Two finite element discretizations for gradient elasticity
Two finite element discretizations for gradient elasticity
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.
finite element method, elastic analysis, microstructures, numerical models.
203-213
Zervos, A.
9e60164e-af2c-4776-af7d-dfc9a454c46e
Papanicolopulos, S. A.
2290480f-e7f6-4569-be52-2cd14d265c13
Vardoulakis, I
fe09b196-51e0-41c6-8484-0a41ef9435f1
March 2009
Zervos, A.
9e60164e-af2c-4776-af7d-dfc9a454c46e
Papanicolopulos, S. A.
2290480f-e7f6-4569-be52-2cd14d265c13
Vardoulakis, I
fe09b196-51e0-41c6-8484-0a41ef9435f1
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.
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Published date: March 2009
Keywords:
finite element method, elastic analysis, microstructures, numerical models.
Identifiers
Local EPrints ID: 75852
URI: http://eprints.soton.ac.uk/id/eprint/75852
ISSN: 0733-9399
PURE UUID: a6bec344-46e9-41fb-8a56-fd0ca2c496a7
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Date deposited: 12 Mar 2010
Last modified: 14 Mar 2024 02:48
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Author:
S. A. Papanicolopulos
Author:
I Vardoulakis
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