Polynomial C1 shape functions on the triangle

Papanicolopulos, S.-A. and Zervos, A. (2012) Polynomial C1 shape functions on the triangle. Computers & Structures, 118, 53-58. (doi:10.1016/j.compstruc.2012.07.003).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/j.compstruc.2012.07.003
ISSNs: 0045-7949 (print)
Related URLs:
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions : Faculty of Engineering and the Environment > Civil, Maritime and Environmental Engineering and Science > Infrastructure Research Group
ePrint ID: 341764
Accepted Date and Publication Date:
24 July 2012In press
March 2013Published
Date Deposited: 02 Aug 2012 16:13
Last Modified: 31 Mar 2016 14:32
Mechanics of energy dissipation in dense granular materials (MEDIGRA)
Funded by: European Commission - FP7 (228051)
1 November 2008 to 31 October 2011
URI: http://eprints.soton.ac.uk/id/eprint/341764

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