Two Finite-Element Discretizations for Gradient Elasticity
Publication: Journal of Engineering Mechanics
Volume 135, Issue 3
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., 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. 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.
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Acknowledgments
The first writer acknowledges the support of the School of Civil Engineering and the Environment, University of Southampton. The second writer acknowledges the support received through his scholarship from the Alexander S. Onassis Public Benefit Foundation. The third writer acknowledges the support of project Pythagoras, cofunded by the European Union (European Social Fund) and National Resources (EPEAEK II).
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 3 • March 2009
Pages: 203 - 213
Copyright
© 2009 ASCE.
History
Received: Sep 5, 2007
Accepted: Oct 15, 2008
Published online: Mar 1, 2009
Published in print: Mar 2009
Notes
Note. Associate Editor: George Z. Voyiadjis
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