This study develops the Local Kriging Method which is based on the local weak form of partial differential equations for solving 2D elastostatics problems. The weighted residual method is used to derive the discretized system equations of the weak form for each local sub-domain. The Kriging interpolation is employed to construct the shape functions for approximation of field variable. In this study, the square shaped local sub-domains are used to alleviate the background mesh for the integration of local weak form over the local sub- domain. Two types of weight functions, which satisfy the requirements of local weak form over the square shaped sub-domain, are examined in this study. The first one is FEM weight function which is constructed by employing the FEM interpolation over the fictitious nodes on the boundary of local sub- domain and the second one is Kriging weight function which is constructed by employing the Kriging interpolation over the fictitious nodes on the boundary of local sub-domain. A number of benchmark examples are presented to verify the efficiency and accuracy of the present method.
