A review of SIF evaluation and modelling of singularities in BEM

Abstract

Various boundary element method (BEM) based approaches to solve crack problems are discussed. The displacement method, J-integral method and the modi®ed crack closure integral (MCCI) method for the evaluation of the stress intensity factors (SIFs) are reviewed. Effects of partial and total modelling of singularities on the accuracy of the results have been presented. Elements capable of partial and total modelling of the wellknown square root singularities, variable order singularities, neighbouring variable order singularities, etc., are also reviewed. Case studies are included to illustrate the effectiveness of the various methods of calculation of the SIFs and the performance of the special elements.

Finite separation method: an efficient boundary element crack modeling technique

“…Although this problem can be easily handled for symmetric conditions [6], several crack modeling techniques have been proposed in the literature [4,7] for overcoming this difficulty for anti-symmetric situations.…”

“…The crack is treated as a single surface, where the crack face opening displacements (i.e., u) are the unknowns. Therefore, the DDM needs two sets of boundary integral formulations, and the hyper-singular term present in the traction equation requires special regularization methods for its integration [7].…”

The solution of Laplacian problems over L‐shaped domains with a singular function boundary integral method

“…This method was shown to be e cient and convergent at the optimal O(h) rate. A review of singular intensity factor evaluation and modelling of singularities in boundary integral methods is provided by Mukhopadhyay et al [19].…”

Fast multipole DBEM analysis of fatigue crack growth

“…There are several techniques available to evaluate the stress intensity factors (SIF) in BEM analysis [26]. In this work, the local mixed-mode SIFs are obtained from the near-crack-tip relative displacements using the one-point formula [27] as where P is the first node away from the crack tip Q; r is the distance from Q to P; u P n and u P s are respectively the opening and sliding displacements at node P; H is a constant defined as…”