Two finite-element discretizations for gradient elasticity

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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.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

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