A method for creating a class of triangular C1 finite elements

Papanicolopulos, S-A; Zervos, A

dc.contributor.author	Papanicolopulos, S-A	en
dc.contributor.author	Zervos, A	en
dc.date.accessioned	2014-03-01T02:07:22Z
dc.date.available	2014-03-01T02:07:22Z
dc.date.issued	2012	en
dc.identifier.issn	00295981	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29545
dc.subject	C1 element	en
dc.subject	Finite element methods	en
dc.subject	Gradient elasticity	en
dc.subject	Triangular element	en
dc.subject.other	Bench-mark problems	en
dc.subject.other	C <sup>1</sup> element	en
dc.subject.other	Element properties	en
dc.subject.other	Finite Element	en
dc.subject.other	Fourth order	en
dc.subject.other	Generic procedures	en
dc.subject.other	Gradient elasticity	en
dc.subject.other	Numerical solution	en
dc.subject.other	Plate bending	en
dc.subject.other	Polynomial interpolation	en
dc.subject.other	Rational design	en
dc.subject.other	Strain gradients	en
dc.subject.other	Triangular elements	en
dc.subject.other	Bending (deformation)	en
dc.subject.other	Elastohydrodynamics	en
dc.subject.other	Finite element method	en
dc.subject.other	Interpolation	en
dc.subject.other	Partial differential equations	en
dc.subject.other	Behavioral research	en
dc.title	A method for creating a class of triangular C1 finite elements	en
heal.type	journalArticle	en
heal.identifier.primary	10.1002/nme.3296	en
heal.identifier.secondary	http://dx.doi.org/10.1002/nme.3296	en
heal.publicationDate	2012	en
heal.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. © 2011 John Wiley & Sons, Ltd.	en
heal.journalName	International Journal for Numerical Methods in Engineering	en
dc.identifier.doi	10.1002/nme.3296	en
dc.identifier.volume	89	en
dc.identifier.issue	11	en
dc.identifier.spage	1437	en
dc.identifier.epage	1450	en