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

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 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.