Torsion of a Truncated Conically Layered Elastic Cone

We obtain the exact solution of the problem of torsion of an elastic conically layered truncated cone. The elastic constants of its layers undergo jumpwise changes on the conical surfaces. The external conical surface is loaded by tangential torsional stresses. The end face of the cone is either restrained or free of loads. The conditions of perfect contact between the layers of the cone are satisfied. The solution of the problem is constructed with the use of integral transforms applied directly to the equation of equilibrium in torsion. We construct a recursive dependence between the constants of solutions of the differential equation of our problem for the neighboring layers. This gives us a possibility to make the number of equations used to determine the constants of solutions independent of the number of layers. The method applied for the solution is presented in detail for the special cases of stratification for which the dependence of stresses on the ratio between the shear moduli of the neighboring layers is established. © 2014, Springer Science+Business Media New York.