An efficient element free method for stress field assessment in 2D linear elastic cracked domains

Abstract

In the present study, a new technique in Discrete Least Squares Meshless method; DLSM; has been adopted for stress assessment of two-dimensional elastic domains including a non-growing crack. DLSM is a real meshless method that does not require mesh both in approximation step and in numerical integration step of the solution procedure due to the use of a collection of the un-structured nodal points instead of the mesh and discrete least squares approach to discretize the governing differential equations which can reduce considerably the pre-processing cost of calculations. However, DLSM encounters some difficulties in accommodating the solution procedure in the vicinity of the non-convex boundaries such as cracks. In recent years, researchers utilize some techniques to overcome this problem such as visibility, transparency and diffraction approaches, but these methods require somehow backward corrective operations within each step of the calculation process and suffer from some limitations in application. In this study, however, a new, straightforward and general applicable method has been used for fixing this problem using Moving Least Squares; MLS; shape functions constructed based on the Voronoi tessellation algorithm. In this method, the domain of interest is divided into Voronoi cells and nodes of support domain are selected based on a neighboring criterion. The accuracy and efficiency of the proposed method has been demonstrated by solving some benchmark examples and comparing the obtained results with analytical or valid finite element analyses’ results.