Theoretical analysis of a class of mixed, C0 continuity formulations for general dipolar Gradient Elasticity boundary value problems

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	2014-03-01T01:27:27Z
dc.date.available	2014-03-01T01:27:27Z
dc.date.issued	2007	en
dc.identifier.issn	0020-7683	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18455
dc.subject	Ciarlet-Raviart method	en
dc.subject	Dipolar gradient elasticity	en
dc.subject	Inf-sup conditions	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	Finite element method	en
dc.subject.other	Gradient methods	en
dc.subject.other	Problem solving	en
dc.subject.other	Tensors	en
dc.subject.other	Ciarlet Raviart method	en
dc.subject.other	Dipolar gradient elasticity	en
dc.subject.other	Inf sup conditions	en
dc.subject.other	Mixed finite elements	en
dc.subject.other	Mixed formulations	en
dc.subject.other	Boundary value problems	en
dc.title	Theoretical analysis of a class of mixed, C0 continuity formulations for general dipolar Gradient Elasticity boundary value problems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijsolstr.2006.04.037	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijsolstr.2006.04.037	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	Mixed weak formulations, with two or three main (tensor) variables, are stated and theoretically analyzed for general multi-dimensional dipolar Gradient Elasticity (biharmonic) boundary value problems. The general structure of constitutive equations is considered (with and without coupling terms). The mixed formulations are based on various generalizations of the so-called Ciarlet-Raviart technique. Hence, C-0 continuity conforming basis functions may be employed in the finite element approximations (or even, C-1 basis functions for the Cauchy stress variable). All the complicated boundary conditions, especially in the multi-dimensional scenario, are naturally considered. The main variables are the displacement vector, the double stress tensor and the Cauchy stress tensor. The latter variable may be eliminated in some of the formulations, depending on the structure of the constitutive equations. The standard continuous and discrete Babuska-Brezzi inf-sup conditions for the constraint equation, as well as, solution uniqueness for both the continuous statements and discrete approximations, are established in all cases. For the purpose of completeness, two one-dimensional mixed formulations are also analyzed. The respective constitutive equations possess general structure (with coupling terms). For the 1-D formulations, all the inf-sup conditions are satisfied, for both the continuous and discrete statements (assuming proper selection of the polynomial spaces for the main variables). Hence, the general Babuska-Brezzi theory results in quasi-optimality and stability. For multi-dimensional problems, the difficulty of deducing the inf-sup condition on the kernel is examined. Certain aspects of methodologies employed to theoretically by-pass this problem, are also discussed. (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.2006.04.037	en
dc.identifier.isi	ISI:000243145300011	en
dc.identifier.volume	44	en
dc.identifier.issue	2	en
dc.identifier.spage	546	en
dc.identifier.epage	572	en