Some implications of an elastic-electrostatic analogy on certain path-independent integrals

Abstract Certain similarities in the structure of the laws governing a class of electrostatic and elastostatic problems are discussed. A variety of path-independent integrals which must apply to these electrostatic phenomena are deduced on the basis of these similarities. As an illustrated example of their use, these integrals are used to generate a novel solution for a well-known problem in the electrostatics of dielectrics, that of the behavior of the induction near the tip of a finite length straight crack in an infinite body subject to uniform applied inductions far from the crack. Finally, observations on further extensions of these analogies, and upon associated path-independent integrals, are also discussed.