equation	en
dc.subject	lagrange interpolation	en
dc.subject	Linear Equations	en
dc.subject	Numerical Integration	en
dc.subject	Numerical Solution	en
dc.subject	Numerical Technique	en
dc.subject	Singular Integral Equation	en
dc.subject	Stress Intensity Factor	en
dc.subject.other	ELASTICITY	en
dc.subject.other	MATERIALS - Crack Propagation	en
dc.subject.other	STRESSES - Analysis	en
dc.subject.other	CAUCHY-TYPE INTEGRALS	en
dc.subject.other	STRESS INTENSITY FACTORS	en
dc.subject.other	MATHEMATICAL TECHNIQUES	en
dc.title	A remark on the numerical solution of singular integral equations and the determination of stress-intensity factors	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF00036670	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF00036670	en
heal.publicationDate	1979	en
heal.abstract	As is well-known, an efficient numerical technique for the solution of Cauchy-type singular integral equations along an open interval consists in approximating the integrals by using appropriate numerical integration rules and appropriately selected collocation points. Without any alterations in this technique, it is proposed that the estimation of the unknown function of the integral equation is further achieved by using the Hermite interpolation formula instead of the Lagrange interpolation formula. Alternatively, the unknown function can be estimated from the error term of the numerical integration rule used for Cauchy-type integrals. Both these techniques permit a significant increase in the accuracy of the numerical results obtained with an insignificant increase in the additional computations required and no change in the system of linear equations solved. Finally, the Gauss-Chebyshev method is considered in its original and modified form and applied to two crack problems in plane isotropic elasticity. The numerical results obtained illustrate the powerfulness of the method. © 1979 Sijthoff & Noordhoff International Publishers.	en
heal.publisher	Kluwer Academic Publishers	en
heal.journalName	Journal of Engineering Mathematics	en
dc.identifier.doi	10.1007/BF00036670	en
dc.identifier.volume	13	en
dc.identifier.issue	3	en
dc.identifier.spage	213	en
dc.identifier.epage	222	en