Photoelastic‐numerical treatment of Beltrami‐Michell boundary value problems

Abstract

One of the main challenges of using photoelasticity has always been its complexity to determining all stress components, for it provides an unfinished solution. Indeed, the use of the Beltrami-Michell Boundary Value Problem remains of practical interest for the study of the stress-separation, when complemented by the photoelasticity analysis to acquire the Dirichlet conditions. The synergy of both is enhanced with the use of Finite Difference Method to work out a photoelasticnumerical hybrid method for stress analysis under plane conditions. On the other hand, while for photoelasticity specially, annular disks under diametral compressive load are usually used as standard models allowing to check the performance of any developed method; because theoretical solutions exist. A comprehensive study has been carried out to show the photoelastic-numerical method in order to investigate the in-plane stress distribution using isochromatic values only on the boundaries of an annular object subjected to diametral compression. Compared with a reference work, the obtained results are more than concluding. The method is fast in the analysis for a low cost.