Least squares asymptotic analysis of photoelastic data from stress concentration regions in plane problems

Abstract

A complete separation of stresses throughout the entire stress concentration region near notches in plane, isotropic, linearly elastic plates is achieved using only conventional, easily obtained photoelastic (difference and directions of principal stresses) data. These data are analysed by a special least squares technique based on previously derived equations which describe the asymptotic character of the rapidly varying stress field near the root of the notch. The paper demonstrates the ability of the technique to predict stress concentrations as well as individual stresses accurately using only a small amount of data of typical experimental accuracy from arbitrary data points within the stress concentration zone.