Extending TSA with a Polar Stress Function to Non-Circular Cutouts

This paper extends ability to thermoelastically stress analyze components containing other than circular discontinuities. Combining recorded temperatures with a stress function for stress analysis (i.e., TSA) has proven to be effective. Previous publications applied TSA to members having various shaped cutouts by employing a stress function in complex variables [1]. A shortcoming of such an approach is that one can typically evaluate the stresses only incrementally around the entire edge of a hole or notch. Real variables are also easier to use than complex variables and a general series-form of the Airy stress function exists in (real) polar coordinates which enables the stresses be determined simultaneously around an entire cutout. The TSA approach using polar coordinates is illustrated here for the case of an elliptical hole in a finite tensile plate. Little information is available for such finite situations, purely analytical solutions are extremely difficult for finite geometries, and both theoretical and numerical approaches are challenging if the external loading is not well known. The number of Airy coefficients to retain is evaluated experimentally, and the TSA results are substantiated independently.