A PU-based meshless Shepard interpolation method satisfying delta property

A novel meshless Shepard interpolation method (MSIM) based on the partition of unity (PU) approach is proposed to solve the elasticity problems. In the proposed MSIM interpolation, the Shepard shape functions are used for the partition of unity and the local cover functions are separately constructed for the nodes on the boundary and inside the domain. Three distinguished features of MSIM are: the interpolation property, the arbitrarily high order consistency, and the low computational expense of the shape functions. These properties are desirable in the realization and implementation of the meshless methods. Numerical examples demonstrate the effectiveness and robustness of the present method.