Singularity analysis for a V-notch with angularly inhomogeneous elastic properties

Abstract

Stress singularity of a V-notch with angularly inhomogeneous elasticity is studied in this work. The characteristic differential equations with respect to the orders of the stress singularity for the V-notch problem are derived by using of asymptotic expansion technique. The boundary conditions on the two radial edges of the V-notch are then expressed by the combination of the orders of the stress singularity and the characteristic angular functions. With the manipulation, the problem is transformed into solving the characteristic ordinary differential equations with variable coefficients under the corresponding boundary conditions, which are solved by the interpolating matrix method developed by us before. The method and treatments presented are suitable for the singularity analyses of the V-notches with any angularly inhomogeneous material properties under the plane and anti-plane loading. As examples, the singularities of the V-notches with three differential types of angularly variable elasticity moduli are evaluated and compared for their orders of the stress singularity.