A Cell Centered Finite Volume Formulation for the Calculation of Stress Intensity Factors in Mindlin-Reissner Cracked Plates

In fracture analysis, the stress intensity factor (SIF) is an important parameter which is needed for describing the stress state at crack tip. In this paper a finite volume formulation is developed for calculating the stress intensity factor (SIF) in Mindlin-Reissner plates with a through-the-thickness crack (through crack). For approximating the field variables and its derivatives the moving least square (MLS) technique is utilized. The problem domain is discretized into a mesh of elements where each element is considered as a control volume (CV). The center of CVs are considered as computational points where the unknown variables are associated with. The equilibrium equations of each CV are written based on the stress resultant forces acting on the boundaries of CV where the first order shear deformation theory (FSDT) is implemented in the formulation. Some benchmark problems of plate with through cracks are solved by the present method and the obtained results are compared with the results of analytical and XFEM numerical methods in order to demonstrate the accuracy of the present formulation. These comparisons illustrate the accuracy of predictions of the present solution method. Nevertheless, it is found that the formulation is free of shear locking property which greatly facilitates the cracked plates analysis due to its dual capabilities of analyzing both thin and moderately thick cracked plates.