## TUBA3

 swMATH ID: 6145 Software Authors: Papanicolopulos, S.-A.; Zervos, A. Description: A method for creating a class of triangular $$C^{1}$$ finite elements Finite elements providing a $$C^{1}$$ 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 $$C^{1}$$ 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 $$C^{1}$$ elements with particular desired properties is still lacking.par This paper presents a methodology by which $$C^{1}$$ elements, such as the TUBA3 element proposed by {it J. H. Argyris} et al.[“The TUBA family of plate elements for the matrix displacement method”, Aeronautical Journal of the Royal Aeronautical Societ, 72, No. 692, 701–709 (1968)], 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. Homepage: http://eprints.soton.ac.uk/300822/ Keywords: finite element methods; $$C^{1}$$ element; triangular element; gradient elasticity Related Software: ABAQUS; FEAPpv; Gmsh Cited in: 8 Publications
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### Cited by 24 Authors

 2 Zervos, Antonis 1 Andreaus, Ugo A. 1 Arroyo, Marino 1 Becker, Gauthier 1 Contrafatto, Loredana 1 Cuomo, Massimo 1 dell’Isola, Francesco 1 Froiio, Francesco 1 Giorgio, Ivan 1 Greco, Leopoldo 1 Lee, Eunjung 1 Lekszycki, Tomasz 1 Lesičar, Tomislav 1 Manteuffel, Thomas A. 1 Millán, Daniel 1 Nguyen, Van-Dung 1 Noels, Ludovic 1 Papanicolopulos, Stefanos-Aldo 1 Placidi, Luca 1 Rizzi, Nicola Luigi 1 Sorić, Jurica 1 Sukumar, Natarajan 1 Tonković, Zdenko 1 Westphal, Chad R.

### Cited in 5 Serials

 4 Computer Methods in Applied Mechanics and Engineering 1 International Journal of Engineering Science 1 International Journal for Numerical Methods in Engineering 1 SIAM Journal on Scientific Computing 1 Mathematics and Mechanics of Solids

### Cited in 2 Fields

 7 Mechanics of deformable solids (74-XX) 5 Numerical analysis (65-XX)