Stress Classification Lines Straight Through Singularities

Abstract

The paper considers geometries of pressure vessels and components for which the theoretical models contain sharp corners, representing singularities. The idea is proposed that a stress classification line passed straight through the singularity can yield linearized stresses that are applicable in pressure vessel design. Using elastic finite element analysis, details of the procedures by which this result can be achieved are given for two examples. One is a sharp corner at the toe of a fillet weld. Membrane and bending stresses are calculated directly in the toe plane, showing little or no dependence on mesh size. The other is an axisymmetric shell with a flat head and a sharp corner at the joint. The objective is to determine the primary-plus-secondary stress intensity on a Stress Classification Line (SCL) through the joint. Two methods are used. One is by determining the zone of valid SCLs and extrapolating the linearized stresses to the joint. The other is by calculating the linearized stresses directly on the SCL through the joint. Conditions for the use of the SCL through the joint for the shell/flat head model are established.