On the first boundary value problem of the photoelastic thin ring

Analytical solutions to the plane problems in terms of stresses for thin annular domains under compression loading are well known in several papers. Moreover, the large majority of the two-dimensional problems in the theory of elasticity are reducible to the solution of their boundary value problems. The two-dimensional photoelasticity methods easily provide the stress tensor components on the boundary, from one photograph only. The Beltrami-Michell equations with the Dirichlet photoelastic data state a well-posed hybrid problem in stress terms. It has been shown that the results obtained from the hybrid method developed in this paper, are applicable to any irregular shaped photoelastic domain of interest. Successful results have been obtained for more complicated forms and loads. The correctness of the results for the circular ring is confirmed and will be discussed in details.