Papanicolopulos, S.-A. and Zervos, A.
A method for creating a class of triangular C1 finite elements
International Journal for Numerical Methods in Engineering, 89, (11), . (doi:10.1002/nme.3296).
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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 TUBA?3 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
|Digital Object Identifier (DOI):
||finite element methods, C1 element, triangular element, gradient elasticity
|12 October 2011||e-pub ahead of print|
|16 March 2012||Published|
||01 Mar 2012 08:54
||17 Apr 2017 17:30
|Further Information:||Google Scholar|
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