Analytical closed-form solution to the stress distribution associated with a hole in finite plates subjected to tension has not been obtained yet. Wherefore, a method developed in this paper is based on a Beltrami-Michell methodology analyzing the Kirsch's problem under finite dimensions conditions of both plane stress and plane strain. This aimed ability is achieved by combining the Beltrami-Michell plane equations, isochromatic information on the boundaries only; and the finite difference method into an effectual hybrid method for analyzing rectangular plates of finite width with circular holes. Furthermore, the Beltrami-Michell methodology suggested may be applied on other plate and cut-out forms.

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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.

The town of Relizane was built near Oued Mina, upstream of which is erected a dam of Sidi M'hamed Benaouda; while the city was protected in its time by a dike dating from the colonial period. Local authorities have recovered the land near the floodplain by building a new dike replacing the old one. However, flood risks persist on the city. Flood risk management plans for this new area should be provided for better protection of citizens and property.