An improved meshless method based on the dimension splitting moving least-squares method for elasticity problems

An improved element-free Galerkin method (IEFGM) is proposed in this paper to solve the two-dimensional elasticity problems. In the IEFGM, the dimension-splitting moving least squares (DS-MLS) method is used to construct the trial functions, and the Galerkin variational weak form coupled with the integral coordinate transformation is applied to derive the final discrete equations of the elastic problems. The DS-MLS method is developed from the dimensional splitting method and the moving least squares (MLS) approximation. Since the shape function of the DS-MLS method is derived independently from the direction of dimensional splitting and the splitting subdivision surface, the dimension and complexity of matrix operations are greatly reduced in solving the shape function of the MLS approximation, thereby improving the calculation efficiency. Some typical examples are discussed to show the effectiveness of the improved meshless method in this paper. From the numerical results, because the DS-MLS method reduces the dimensionality when solving the shape functions, the improved meshless method in this paper can consume less CPU time and acquire a higher accuracy solution than the EFG method.

Automated summary

In this paper, an improved element-free Galerkin method (IEFGM) is proposed to solve two-dimensional elasticity problems. The IEFGM utilizes the dimension-splitting moving least squares (DS-MLS) method for constructing trial functions and the Galerkin variational weak form with integral coordinate transformation to obtain discrete equations for the elastic problems. The DS-MLS method, developed from dimensional splitting and moving least squares approximation, reduces the dimension and complexity of matrix operations, thus improving calculation efficiency. Several examples demonstrate the effectiveness of the improved meshless method in terms of reduced CPU time and higher accuracy solution compared to the EFG method.