Some C0-continuous mixed formulations for general dipolar linear gradient elasticity boundary value problems and the associated energy theorems

Markolefas, SI; Tsouvalas, DA; Tsamasphyros, GI

dc.contributor.author	Markolefas, SI	en
dc.contributor.author	Tsouvalas, DA	en
dc.contributor.author	Tsamasphyros, GI	en
dc.date.accessioned	2014-03-01T01:29:13Z
dc.date.available	2014-03-01T01:29:13Z
dc.date.issued	2008	en
dc.identifier.issn	0020-7683	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19159
dc.subject	Dipolar gradient elasticity	en
dc.subject	Mixed finite elements	en
dc.subject	Mixed formulations	en
dc.subject.classification	Mechanics	en
dc.subject.other	Elasticity	en
dc.subject.other	Stress measurement	en
dc.subject.other	Tensors	en
dc.subject.other	Theorem proving	en
dc.subject.other	Dipolar gradient elasticity	en
dc.subject.other	Mixed finite elements	en
dc.subject.other	Mixed formulations	en
dc.subject.other	Boundary value problems	en
dc.title	Some C0-continuous mixed formulations for general dipolar linear gradient elasticity boundary value problems and the associated energy theorems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijsolstr.2008.01.021	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijsolstr.2008.01.021	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	The goal of this work is a systematic presentation of some classes of mixed weak formulations, for general multi-dimensional dipolar gradient elasticity (fourth order) boundary value problems. The displacement field main variable is accompanied by the double stress tensor and the Cauchy stress tensor (case 1 or mu - tau - u formulation), the double stress tensor alone (case 2 or mu - u formulation), the double stress, the Cauchy stress, the displacement second gradient and the standard strain field (case 3 or mu - tau - kappa - epsilon - u formulation) and the displacement first gradient, along with the equilibrium stress (case 4 or u - theta - gamma formulation). In all formulations, the respective essential conditions are built in the structure of the solution spaces. For cases 1, 2 and 4, one-dimensional analogues are presented for the purpose of numerical comparison. Moreover, the standard Galerkin formulation is depicted. It is noted that the standard Galerkin weak form demands C-1-continuous conforming basis functions. On the other hand, up to first order derivatives appear in the bilinear forms of the current mixed formulations. Hence, standard C-0-continuous conforming basis functions may be employed in the finite element approximations. The main purpose of this work is to provide a reference base for future numerical applications of this type of mixed methods. In all cases, the associated quadratic energy functionals are formed for the purpose of completeness. (C) 2008 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.2008.01.021	en
dc.identifier.isi	ISI:000255811200008	en
dc.identifier.volume	45	en
dc.identifier.issue	11-12	en
dc.identifier.spage	3255	en
dc.identifier.epage	3281	en