A three-dimensional C1 finite element for gradient elasticity

Papanicolopulos, S-A; Zervos, A; Vardoulakis, I

dc.contributor.author	Papanicolopulos, S-A	en
dc.contributor.author	Zervos, A	en
dc.contributor.author	Vardoulakis, I	en
dc.date.accessioned	2014-03-01T01:29:41Z
dc.date.available	2014-03-01T01:29:41Z
dc.date.issued	2009	en
dc.identifier.issn	0029-5981	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19337
dc.subject	C1 element	en
dc.subject	Elasticity with microstructure	en
dc.subject	Finite element methods	en
dc.subject	Gradient elasticity	en
dc.subject	Higher-order continuum	en
dc.subject	Solids	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.other	Benchmarking	en
dc.subject.other	Differential equations	en
dc.subject.other	Elastohydrodynamics	en
dc.subject.other	Finite element method	en
dc.subject.other	Interpolation	en
dc.subject.other	Microstructure	en
dc.subject.other	Three dimensional	en
dc.subject.other	Alternative approaches	en
dc.subject.other	Alternative methods	en
dc.subject.other	Boundary values	en
dc.subject.other	C element	en
dc.subject.other	Computational costs	en
dc.subject.other	Displacement fields	en
dc.subject.other	Finite element discretizations	en
dc.subject.other	Finite element methods	en
dc.subject.other	Gradient elasticity	en
dc.subject.other	Hexahedral elements	en
dc.subject.other	Higher-order continuum	en
dc.subject.other	Patch tests	en
dc.subject.other	Rates of convergences	en
dc.subject.other	Single elements	en
dc.subject.other	Strain gradients	en
dc.subject.other	Virtual works	en
dc.subject.other	Elasticity	en
dc.title	A three-dimensional C1 finite element for gradient elasticity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1002/nme.2449	en
heal.identifier.secondary	http://dx.doi.org/10.1002/nme.2449	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	In gradient elasticity strain gradient terms appear in the expression of virtual work, leading to the need for C-1 continuous interpolation in finite element discretizations of the displacement field only. Employing such interpolation is generally avoided in favour of the alternative methods that interpolate other quantities as well as displacement, due to the scarcity of C-1 finite elements and their perceived computational cost. In this context, the lack of three-dimensional C-1 elements is of particular concern. In this paper we present a new C-1 hexahedral element which, to the best of our knowledge, is the first three-dimensional C-1 element ever constructed. It is shown to pass the single element and patch tests, and to give excellent rates of convergence in benchmark boundary value problems of gradient elasticity. It is further shown that C-1 elements are not necessarily more computationally expensive than alternative approaches, and it is argued that they may be more efficient in providing good-quality solutions. Copyright (C) 2008 John Wiley & Sons, Ltd.	en
heal.publisher	JOHN WILEY & SONS LTD	en
heal.journalName	International Journal for Numerical Methods in Engineering	en
dc.identifier.doi	10.1002/nme.2449	en
dc.identifier.isi	ISI:000264204700003	en
dc.identifier.volume	77	en
dc.identifier.issue	10	en
dc.identifier.spage	1396	en
dc.identifier.epage	1415	en