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Convergence and performance of the h- and p-extensions with mixed finite element C0-continuity formulations, for tension and buckling of a gradient elastic beam

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dc.contributor.author Tsamasphyros, GI en
dc.contributor.author Markolefas, S en
dc.contributor.author Tsouvalas, DA en
dc.date.accessioned 2014-03-01T01:26:03Z
dc.date.available 2014-03-01T01:26:03Z
dc.date.issued 2007 en
dc.identifier.issn 0020-7683 en
dc.identifier.uri https://dspace.lib.ntua.gr/xmlui/handle/123456789/17902
dc.subject Babuška-Brezzi conditions en
dc.subject Biharmonic equation en
dc.subject Buckling en
dc.subject Finite elements en
dc.subject Gradient elasticity en
dc.subject h- and p-Extensions en
dc.subject Mixed methods en
dc.subject Sixth-order equations en
dc.subject.classification Mechanics en
dc.subject.other Buckling en
dc.subject.other Convergence of numerical methods en
dc.subject.other Differential equations en
dc.subject.other Finite element method en
dc.subject.other Tensile testing en
dc.subject.other Basis functions en
dc.subject.other Gradient elastic beam en
dc.subject.other Gradient elasticity en
dc.subject.other H- and p-Extensions en
dc.subject.other Sixth-order equations en
dc.subject.other Beams and girders en
dc.title Convergence and performance of the h- and p-extensions with mixed finite element C0-continuity formulations, for tension and buckling of a gradient elastic beam en
heal.type journalArticle en
heal.identifier.primary 10.1016/j.ijsolstr.2006.12.023 en
heal.identifier.secondary http://dx.doi.org/10.1016/j.ijsolstr.2006.12.023 en
heal.language English en
heal.publicationDate 2007 en
heal.abstract Mixed formulations with C-0-continuity basis functions are employed for the solution of some types of one-dimensional fourth- and sixth-order equations, resulting from axial tension and buckling of gradient elastic beams, respectively. A basic characteristic of gradient elasticity type equations is the appearance of boundary layers in the higher-order derivatives of the displacements (e.g., in the stress fields). This is due to the small parameters (related to the size of the microstructure) entering the governing equations. The proposed mixed formulations are based on generalizations of the well-known Ciarlet-Raviart mixed method, where the new main variables are related to second-order (or fourth order, for the buckling problem) derivatives of the displacement field. The continuous and discrete Babuska-Brezzi inf-sup conditions are established. The mixed formulations are numerically tested for both the uniform h- and p-extensions. With regard to the axial tension problem, the standard quasi-optimal rates of convergence are numerically verified in all cases (i.e., algebraic rate of convergence for the h-extension and exponential rate for the p-extension). On the other hand, the h-extension observed convergence rates of the critical (buckling) load for the second model problem are slightly higher than the theoretical ones found in the literature (especially for polynomial order p = 1). The respective observed rates of convergence of the buckling load for the p-extension are still exponential. (C) 2006 Elsevier Ltd. All rights reserved. en
heal.publisher PERGAMON-ELSEVIER SCIENCE LTD en
heal.journalName International Journal of Solids and Structures en
dc.identifier.doi 10.1016/j.ijsolstr.2006.12.023 en
dc.identifier.isi ISI:000247989700029 en
dc.identifier.volume 44 en
dc.identifier.issue 14-15 en
dc.identifier.spage 5056 en
dc.identifier.epage 5074 en


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