Body-force stress fields defined by caustic rosettes

Abstract

The method of reflected caustics was extended to the study of elastic fields due to body forces. It was shown that gage perforations create caustics under the influence of body forces which are different in shape and size than those developed in usual cases. The elastic solution of a perforated strip under the influence of an external loadp and body forcesqy was developed by defining a two-term Muskhelishvili complex stress function ϕ(z). The equations of the caustics and their initial curves were established. It was shown that as the body force intensity,q, was increased relative to the external loading,p, the classical two-lobe caustic for perforated strips without body forces evoluted to an open curve and, for a further increase ofq, to a three-lobe caustic. As the body force to external force ratio was increased this third lobe was rapidly increased, relative to the two principal lobes, whereas the position of the center of the caustic was displaced along the loading axis. The maximum diametersD _t of the caustics along the loading axis of the plate yield enough information for evaluating the body force intensity, if the mechanical properties of the material and the geometry of the optical set-up are known.