Multicusp caustics formed from reflections of warped surfaces.

The optical method of caustics developed mainly for studying singularities in stress fields was extended to define quantitatively the slope variation of warped surfaces. The existing theory was concerned with the study of infinitesimal but abrupt variations of thickness in elastic and plastic stress fields containing stress singularities due to either loading or geometry. In this paper the theory of caustics was extended to study the warping of any surface due mainly to twisting loads- While the caustics developed in previous uses were generalized epicycloid surfaces with or without a single cusp line, in the cases studied in this paper multicusp surfaces were developed. The quantitative interrelationship between the shape and size of the caustic and the respective mode of twisting of the surface was established, and interesting properties of these surfaces were disclosed. Applications to twisted elliptic, triangular, and square elastic bars clearly illustrate the importance of the method.