[en] The natural neighbour method can be considered as belonging to the meshless methods. Classically, the development of this method is based on the virtual work principle. In the present paper, we use the natural neighbour method for 2D domains starting from the Fraeijs de Veubeke variational principle and we approximate separately the displacement field, the stress field and the strain field: the assumed strains and the assumed stresses are constant over each Voronoi cell, the assumed surface reactions are constant along the edge where the displacements are imposed, while the assumed displacements are interpolated by Laplace interpolants. In the absence of body forces, it is shown that the calculation of integrals on the area of the solid domain can be avoided: only integrals on the edges of the Voronoi cells are necessary. On the other hand, displacements can be imposed in the average sense on some boundaries of the domain. Patch tests and sot-tie applications in the elastic domain are given in the paper and show the effectiveness of the method. Copyright (C) 2007 John Wiley
Disciplines :
Mathematics Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Cescotto, Serge ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Mécanique des solides
Li, Xiang
Language :
English
Title :
A natural neighbour method for linear elastic problems based on Fraeijs de Veubeke variational principle
Publication date :
2007
Journal title :
International Journal for Numerical Methods in Engineering
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