Calculation of Stresses Within the Boundary of Photoelastic Models

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Abstract
A method is proposed for the determination of the internal stresses in a two-dimensional system from data furnished by a photoelastic analysis. The method involves the numerical integration of the Laplace difference equation over a region with known boundary values by the iteration of a set of improvement formulas. The underlying theory is discussed briefly, reference being made to a more mathematical treatment appearing in another paper by the authors. New procedures for increasing the speed and accuracy of such computations are described and application is made to a typical photoelastic study. In this the complete system of internal stresses is computed, using the data obtained from the usual fringe photograph, without recourse to isoclinic lines, or other supplementary experimental measurements. The method is also applicable to other problems of potential theory which involve the vanishing of the Laplacian. This includes electric fields, steady-state heat conduction, shapes of membranes, and problems in hydrodynamics and gravitation.

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