Incursion on Contact Problems using a Meshless method

Contact is one of the most important problems in many engineering fields. In the case of mechanical engineering, it is most important in the analysis of processes such as forging or sheet metal stamping. In this work, the contact problem is extended to a meshless method, the Natural Neigh-bour Radial Point Interpolation Method (NNRPIM). In the NNRPIM the Natural Neighbour concept is used in order to enforce the nodal connectivity. Using the Voronoï diagrams, constructed from the unstructured set of nodes discretizing the problem domain, it is possible to obtain the "influence-cells", which are in fact influence-domains entirely nodal dependent. From the Delaunay triangles, the dual of the Voronoï cells, a node-depending background mesh is created. This integration mesh is used in the numerical integration of the NNRPIM interpolation functions, which are constructed using the Radial Point Interpolators (RPI). The obtained interpolation functions possess the delta Kronecker property, which simplify the imposition of natural and essential boundary conditions