Separating Stresses Thermoelastically in a Central Circularly Perforated Plate Using an Airy Stress Function

Abstract

Abstract: Thermoelastic stress analysis (TSA) is a contemporary full‐field, non‐contacting method of experimental stress analysis. In a cyclically loaded structure which experiences adiabatic and reversible conditions, the measured local change in temperature is proportional to the change in stress. Under isotropy, the technique measures information on the sum of the principal stresses. As engineering analyses often necessitate knowing the individual components of stress, additional experimental methods or information are frequently required to ‘separate the stresses’. The ability to evaluate individual stresses reliably in a uniaxially loaded finite plate with a central circular hole from TSA‐recorded information without supplementary experimental data is demonstrated here. Measured temperature data are combined with an Airy stress function and some limited traction‐free conditions. The present inverse technique does not presuppose knowledge of the external geometry or boundary conditions, overcomes the traditional difficulties of unreliable edge data, and reduces the number of coefficients needed by satisfying the traction‐free conditions analytically on the edge of the hole. Particular attention is paid to determining a realistic value for the needed number of Airy coefficients.