On the Saint—Venant torsion of elastic diatomic bars

Abstract

Basic equations of the theory of elastic diatomic media, each particle of which includes two different atoms, are given. Upon using the semi-inverse method of Saint—Venant, the shearing stresses in a cylindrical bar undergoing pure torsion are derived. Satisfaction of the balance equations and of the boundary conditions leads to a pair of Neumann problems of the potential theory solved by appeal to the classical Saint—Venant procedure. A numerical example involving an elliptic cross-section is solved and illustrated by a graph.