Deformed boundaries determined by the method of caustics

Abstract

The caustics formed by illuminating straight deformable boundaries by a parallel, convergent or divergent light beam were used to determine the load distribution along these boundaries. A universal method based on the characteristic geometric elements of the corresponding caustics (pseudocaustics) was developed. This method leads to a system of singular integral equations, which was solved numerically by a collocation method of successive approximations. The singular points of the integrals were removed by integrating along regular paths determined by the optically obtained pseudocaustics. This procedure constitutes a new combined numerical-experimental method for solving singular integral equations with singularities of the Cauchy type. Several examples are given to show the potentialities of the method.