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Polynomial C1 shape functions on the triangle

Polynomial C1 shape functions on the triangle
Polynomial C1 shape functions on the triangle
We derive generic formulae for all possible C1 continuous polynomial interpolations for triangular elements,
by considering individual shape functions, without the need to prescribe the type of the degrees
of freedom in advance. We then consider the possible ways in which these shape functions can be combined
to form finite elements with given properties. The simplest case of fifth-order polynomial functions
is presented in detail, showing how two existing elements can be obtained, as well as two new elements,
one of which shows good numerical behaviour in numerical tests.
0045-7949
53-58
Papanicolopulos, S.-A.
14e2f9f3-89f9-456b-a9e4-afb65da60f67
Zervos, A.
9e60164e-af2c-4776-af7d-dfc9a454c46e
Papanicolopulos, S.-A.
14e2f9f3-89f9-456b-a9e4-afb65da60f67
Zervos, A.
9e60164e-af2c-4776-af7d-dfc9a454c46e

Papanicolopulos, S.-A. and Zervos, A. (2013) Polynomial C1 shape functions on the triangle. Computers & Structures, 118, 53-58. (doi:10.1016/j.compstruc.2012.07.003).

Record type: Article

Abstract

We derive generic formulae for all possible C1 continuous polynomial interpolations for triangular elements,
by considering individual shape functions, without the need to prescribe the type of the degrees
of freedom in advance. We then consider the possible ways in which these shape functions can be combined
to form finite elements with given properties. The simplest case of fifth-order polynomial functions
is presented in detail, showing how two existing elements can be obtained, as well as two new elements,
one of which shows good numerical behaviour in numerical tests.

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More information

Accepted/In Press date: 24 July 2012
Published date: March 2013
Related URLs:
Organisations: Infrastructure Group

Identifiers

Local EPrints ID: 341764
URI: http://eprints.soton.ac.uk/id/eprint/341764
DOI: doi:10.1016/j.compstruc.2012.07.003
ISSN: 0045-7949
PURE UUID: fc5669c8-4b6f-456d-8c8a-f9aae8fd0dc1
ORCID for A. Zervos: ORCID iD orcid.org/0000-0002-2662-9320

Catalogue record

Date deposited: 02 Aug 2012 16:13
Last modified: 15 Mar 2024 03:16

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Contributors

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

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