Photoelastic stress analysis of an elliptical hole in a thick plate subjected to uniform in-plane compressive Loading

A three-dimensional photoelastic analysis was conducted to determine the stress distribution and concentration around the periphery of a centrally located elliptical hole in a plate of finite thickness. The edge of the plate was subjected to a uniformly distributed compressive uniaxial in-plane load. The principle of superposition was employed to study the effect of uniform biaxial loading.Elliptical holes with five different major/minor axis ratios () ranging from 1.0 to 2.64 were investigated. Among the results of this study, it was established that the variation of the principal stresses at the edge of the hole is not linear across the plate thickness. It was also found that in loading the plate in a direction parallel to the major axis of the ellipse, the value of the maximum tangential principal stress () occurs in a plane other than the middle plane of the plate. However, in loading the plate in a direction either parallel or perpendicular to the major axis, the maximum transverse stress ( _z ) occurs at the middle plane. In addition, the maximum value of ( _z ) was about 20 percent of the maximum value of the tangential stress for all models tested. Furthermore, the effect of the bixial loading has reduced the value of the maximum tangential stress at the periphery of the hole as compared with uniaxial loading.As a three-dimensional theoretical solution does not exist for this problem, the present findings were correlated with the well established two-dimensional solutions.