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

Tsamasphyros, GI; Markolefas, S; Tsouvalas, DA

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