Stress singularity analysis for the V-notch with a novel semi-analytical boundary element

The stress singularity occurs near a V-notch. The conventional boundary element method can only approach to the exact results with gradually refined mesh. In this paper, by introducing the Williams asymptotic expansion, a novel semi-analytical element is proposed. The new element models the geometry and the known physical fields with linear interpolation, while the unknown physical fields will be simulated by the asymptotic expansion. The new element introduces six unknowns: two displacement components at the notch tip and four amplitude coefficients in the asymptotic expansion. By collocating two semi-analytical elements on both sides of the notch, the unknown displacement fields can be depicted with the asymptotic expansion, while the remaining part can be modeled by means of the conventional boundary element. The direct integral method and singular integral separation technique are adopted for the different kinds of singular integrals in the boundary integral equations. After the system of equations are solved, not only the unknown boundary physical quantities, but also the first four amplitude coefficients in the asymptotic expansion can be determined at the same time. The stress intensity factors can be determined from the amplitude coefficients in the asymptotic expansions without any post processing.