Moving Least Squares method has been extensively used for formulation of shape function in a number of Mesh free methods. The MLS method requires construction of compact support of nodes over which its corresponding weight is non - zero. The commonly used shape of compact support is circular (in case of 2D) or rectangular. The size of this compact support is determined manually and requires adjustment when density of nodal distribution changes over the domain. Having a large and uniform compact support undermines the idea of using MLS method to formulate the shape function. To capture any steep variations in stress requires as small a compact support as possible. A large compact support can smoothen out the stress variations. On the other hand, the compact support size should be large enough such that any point (Evaluation or Gauss point) is covered by a minimum number of compact supports to avoid invertability issues in MLS method.
A new method of determining compact support based on Natural Neighbors is proposed by which the compact support size and shape of all nodes are automatically formed. This method is used in MLS method of shape function formulation. Example problems have been solved using this method to determine its ability to accommodate changes in density of nodal distribution.