Transient Galerkin finite volume solution of dynamic stress intensity factors

Abstract

Transient Galerkin finite volume method (GFVM) is developed to solve time-dependent problems and analysis of the dynamic stress intensity factors (DSIFs) for cracked problem. An interesting feature of the developed method is its matrix free operations; therefore, it obviously reduces the computation workloads for dynamic cases with small time marching. The two-point displacement extrapolation method is used for calculating the stress intensity factors (SIFs). To show the ability of this method, the structural problem, such as a beam under dynamic load, is considered as the first case study. The computed transient deflections are used for evaluating the accuracy of the GFVM in comparison with the results of the explicit finite element method (explicit-FEM) and meshless method solvers. A comparison of the CPU time consumption of the GFVM and explicit-FEM solvers shows that the GFVM entails lesser time consumption than the explicit-FEM, without reducing the accuracy of the results. In the second case study, the SIFs are computed for plate with inner crack under constant loading. For the third and fourth case study, the ability of the proposed GFVM solver to cope with DSIFs for a plate with an edge crack and L-shape plate with an inclined crack under dynamic load were tested. The comparison indicates that the GFVM not only provide compatible accuracy close to other common numerical solvers, also offers considerable CPU-time consumption, in comparison with the methods that requires matrix manipulations.