Determining individual stresses around a near-edge hole in a plate subjected to an offset load using thermoelasticity

Abstract

The paper combines an Airy’s stress function in real, polar coordinates with the experimental method of thermoelastic stress analysis (TSA) to determine the individual stresses in an aluminum half-plane which contains a near-edge circular hole, the plate being subjected to a concentrated edge load away from the hole. The coefficients of the stress function are evaluated from the thermoelastically measured data using the least squares method. Imposing the traction-free conditions analytically, rather than discretely, on the edge of the hole significantly reduces the number of coefficients one must retain in the stress function, the number of equations involved in the least squares process, and in some cases the amount of measured input data needed. Problems such as the present one can also be solved from photoelastically recorded isochromatics. However, whereas the latter approach necessitates time-consuming iterative non-linear least squares, the present TSA-based scheme only requires linear least squares. TSA, which can be applied to the actual material of interest (no model or coating is needed, other than perhaps being painted flat black to enhance the uniformity and emissivity of the material) benefits from the availability of contemporary commercial systems capable of providing extensive amounts of data in a matter of minutes