Two finite-element discretizations for gradient elasticity

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

dc.contributor.author	Zervos, A	en
dc.contributor.author	Papanicolopulos, S-A	en
dc.contributor.author	Vardoulakis, I	en
dc.date.accessioned	2014-03-01T01:32:14Z
dc.date.available	2014-03-01T01:32:14Z
dc.date.issued	2009	en
dc.identifier.issn	0733-9399	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20093
dc.subject	Elastic analysis	en
dc.subject	Finite element method	en
dc.subject	Microstructures	en
dc.subject	Numerical models	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.other	Benchmarking	en
dc.subject.other	Computational efficiency	en
dc.subject.other	Differential equations	en
dc.subject.other	Elasticity	en
dc.subject.other	Elastohydrodynamics	en
dc.subject.other	Interpolation	en
dc.subject.other	Microstructure	en
dc.subject.other	Numerical methods	en
dc.subject.other	Approximate solutions	en
dc.subject.other	Bench-mark problems	en
dc.subject.other	Boundary values	en
dc.subject.other	Discretizations	en
dc.subject.other	Displacement formulations	en
dc.subject.other	Elastic analysis	en
dc.subject.other	Finite-element discretization	en
dc.subject.other	Gradient elasticities	en
dc.subject.other	Isoparametric elements	en
dc.subject.other	Material parameters	en
dc.subject.other	Micro deformations	en
dc.subject.other	Mindlin	en
dc.subject.other	Numerical models	en
dc.subject.other	Straight edges	en
dc.subject.other	Finite element method	en
dc.subject.other	displacement	en
dc.subject.other	elasticity	en
dc.subject.other	finite element method	en
dc.subject.other	interpolation	en
dc.subject.other	microstructure	en
dc.subject.other	numerical model	en
dc.title	Two finite-element discretizations for gradient elasticity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1061/(ASCE)0733-9399(2009)135:3(203)	en
heal.identifier.secondary	http://dx.doi.org/10.1061/(ASCE)0733-9399(2009)135:3(203)	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	We present and compare two different methods for numerically solving boundary value problems of gradient elasticity. The first method is based on a finite-element discretization using the displacement formulation, where elements that guarantee continuity of strains (i.e., C1 interpolation) are needed. Two such elements are presented and shown to converge: a triangle with straight edges and an isoparametric quadrilateral. The second method is based on a finite-element discretization of Mindlin's elasticity with microstructure, of which gradient elasticity is a special case. Two isoparametric elements are presented, a triangle and a quadrilateral, interpolating the displacement and microdeformation fields. It is shown that, using an appropriate selection of material parameters, they can provide approximate solutions to boundary value problems of gradient elasticity. Benchmark problems are solved using both methods, to assess their relative merits and shortcomings in terms of accuracy, simplicity and computational efficiency. C1 interpolation is shown to give generally superior results, although the approximate solutions obtained by elasticity with microstructure are also shown to be of very good quality. © 2009 ASCE.	en
heal.publisher	ASCE-AMER SOC CIVIL ENGINEERS	en
heal.journalName	Journal of Engineering Mechanics	en
dc.identifier.doi	10.1061/(ASCE)0733-9399(2009)135:3(203)	en
dc.identifier.isi	ISI:000263400400010	en
dc.identifier.volume	135	en
dc.identifier.issue	3	en
dc.identifier.spage	203	en
dc.identifier.epage	213	en