A completely meshless analysis of cracks in isotropic functionally graded materials

In the present study, a completely meshless analysis of two-dimensional cracks in non-homogeneous, isotropic, and linear elastic functionally graded materials (FGMs) is developed. The meshless local Petrov Galerkin method is applied and the equilibrium equations are considered to drive the local symmetric weak formulations. The moving least-squares approximation is used to interpolate the solution variables and the penalty method is applied to impose the essential boundary conditions. Also, a new technique for defining local sub-domain and support domain is proposed. Using the technique, more nodes are considered in the direction of material variation and extra nodes are located near the crack tip of the FGM body to obtain an accurate meshless model. The based functions are also enriched in order to capture singularities around the crack tip. Several numerical examples containing both mode-I and mixed-mode conditions are presented and the results are compared with the available solutions in the literature which shows a good agreement.