Stress singularity analysis for orthotropic V-notches in the generalised plane strain state

Abstract

The singularity for the V-notch under the generalised plane deformation is investigated by the combination of the asymptotic analysis with the interpolating matrix method developed by part of the authors before. The displacement asymptotic expansions at the vicinity of the V-notch vertex are introduced into the equilibrium equations, which are transformed into a set of characteristic ordinary differential equations with respect to the notch singularity orders. The boundary conditions and interfacial compatibility conditions are also represented by the combination of the singularity orders and characteristic angular functions. The determination of the singularity orders and characteristic angular functions are transformed into solving the ordinary differential equations with variable coefficients, which are solved by the interpolating matrix method. The present method is suitable for the singularity analysis for isotropic and orthotropic V-notches. It is versatile for analysing the stress singularity of single material V-notches, bi-material V-notches, interface edges and cracks. The correctness of the results by the proposed method is ensured by the comparison with the published ones.