The Analysis of Three-dimensional Stress Singularities by using A Quasi-spherical Coordinate System

摘要

To avoid the inherent singularity of the spherical coordinates at their poles, a quasi-spherical coordinate system is developed. In this coordinate system, a finite element procedure is proposed to determine the three-dimensional singularities of stress at three-dimensional vertices in which the Cartesian displacement fields are proportional to the (+1)-th power of the distance from the vertices. The resulting global equation is a second order characteristic matrix equation. Two demonstrating problems are investigated. It can be seen that the formulation yield satisfactory results.