Imposing essential boundary conditions in the natural element method by means of density-scaled -shapes

A new method is proposed for the &exactʹ imposition of essential boundary conditions in the context of the natural element method (NEM). This is a new technique in the "eld of Computational Mechanics and can be considered as a meshless method. Unlike most of these methods, the NE shape functions are strictly interpolant and the essential boundary conditions can be imposed by directly substituting the corresponding terms in the system of equations. However, these shape functions are not strictly linear over non-convex boundaries and the approach does not make the test functions vanish over the whole essential boundary region. A modi"cation of the initial NEM version is considered based on a-shapes and a-complexes, which are widely used in the "eld of scienti"c visualization. Using a-shapes in the context of the NEM allows the construction of models entirely in terms of nodes and also ensures the linear precision of the interpolant over convex and non-convex boundaries. Results on some benchmark problems are presented after a theoretical description of the method