Symmetric-Galerkin boundary element analysis of the dynamic stress intensity factors in the frequency domain

A two-dimensional symmetric-Galerkin boundary integral formulation for the analysis of the dynamic stress intensity factors (DSIFs) in the frequency domain is described. A quadratic element is employed, allowing the use of the modified quarter-point element at the crack tip. For singular and hypersingular integrals, this formulation is decomposed into two parts: the first part is identical to those for elastostatics while the second part, at most, contains only logarithmic singularities. The treatment of the elastostatic singular and hypersingular integrals is carried out by means of an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Test examples are presented for the calculation of the DSIFs due to harmonic loading as well as wave scattering from a crack.