Determining the Stress Singularity Exponents of Plane V-notches in Bonded Bimaterial

摘要

This paper proposes a new way to determine the singularity orders of plane V-notch problems for engineering purpose. Based on the assumption of asymptotic displacement field near the V-notch tip, the governing equations of the elastic theory are transformed into the eigenvalue problems of ordinary differential equations (ODEs) around the notch tip. Then the interpolating matrix method established by the first author is further developed numerically to analyze the general eigenvalue problems of ODEs. Thus, the values of the singularity orders of the V-notches are determined through solving the corresponding ODEs by the interpolating matrix method. A numerical example is given to illustrate the accuracy and effectiveness of the method.