Hybrid stress analysis of a near-surface circular hole in finite structures

The ability to stress-analyze complicated structures from recorded load-induced temperatures is demonstrated. The considered structures have a near-surface hole and subjected to a concentrated load. The complexity of the structure is simplified by conformal mapping, the traction-free condition on the boundary of the hole is analytically satisfied by analytic continuation, and the equilibrium and compatibility conditions are satisfied by means of Airy stress function in complex-variable formulation. For isotropic member that is cyclically loaded within its elastic range, the produced in-phase temperature variations are linearly proportional to the local changes in the normal stresses. Even though no recorded thermal data were used at or near to the edges, the present hybrid method simultaneously separates the load-induced temperatures into the individual stress components, determines reliably the boundary stress and hence the stress concentration, and smooths the measured input data. Unlike prior capabilities of using geometrical symmetry to simply the stress function representation, the present analysis retains all the terms in the stress functions. Therefore, the considered hybrid stress analysis approach of such complex structures extends significantly the applicability of thermoelastic stress analysis compared to prior capabilities and is considered to be the most complicated formulation of the hybrid complex-variable method to date. To support the reliability of the present hybrid method, the results were compared with finite element predictions and previous results based on Mitchell solution.