A meshless local moving Kriging method for two-dimensional solids

An improved meshless local Petrov–Galerkin method (MLPG) for stress analysis of two‐dimensional solids is presented in this paper. The MLPG method based on the moving least‐squares approximation is one of the recent meshless approaches. However, accurate imposition of essential boundary conditions in the MLPG method often presents difficulties because the MLPG shape functions does not possess the Kronecker delta property. In order to eliminate this shortcoming, this approach uses the moving Kriging interpolation instead of the traditional moving least‐square approximation to construct the MLPG shape functions, and then, the Heaviside step function is used as the test function over a local sub‐domain. In this method, the essential boundary conditions can be enforced as the FEM, no domain integration is needed and only regular boundary integration is involved. In addition, the sensitivity of several important parameters of the present method is mainly studied and discussed. Comparing with the original meshless local Petrov–Galerkin method, the present method has simpler numerical procedures and lower computation cost. The effectiveness of the present method for two‐dimensional solids problem is investigated by numerical examples in this paper.