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 s rr ¼ t rq ¼ 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-diameterto-plate-thickness ratio of only two, result in some threedimensional effects, these are relatively small and the agreement between the thermoelastic values, those from recorded strains and FEM-predicted surface stresses is good.

Determining Individual Stresses Throughout a Pinned Aluminum Joint by Reflective Photoelasticity

“…If desired, one could coat the pin and thereby evaluate its stresses. The general idea of combining a stress function with measured data is applicable to other experimental approaches of stress/strain analysis [26][27][28][29][30][31][32][33][34][35][36][37][38]. While the present use of 48 coefficients and 440 side conditions was based on previous experience, Refs.…”

“…While the present use of 48 coefficients and 440 side conditions was based on previous experience, Refs. [35][36][37] provide systematic rational for selecting an appropriate number of coefficients. In addition to correlating experimental results with those from 2-and 3-dimenional FEM, subsequent (unpublished) related research includes applying the present technique to stress analyze a pinned wood connection [23], as well as assessing the influence of varying the number and source locations of the measured input data.…”

“…The current use of 48 coefficients was influenced by experience rather than any highly systematic study [22,23], but subsequent efforts employ rational approaches for selecting essentially a minimum or optimum number of coefficients [35][36][37]. Present results use the known boundary conditions of equation (9) with edges BC, DE, EF and FG of Fig.…”

“…Stresses in a composite have been determined by combining measured strains (from strain gages) and a stress function [28], whereas Rhee and Rowlands [29] combined moiré-measured displacements and a stress function to evaluate stress intensity factors in orthotropic composites. Several articles [30][31][32][33][34][35][36][37][38] have utilized a stress function to evaluate stresses or stress intensity factors from measured temperatures. In all of these cases, the measured data as processed using a stress function agree well with those from FEM, strain gages or theory.…”

Experimentally Determined Stresses Associated with Elliptical Holes Using Polar Coordinates

“…The latter TSA concept again uses complex variables and mapping. Previous stress analyses that utilise an Airy stress function in polar coordinates (real variables) to process recorded temperature information are restricted to round holes [31, 32]. The authors are unaware of prior utilisation of polar coordinates to experimentally evaluate the stresses associated with holes or notches, which are other than circular.…”