Journal
JOURNAL OF ENGINEERING MECHANICS
Volume 135, Issue 3, Pages 203-213Publisher
ASCE-AMER SOC CIVIL ENGINEERS
DOI: 10.1061/(ASCE)0733-9399(2009)135:3(203)
Keywords
Finite element method; Elastic analysis; Microstructures; Numerical models
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Funding
- School of Civil Engineering and the Environment, University of Southampton
- Alexander S. Onassis Public Benefit Foundation
- European Union
- National Resources (EPEAEK II)
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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., C-1 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.
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