Singularity characteristic analysis for a V-notch in angularly heterogeneous moderately thick plate

Abstract

The stress singularity order and characteristic angular function for a V-notch in a moderately thick plate with angularly heterogeneous elastic property are investigated where the first-order shear deformation plate theory is used. By introducing the typical terms in the asymptotic expansions of the displacement field near the singular point, the governing equations and radial boundary conditions of an angularly heterogeneous V-notch in a moderately thick plate are transformed into the characteristic ordinary differential equations with varying coefficients, which are uncoupled with respect to the in-plane displacement, anti-plane displacement and rotating angle of the mid-plane, respectively. The singularity order and characteristic angular function of the V-notch are yielded by applying the interpolating matrix method to solve the established characteristic equations. The present method is suitable for the singularity characteristic analysis for the V-notch under different radial boundary conditions and different elastic modulus variation models. The singularities for the V-notches in three differential elastic modulus variation models are evaluated and their singularity orders are compared. It is found that the stress singularity for the V-notch whose elastic modulus varies as a power function is the most serious, while the one whose elastic modulus varies as an exponential function is the weakest when free–free radial boundary condition is considered. The stress singularity for the V-notch under clamped–clamped boundary condition is the weakest, however, the one under free–free boundary condition is the strongest when the elastic modulus varies as a power function.