Analysis on Stress Singularity of Plane Joints With the Differential Quadrature Method

Abstract

A novel differential quadrature method (DQM) for analysis of the stress singularity index was proposed. Firstly, the radial asymptotic expansion scheme of the displacement field at the connection point of the plane joint was substituted into the governing equation of plane elasticity, and the eigenvalue problem of ordinary differential equations (ODEs) about the stress singularity index was obtained. Then, based on the DQM theory, the eigenvalue problem of ordinary differential equations was transformed into the eigenvalue problem of standard generalized algebraic equations. The stress singularity index at the connection point of the bi-material plane joint was calculated at one time, and the corresponding displacement and stress characteristic functions at the connection point were obtained at the same time. The numerical results show that, the DQM is correct in calculation of the stress singularity index at the connection point of the plane joint.