A method for creating a class of triangular C1 finite elements

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Abstract

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 TUBA3 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.

Original languageEnglish
Pages (from-to)1437-1450
Number of pages14
JournalInternational Journal for Numerical Methods in Engineering
Volume89
Issue number11
DOIs
Publication statusPublished - 16 Mar 2012

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