Abstract
This paper focuses on tackling the two drawbacks of the dual boundary element method (DBEM) when solving crack problems with a discontinuous triangular element: low accuracy of the calculation of integrals with singularity and crack front element must be utilized to model the square-root property of displacement. In order to calculate the integrals with higher order singularity, the triangular elements are segmented into several subregions which consist of subtriangles and subpolygons. The singular integrals in those subtriangles are handled by the singularity subtraction technique in the integration space and can be regularized and accurately calculated. For the nearly singular integrals in those subpolygons, the element subdivision technique is employed to improve the calculation accuracy. In addition, considering the location of the crack front in the element, special crack front elements are constructed based on a 6-node discontinuous triangular element, in which the displacement extrapolation method is introduced to obtain the stress intensity factors (SIFs) without consideration of orthogonalization of the crack front mesh. Several numerical results are investigated to fully verify the validation of the presented approach.
Highlights
Accurate computation of the stress intensity factors (SIFs) is of great importance for analysis of 3D fracture mechanical problems
In the application of the finite element method (FEM) or boundary element method (BEM) in crack problems, special crack front elements are usually employed to model the square-root distribution of the displacements nearby the crack front
SIFs of three modes obtained by our method show a high convergence rate as the number of elements increases
Summary
Accurate computation of the SIFs is of great importance for analysis of 3D fracture mechanical problems. For such problems, it is necessary to accurately calculate the SIFs, which can characterize the fracture property. E major difficulty in the calculation of SIFs is approximation of the displacement distribution nearby the crack front. In the application of the FEM or BEM in crack problems, special crack front elements are usually employed to model the square-root distribution of the displacements nearby the crack front. Many special crack front elements have been defined to capture the asymptotic behavior of a specific node in the FEM [1]. E crack front elements of the triangular type have not been found by authors [8, 9]. Due to the general geometric adaptability of the triangular mesh, a special triangular crack front element of which one edge lies in the crack front for the BEM is necessary
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