A LEAST-SQUARES APPROACH TO THE PRACTICAL USE OF THE HOLE METHOD IN PHOTOELASTICITY

The use of a small circular hole in elastostatic photoelasticity to de termine the stress tensor for any two-dimensional general loading situ ation is well known. The original application required fringe-order in formation at four points on the boundary, on opposite sides, along the axes of symmetry or principal stress directions. Later, to obtain gre ater precision, it was adapted so that fringe information inside the f ield could be used. This led to the also limited use of fringe-order i nformation from four points at 1.4 and two times the radius of the hol e, along the principal axes of symmetry. More recent work has even all owed the use of fringe-order information, at a fixed radius, anywhere along the two principal axes of symmetry. The greatest limitation of a ll of these approaches is that the majority of the fringe-order inform ation that is available, away from the axes of symmetry, is not utiliz ed at all. The current work presents a least-squares approach to the h ole method that allows the simultaneous use of information anywhere an d at any radial distance from the center of the hole inside the stress field. The objectives of this paper are: to apply the use of the leas t-squares approach to the hole method in photoelasticity; and, to show the consistent and practical application of this least-squares approa ch to the hole method. The achievement of this last objective permits the use of the values of specimen birefringence at a large number of p oints, taken from anywhere in the field around the hole.