Two finite-element discretizations for gradient elasticity / A. Zervos in Journal of engineering mechanics, Vol. 135 N°3 (Mars 2009)  

Public ISBD [article]  inJournal of engineering mechanics > Vol. 135 N°3 (Mars 2009) . - pp. 203-213 Titre : Two finite-element discretizations for gradient elasticity Type de document : texte imprimé Auteurs : A. Zervos, Auteur ; S.-A. Papanicolopulos, Auteur ; I. Vardoulakis, Auteur Article en page(s) : pp. 203-213 Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Finite element method Elastic analysis Microstructures Numerical models. Résumé : 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. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JENMDT000 [...] [article] Two finite-element discretizations for gradient elasticity [texte imprimé] / A. Zervos, Auteur ; S.-A. Papanicolopulos, Auteur ; I. Vardoulakis, Auteur . - pp. 203-213. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 135 N°3 (Mars 2009) . - pp. 203-213 Mots-clés : Finite element method Elastic analysis Microstructures Numerical models. Résumé : 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. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JENMDT000 [...]

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