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A method for creating a class of triangular C1 finite elements

Record type: Article

Finite elements providing a C1 continuous interpolation are useful in the numerical solution of problems where the underlying partial differential equation is of fourth order, such as beam and plate bending and deformation of strain-gradient-dependent materials. Although a few C1 elements have been presented in the literature, their development has largely been heuristic, rather than the result of a rational design to a predetermined set of desirable element properties. Therefore, a general procedure for developing C1 elements with particular desired properties is still lacking.

This paper presents a methodology by which C1 elements, such as the TUBA?3 element proposed by Argyris et al., can be constructed. In this method (which, to the best of our knowledge, is the first one of its kind), a class of finite elements is first constructed by requiring a polynomial interpolation and prescribing the geometry, the location of the nodes and the possible types of nodal DOFs. A set of necessary conditions is then imposed to obtain appropriate interpolations. Generic procedures are presented, which determine whether a given potential member of the element class meets the necessary conditions. The behaviour of the resulting elements is checked numerically using a benchmark problem in strain-gradient elasticity

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Citation

Papanicolopulos, S.-A. and Zervos, A. (2012) A method for creating a class of triangular C1 finite elements International Journal for Numerical Methods in Engineering, 89, (11), pp. 1437-1450. (doi:10.1002/nme.3296).

More information

e-pub ahead of print date: 12 October 2011
Published date: 16 March 2012
Keywords: finite element methods, C1 element, triangular element, gradient elasticity
Organisations: Infrastructure Group

Identifiers

Local EPrints ID: 300822
URI: http://eprints.soton.ac.uk/id/eprint/300822
ISSN: 0029-5981
PURE UUID: 9720743c-1894-47c2-b42d-62a83c25289e
ORCID for A. Zervos: ORCID iD orcid.org/0000-0002-2662-9320

Catalogue record

Date deposited: 01 Mar 2012 08:54
Last modified: 18 Jul 2017 06:14

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Contributors

Author: S.-A. Papanicolopulos
Author: A. Zervos ORCID iD

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