Stress distributions and intensities at corners of equilateral triangular holes

Theocaris, PS; Petrou, L

dc.contributor.author	Theocaris, PS	en
dc.contributor.author	Petrou, L	en
dc.date.accessioned	2014-03-01T01:06:40Z
dc.date.available	2014-03-01T01:06:40Z
dc.date.issued	1986	en
dc.identifier.issn	0376-9429	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9555
dc.subject	Conformal Map	en
dc.subject	Stress Distribution	en
dc.subject	Stress Field	en
dc.subject.classification	Mechanics	en
dc.subject.other	MATERIALS - Fracture	en
dc.subject.other	STRESSES	en
dc.subject.other	PLEXIGLASS	en
dc.subject.other	PMMA	en
dc.subject.other	STRESS INTENSITY FACTOR	en
dc.subject.other	PLASTICS	en
dc.title	Stress distributions and intensities at corners of equilateral triangular holes	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF00044050	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF00044050	en
heal.language	English	en
heal.publicationDate	1986	en
heal.abstract	The problem of the stress distribution in an infinite medium which was weakened by an equilateral triangular hole under tension at infinity, was studied. The triangular hole and its exterior was conformally mapped into the interior of a unit circle by using the Schwarz-Christoffel transformation. The stress function Φ(z) was defined by Muskhelishvili's complex-function theory and the conformal mapping technique. The Schwarz-Christoffel transformation was expressed as a truncated series with a finite numbers of terms. This function represents an equilateral triangle with rounded-off corners mapped into the unit circle. A change of the stress field around the triangular hole was investigated. It was shown that for the transformation function with two-or more-terms of the series, the stress field along the boundary of the respective triangular hole remained unchanged, except for the values of stresses in the near vicinity of the apieces of the corners. It was shown that by introducing substitute singular points lying in the vicinity of the centers of curvature of the rounded corners, the discrepancies in stresses appearing in their vicinity disappeared, and their exact values were attained. These points correspond to the points of the zeroing of the first derivative of the mapping function and coincide with the centers of the initial curves of the caustics traced at each corner for the particular loading mode of the plate. All these results were experimentally verified by using the optical method of reflected caustics. © 1986 Martinus Nijhoff Publishers.	en
heal.publisher	Martinus Nijhoff, The Hague/Kluwer Academic Publishers	en
heal.journalName	International Journal of Fracture	en
dc.identifier.doi	10.1007/BF00044050	en
dc.identifier.isi	ISI:A1986F017500003	en
dc.identifier.volume	31	en
dc.identifier.issue	4	en
dc.identifier.spage	271	en
dc.identifier.epage	289	en