Multiple-crack analysis with the quasi-higher-order symmetric Galerkin boundary element method

This paper describes the application of the symmetric Galerkin boundary element method (SGBEM) for the analysis of a two-dimensional linear elastic crack problem. The direct SGBEM for the multiple-crack problem is derived using the Betti reciprocal theorem, resulting in a completely symmetric matrix. The auxiliary fictitious state is used to obtain the equations. This approach can deal with any number of traction-free cracks within a single domain. Two-stage interpolation method called the ‘quasi-higher-order element method’ (QHOEM) is then proposed to solve the double integrals. In the initial stage, it uses higher-order elements to interpolate the field variables and, for the numerical integration involved, it further uses interpolation functions to decompose the higher-order elements into lower-order elements so that the existing analytical integration can be applied. Thus, it can be embedded into the present codes with ease and also reduces the computational cost. A finite rectangular plate containing a slanting crack and a kinked crack has been analysed to check the accuracy of the proposed method. A load-carrying fillet welded joint containing several cracks is then analysed, and the stress intensity factors at the crack tips are found to be in complete agreement with the dual-boundary-element method results.