CIRCULARLY CYLINDRICAL AND PLANE LAYERED MEDIA IN ANTIPLANE ELASTOSTATICS

In this paper we consider, within the framework of the linear theory o f elasticity, the problem of circularly cylindrical and plane layered media under antiplane deformations. The layers are, in the first insta nce, coaxial cylinders of annular cross-sections with arbitrary radii and different shear moduli. The number of layers is arbitrary and the system is subjected to arbitrary loading (singularities). The solution is derived by applying the heterogenization technique recently develo ped by the authors. Our formulation reduces the problem to solving lin ear functional equations and leads naturally to a group structure on t he set t of real numbers such that - 1 < t < 1. This allows us to writ e down the solution explicitly in terms of the solution of a correspon ding homogeneous problem subjected to the same loading. In the course of these developments, it is discovered that certain types of inclusio ns do not disturb a uniform longitudinal shear. That these inclusions, which may be termed ''stealth,'' are important in design and hole rei nforcements is pointed out. By considering a limiting case of the afor ementioned governing equations, the solution of plane layered media ca n be obtained. Alternatively, our formulation leads, in the case of pl ane layered media, to linear functional equations of the finite differ ence type which can be solved by several standard techniques.