Comparison of different numerical methods for calculating stress intensity factors in analysis of fractured structures

In this research, an efficient Galerkin Finite Volume Method (GFVM) along with the h–refinement adaptive process and post–processing error estimation analysis is presented for fracture analysis. The adaptive strategy is used to produce more accurate solution with the least computational cost. To investigate the accuracy and efficiency of the developed model, the GFVM is compared with two versions of the Finite Element Method known in solid mechanics, the adaptive Galerkin Finite Element Method (GFEM) and Extended Finite Element Method (XFEM), for the two dimensional fracture analysis of structures. After the discretization of the governing equations, the above three methods are implemented in FORTRAN. In the adaptive GFVM and GFEM methods, the discrete crack concept is used to model the crack surface, but in the XFEM, the crack surface is modeled through the enrichment of the displacement approximation around the crack. Several test cases are used to validate the developed dimensional numerical models for the analysis of cracked structures. After verification, the fracture analysis of a plate under pure mode I and mixed mode I/II is performed using the above-mentioned numerical methods. The numerical results show that three methods accurately calculate the stress intensity factors. The average percent error of the XFEM, adaptive GFEM and adaptive GFVM is ,  and , respectively. The results show that the CPU time of the adaptive GFVM is 5.5 and 3 times less than the XFEM and adaptive GFEM, respectively.