A completely meshless analysis of cracks in isotropic functionally graded materials

Abstract

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.

Three-dimensional thermo-mechanical analysis of continuous casting and comparison with two-dimensional models

“…22 In meshless methods, which are based on global weak formulations, special techniques should be employed for meshless evaluation of domain integrals. [23][24][25] In recent years, the MLPG method has been developed in solving a wide range of important engineering problems, taking into account both 2D [26][27][28][29][30][31][32] and 3D [33][34][35][36][37][38][39][40] models. Although the MLPG method shows high capability and precision in solving various types of engineering problems, 41 so far, it has been less used in thermo-mechanical analysis of phase change problems.…”

“…In recent years, the MLPG method has been developed in solving a wide range of important engineering problems, taking into account both 2D 26–32 and 3D 33–40 models. Although the MLPG method shows high capability and precision in solving various types of engineering problems, 41 so far, it has been less used in thermo-mechanical analysis of phase change problems.…”

Extended radial point interpolation method for dynamic crack analysis in functionally graded materials

“…In 2006, Sladek et al applied meshless local Petrov-Galerkin method to evaluate fracture parameters for crack problems in FGM [17]. In 2009, Koohkan et al presented a new technique with J-integral to calculate the SIF values for FGM crack problems [18].…”