Problems of the flamant-boussinesq and kelvin type in dipolar gradient elasticity

Georgiadis, HG; Anagnostou, DS

dc.contributor.author	Georgiadis, HG	en
dc.contributor.author	Anagnostou, DS	en
dc.date.accessioned	2014-03-01T01:29:03Z
dc.date.available	2014-03-01T01:29:03Z
dc.date.issued	2008	en
dc.identifier.issn	0374-3535	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19101
dc.subject	Concentrated loads	en
dc.subject	Dipolar stresses	en
dc.subject	Flamant-Boussinesq problem	en
dc.subject	Gradient elasticity	en
dc.subject	Green's functions	en
dc.subject	Kelvin problem	en
dc.subject	Laplace transforms	en
dc.subject	Microstructure	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Materials Science, Multidisciplinary	en
dc.subject.classification	Mechanics	en
dc.subject.other	Continuum mechanics	en
dc.subject.other	Gradient methods	en
dc.subject.other	Green's function	en
dc.subject.other	Laplace transforms	en
dc.subject.other	Microstructure	en
dc.subject.other	Two dimensional	en
dc.subject.other	Concentrated loads	en
dc.subject.other	Dipolar stresses	en
dc.subject.other	Flamant-Boussinesq problem	en
dc.subject.other	Kelvin problem	en
dc.subject.other	Elasticity	en
dc.title	Problems of the flamant-boussinesq and kelvin type in dipolar gradient elasticity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s10659-007-9129-x	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s10659-007-9129-x	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	This work studies the response of bodies governed by dipolar gradient elasticity to concentrated loads. Two-dimensional configurations in the form of either a half-space (Flamant-Boussinesq type problem) or a full-space (Kelvin type problem) are treated and the concentrated loads are taken as line forces. Our main concern is to determine possible deviations from the predictions of plane-strain/plane-stress classical linear elastostatics when a more refined theory is employed to attack the problems. Of special importance is the behavior of the new solutions near to the point of application of the loads where pathological singularities and discontinuities exist in the classical solutions. The use of the theory of gradient elasticity is intended here to model material microstructure and incorporate size effects into stress analysis in a manner that the classical theory cannot afford. A simple but yet rigorous version of the generalized elasticity theories of Toupin (Arch. Ration. Mech. Anal. 11:385-414, 1962) and Mindlin (Arch. Ration. Mech. Anal. 16:51-78, 1964) is employed that involves an isotropic linear response and only one material constant (the so-called gradient coefficient) additional to the standard Lamé constants (Georgiadis et al., J. Elast. 74:17-45, 2004). This theory, which can be viewed as a first-step extension of the classical elasticity theory, assumes a strain-energy density function, which besides its dependence upon the standard strain terms, depends also on strain gradients. The solution method is based on integral transforms and is exact. The present results show departure from the ones of the classical elasticity solutions (Flamant-Boussinesq and Kelvin plane-strain solutions). Indeed, continuous and bounded displacements are predicted at the points of application of the loads. Such a behavior of the displacement fields is, of course, more natural than the singular behavior present in the classical solutions. © 2007 Springer Science+Business Media B.V.	en
heal.publisher	SPRINGER	en
heal.journalName	Journal of Elasticity	en
dc.identifier.doi	10.1007/s10659-007-9129-x	en
dc.identifier.isi	ISI:000251172500004	en
dc.identifier.volume	90	en
dc.identifier.issue	1	en
dc.identifier.spage	71	en
dc.identifier.epage	98	en