Boundary state method in solving torsion problems for transversely isotropic bodies of revolution

Abstract

The aim of this work is to develop the method of boundary states for the class of torsion problems as applied to transversely isotropic elastic bodies of revolution. Efforts, displacements, or a combination of both are used as twisting conditions at the border. Proceeding from the general solution to the problem of cross section warping, the basis of the space of internal states is formed. The search for an internal state is reduced to the study of the boundary state isomorphic to it. The solution is a Fourier series. The proposed technique is implemented in solving the first main problem for a body in the form of a truncated cone; the second main problem for a circular cylinder; and the main mixed problem for a non-canonical body of revolution. The solution was verified and the calculation accuracy was assessed. The obtained characteristics of the elastic field have a polynomial form. The elastic field in each problem satisfies the specified boundary conditions in the form of their distribution over the surface and does not satisfy them only in the integral sense.