Algorithms for integrated photoelasticity —Axisymmetric cases

The method of integrated photoelasticity can be very elegantly used to determine the stress distribution in the case of torsionless axisymmetry. The mathematical formulation of such problems often yields Abel's integral equation. One of the ways to solve these equations is by approximating either the known (experimentally determined) or the unknown function by polynomials. The integral equation is thus converted to a system of linear, simultaneous algebraic equations with the coefficients of the approximating polynomial as unknowns. The degree of the approximating polynomial cannot be fixeda priori. The present paper postulates a scheme in which the degree of the approximating polynomial is increased in steps of one, starting from one. Solutions are computed for each degree of the polynomial. It is then possible to pick the solution from the available family of solutions. The computational aspect of the exercise can be very easily taken care of by the algorithms proposed and validated in this paper. The over-determined system of simultaneous equations is solved by the method of singular value decomposition (SVD). The proposed method is validated by first applying it to a test problem. Two cases, which are solved earlier, are then analyzed and the results are compared.