A method for creating a class of triangular C1 finite elements
Papanicolopulos, S.-A. and Zervos, A. (2012) A method for creating a class of triangular C1 finite elements. International Journal for Numerical Methods in Engineering, 89, (11), 1437-1450. (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
|Keywords:||finite element methods, C1 element, triangular element, gradient elasticity|
|Subjects:||Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
|Divisions:||Faculty of Engineering and the Environment > Civil, Maritime and Environmental Engineering and Science > Infrastructure Research Group
|Date Deposited:||01 Mar 2012 08:54|
|Last Modified:||27 Mar 2014 20:19|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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