Evaluation of Concentrated Oblique Load at the Apex of a Wedge by the Method of Caustics
Identifiers and Pagination:Year: 2012
First Page: 90
Last Page: 99
Publisher Id: TOMEJ-6-90
Article History:Received Date: 06/06/2012
Revision Received Date: 26/07/2012
Acceptance Date: 27/07/2012
Electronic publication date: 24/8/2012
Collection year: 2012
open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: (https://creativecommons.org/licenses/by/4.0/legalcode). This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The experimental method of caustics was used for the evaluation of the stress-singularities created by concentrated oblique load applied at the apex of a wedge or on the horizontal straight boundary of a half-plane. The wedge 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 concentrated 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 strongly illuminated and forms a caustic. It was proved that the shape and size of the caustic depend on the stress singularity at the point of application of the load. The parametric equations of caustics created by such a singularity were studied in relation with the loading mode of the wedge. Thus, by measuring the dimensions of the caustic, one can evaluate the state of stress at the singularity. The experimental evidence, based on the above method on Plexiglas (PMMA) wedges, corroborated existing elastic theories concerning the order of singularities for concentrated loads. The relations for the calculation of the load, the components of stress and the concentration factor based on the geometrical characteristic of caustics, which were reflected from the front face of the wedge, were given.