A natural neighbour method based on Fraeijs de Veubeke variational principle for materially non-linear problems

The natural neighbour method can be considered as one of many variants of the meshless methods. In the present paper, a new approach based on the Fraeijs de Veubeke (FdV) functional, which is initially developed for linear elasticity, is extended to the case of geometrically linear but materially non-linear solids. The new approach provides an original treatment to two classical problems: the numerical evaluation of the integrals over the domain A and the enforcement of boundary conditions of the type u _i  =  ũ _i on S _u . In the absence of body forces (F _i  =  0), it will be shown that the calculation of integrals of the type can be avoided and that boundary conditions of the type u _i  =  ũ _i on S _u can be imposed in the average sense in general and exactly if ũ _i is linear between two contour nodes, which is obviously the case for ũ _i  =  0.