Meshless method based on the Petrov-Galerkin discretization scheme

In this paper,a meshless method called as meshless natural neighbour Petrov-Galerkin method(MNNPG) is developed for elasto-statics based on the generalized meshless local Petrov-Galerkin method(MLPG).The natural neighbour interpolation is used to approximate the trial function and the Shepard function is chosen to be the test function over a circular local sub-domain.As this method joins the advantages of natural neighbour interpolation and meshless local Petrov-Galerkin method together,no background cells are needed for domain integration,no stiffness matrix assembly is required and no special treatment is needed to impose the essential boundary conditions.To improve the accuracy of presented method,the piecewise mid-point integration scheme is used to evaluate the domain integrals.In numerical examples,the accuracy and convergence of the presented method are studied and accurate results are obtained.