Discrepancies and errors between caustics from approximate and exact solutions

Theocaris, PS

dc.contributor.author	Theocaris, PS	en
dc.date.accessioned	2014-03-01T01:06:51Z
dc.date.available	2014-03-01T01:06:51Z
dc.date.issued	1987	en
dc.identifier.issn	00137944	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9635
dc.subject	Exact Solution	en
dc.subject.other	IMAGE PROCESSING - Image Analysis	en
dc.subject.other	MATHEMATICAL TECHNIQUES - Error Analysis	en
dc.subject.other	STRESSES - Evaluation	en
dc.subject.other	STRUCTURAL DESIGN - Loads	en
dc.subject.other	ELASTIC ISOTROPIC HALF-PLANES	en
dc.subject.other	INTERFACIAL CRACK	en
dc.subject.other	MULTI-PHASE PLATE	en
dc.subject.other	PLATES	en
dc.title	Discrepancies and errors between caustics from approximate and exact solutions	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/0013-7944(87)90176-7	en
heal.identifier.secondary	http://dx.doi.org/10.1016/0013-7944(87)90176-7	en
heal.publicationDate	1987	en
heal.abstract	The plane problem of a biphase plate containing an internal crack along the straight interface of the two phases was examined when the biphase plate is subjected to a biaxial load at infinity. The closed form expressions for the equations of the initial curves and the caustics formed around the crack tips were established by using the formulation for the complex stress function of this problem given by Rice and Sih. Similar equations were also established based on the two-term approximate solution as it was introduced by Liebowitz and co-workers and formulated by Piva and Viola. Comparisons of the discrepancies and errors between the two solutions were established and plotted in convenient diagrams. It was shown that the geometric characteristics of the optical set-up for forming the caustics played an important role in the accuracy of the results of the approximate solution and especially the optical magnification factor of the set-up. Furthermore, and more important is the influence of the radius of the initial curve normalized to the semi-length of the crack. For values of this ratio below some limit, the approximate results may be considered as sufficiently accurate. The solution was reduced to a monophase plate and this result made this study valid for the basic problem of an internal crack in an infinite elastic and isotropic plate. Important results were derived concerning the appropriate use of the method of caustics to evaluate SIFs at singularities in the stress field. © 1987.	en
heal.journalName	Engineering Fracture Mechanics	en
dc.identifier.doi	10.1016/0013-7944(87)90176-7	en
dc.identifier.volume	27	en
dc.identifier.issue	4	en
dc.identifier.spage	391	en
dc.identifier.epage	411	en