SINGULARp-VERSION FINITE ELEMENTS FOR STRESS INTENSITY FACTOR COMPUTATIONS

Abstract

SUMMARYThe finite element analysis of linear elastic fracture mechanics problems is complicated by the presence of the singular and finite non-singular stress distributions in the crack tip region. The availability of a constant stress term in addition to the singular term in the standard h-version singular finite elements is insufficient to model the finite nonsingular stress zone. A p-version singular finite element capable of modelling the higher-order non-singular stress terms in addition to the singular term and the constant term is presented. The formulation for the displacement substitution technique for computing the stress intensity factors using singular p-version triangular finite elements is developed. Unlike the standard h-version formulation, the stress intensity factors computed using the p-version displacement substitution technique do not depend on the specific arrangement and length of the quarter point elements, and require simple mesh designs as well as fewer number of degrees of freedom. Numerical studies comparing the convergence of the stress intensity factors computed by the p-version method against other available alternatives such as the h-version method and the contour integral method are presented to demonstrate the effectiveness of the present developments.

Stress intensity factor error index for finite element analysis with singular elements

“…In any case, the validity of m can be judged by the discrepancy between plots on a figure like Figure 5 and the origin when L/a is made small, in case that analytical SIF solutions are known. Note that the m presented in the numerical examples in this paper satisfies this condition (at least for K I whose accuracy is important for practical problems) and that our error index approximates the SIF error closely for ∆K Recently, Rahulkumar et al [11] proposed an approach to use higher order SEs for an accurate SIF evaluation with a coarse mesh division. However, judging from the results of mixed mode problems discussed in the previous section, it still remains necessary to try to find a proper mesh refinement in the θ direction (selection of m) even though higher order elements are used.…”

Direct Evaluation of the Stress Intensity Factors for the Single and Multiple Crack Problems Using the P-Version Finite Element Method and Contour Integral Method

“…In the three-dimensional elastic viscoelastic problems in the hydraulic structure [20], seepage analysis [21], the mechanical response of the arteries in the field of biomechanics of bone problems [22] and sandwich and Kirchhoff plate deformation analysis [23,24], the P-FEM has been also successfully applied. The application of P-FEM in elastic fracture mechanics (including the calculation of SIF and predicting the growth of irregular crack fronts) can be found in references [25][26][27][28][29].…”

Enriched partition-of-unity finite element method for stress intensity factors at crack tips

“…Uni-axial tension rð¼ 1:0Þ is applied along the shorter edges. The same problem was previously solved by Szab o et al [14] using the Contour Integral method, and separately by Rahulkumar et al [15] and Tada et al [16] using singular p-version FEM. Their results are used as benchmarks.…”