Thermoelastic Determination of Individual Stresses in Vicinity of a Near-Edge Hole Beneath a Concentrated Load

Abstract

Thermoelastic data are combined with an Airy stress function to determine the individual stresses on and near the boundary of a circular hole which is located below a concentrated edge-load in a plate. Coefficients of the stress function are evaluated from the measured temperatures and the local traction-free conditions are satisfied by imposing \( {\sigma_{r{\rm{r}}}} = {\tau_{r\theta }} = 0 \) analytically on the edge of the hole. The latter has the advantage of reducing the number of coefficients in the stress function series. The method simultaneously smoothes the measured input data, satisfies the local boundary conditions and evaluates individual stresses on, and in the neighbourhood of, the edge of the hole. Attention is paid to how many coefficients to retain in the stress function series. Although the presence of high stress concentration factors, together with a hole-diameter-to-plate-thickness ratio of only two, result in some three-dimensional effects, these are relatively small and the agreement between the thermoelastic values, those from recorded strains and FEM-predicted surface stresses is good.