Further Work on the General Three-Dimensional Photoelastic Problem

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Abstract
It is known that purely photoelastic procedures cannot solve the general three-dimensional stress problem. Photoelasticity furnishes data from which only the principal shears can be determined, but not the principal stresses. A new, general, and practical method of solution which has been described previously (1, 2) is reviewed briefly, and possible variations in procedure are discussed. This method combines the photoelastic data from frozen stress patterns with a numerical integration of one of the differential equations of equilibrium in Cartesian coordinates. The actual principal stresses at each point of a homogeneous and isotropic body of arbitrary shape subjected to a general system of loads are thereby determined. The method has been applied previously to a sphere subjected to diametral compressive loads of 172 lb. The present paper contains the results from a second sphere subjected to 79.6 lb which show that the degree of reproducibility of results is high. Very good agreement is also shown to exist with a theoretical solution of the same problem by Sternberg and Rosenthal (3) The paper also contains the solution of a short rectangular parallelepiped loaded through a small flat circular die. The investigation was conducted in the Photoelastic Laboratory of the Mechanics Department of Illinois Institute of Technology.

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