Stress singularities at concentrated loads

TLDR: In this paper, the authors studied the stress singularity created by a concentrated load applied at the boundary of a half-plane by transforming it into an optical singularity by the optical method of caustics.

Abstract: The stress singularity created by a concentrated load applied at the boundary of a half-plane was studied by transforming it into an optical singularity by the optical method of caustics. The half-plane was considered to be elastic, isotropic and under generalized plane-stress conditions. According to the method of caustics, the light rays impinging normally at the thin plate are partly reflected from either the front or the rear faces of the plate. The reflected rays are deviated because of the important constraint of the plate at the vicinity of the applied load and the significant variation of the refractive index there. The deviated light rays, when projected on a reference screen, are concentrated along a singular curve which is, therefore, strongly illuminated and forms a caustic. It is shown that the shape and size of the caustic depends on the stress singularity at the point of application of the load. Thus, by measuring the dimensions of this singular curve, one can evaluate the state of stress at the singularity. The characteristic properties of the caustic created by such a singularity were studied in relation with the loading mode of the plate.