A mathematical theory of elasticity for photoelastic experimental hybrid method

In this paper, the mathematical theory of elasticity that enables the construction of representative stress functions for photoelastic experimental hybrid method (PEHM) is revisited and reviewed. PEHM has been shown as an important and powerful tool used by experimental stress analysts to predict the stress state in complex engineering structures. To demonstrate the utility of stress functions from the mathematical theory of elasticity in real engineering applications, the contact problem of a mechanical seal with a rectangular cross-section as well as a plate with a central hole are considered. It was found that when the stress functions are applied to the contact problem of a mechanical seal with rectangular cross section, the contact stresses on the upper side were larger compared to those on the front side. The highest stresses on the front side were concentrated in the region around the extrusion gap. When a comparison between theoretical and experimental stress concentration factors (SCF) was done, it was found that there was remarkable agreement between theoretical and experimental results. Therefore, the mathematical theory of elasticity from this study shows that it can provide stress functions that serve as an invaluable input tool to predict the SCF using the photoelastic experimental hybrid method.