Deformed boundaries determined by the method of caustics

Author:

Theocaris P S1,Razem C1

Affiliation:

1. Department of Theoretical and Applied Mechanics, The National Technical University, Athens

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.

Publisher

SAGE Publications

Subject

Applied Mathematics,Mechanical Engineering,Mechanics of Materials,Modelling and Simulation

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