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

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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

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