A three dimensional C1 finite element for gradient elasticity
A three dimensional C1 finite element for gradient elasticity
In gradient elasticity strain gradient terms appear in the expression of virtual work, leading to the need for C1 continuous interpolation in finite element discretizations of the displacement field only. Employing such interpolation is generally avoided in favour of the alternative methods that interpolate other quantities as well as displacement, due to the scarcity of C1 finite elements and their perceived computational cost. In this context, the lack of three-dimensional C1 elements is of particular concern. In this paper we present a new C1 hexahedral element which, to the best of our knowledge, is the first three-dimensional C1 element ever constructed. It is shown to pass the single element and patch tests, and to give excellent rates of convergence in benchmark boundary value problems of gradient elasticity. It is further shown that C1 elements are not necessarily more computationally expensive than alternative approaches, and it is argued that they may be more efficient in providing good-quality solutions
solids, finite element methods, gradient elasticity, elasticity with microstructure, higher-order continuum, C1 element
1396-1415
Papanicolopulos, S.-A.
14e2f9f3-89f9-456b-a9e4-afb65da60f67
Zervos, A.
9e60164e-af2c-4776-af7d-dfc9a454c46e
Vardoulakis, I.
12908544-3fc4-4ea6-9068-89ff3e532ff0
5 March 2009
Papanicolopulos, S.-A.
14e2f9f3-89f9-456b-a9e4-afb65da60f67
Zervos, A.
9e60164e-af2c-4776-af7d-dfc9a454c46e
Vardoulakis, I.
12908544-3fc4-4ea6-9068-89ff3e532ff0
Papanicolopulos, S.-A., Zervos, A. and Vardoulakis, I.
(2009)
A three dimensional C1 finite element for gradient elasticity.
International Journal for Numerical Methods in Engineering, 77 (10), .
(doi:10.1002/nme.2449).
Abstract
In gradient elasticity strain gradient terms appear in the expression of virtual work, leading to the need for C1 continuous interpolation in finite element discretizations of the displacement field only. Employing such interpolation is generally avoided in favour of the alternative methods that interpolate other quantities as well as displacement, due to the scarcity of C1 finite elements and their perceived computational cost. In this context, the lack of three-dimensional C1 elements is of particular concern. In this paper we present a new C1 hexahedral element which, to the best of our knowledge, is the first three-dimensional C1 element ever constructed. It is shown to pass the single element and patch tests, and to give excellent rates of convergence in benchmark boundary value problems of gradient elasticity. It is further shown that C1 elements are not necessarily more computationally expensive than alternative approaches, and it is argued that they may be more efficient in providing good-quality solutions
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More information
e-pub ahead of print date: 8 September 2008
Published date: 5 March 2009
Keywords:
solids, finite element methods, gradient elasticity, elasticity with microstructure, higher-order continuum, C1 element
Organisations:
Civil Engineering & the Environment
Identifiers
Local EPrints ID: 74066
URI: http://eprints.soton.ac.uk/id/eprint/74066
ISSN: 0029-5981
PURE UUID: bc923694-0244-4d33-afb0-79f04835d506
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Date deposited: 11 Mar 2010
Last modified: 14 Mar 2024 02:48
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Author:
S.-A. Papanicolopulos
Author:
I. Vardoulakis
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