An improved moving least-squares Ritz method for two-dimensional elasticity problems

We propose an improved moving least-squares Ritz (IMLS-Ritz) method with its element-free framework developed for studying two-dimensional elasticity problems. Using the IMLS approximation for the field variables, the discretized governing equations of the problem are derived via the Ritz procedure. In the IMLS, an orthogonal function system with a weight function is employed as the basis for construction of its displacement field. By using the element-free IMLS-Ritz method, solutions of the two-dimensional elasticity problems are obtained. The applicability of the element-free IMLS-Ritz method is illustrated through three selected example problems. The convergence characteristics of the method are examined by varying the number of nodes and geometric parameters of these examples. The accuracy of the method is validated by comparing the computed results with the EFG and exact solutions.