Premium
A natural neighbour method for linear elastic problems based on Fraeijs de Veubeke variational principle
Author(s) -
Cescotto Serge,
Li Xiang
Publication year - 2007
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1982
Subject(s) - voronoi diagram , domain (mathematical analysis) , displacement field , mathematics , laplace transform , variational principle , constant (computer programming) , virtual work , displacement (psychology) , field (mathematics) , mathematical analysis , linear elasticity , stress field , enhanced data rates for gsm evolution , geometry , physics , computer science , finite element method , psychology , pure mathematics , psychotherapist , thermodynamics , programming language , telecommunications
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 some applications in the elastic domain are given in the paper and show the effectiveness of the method. Copyright © 2007 John Wiley & Sons, Ltd.