On the Theory of Rods. II. Developments by Direct Approach

This paper, which may be regarded as a companion to part I under the same title, is concerned with some aspects of both the nonlinear and the linear theories of elastic rods by a direct approach based on the theory of a Cosserat curve with two directors. Special attention is given to the development of the linear isothermal theory of straight isotropic rods of variable cross-section possessing two axes of symmetry. The resulting equations, which are applicable to rods of non-uniform section, separate into those appropriate for extensional, torsional and flexural modes of deformation. Application of these results to torsion and flexure of non-uniform rods are considered, and the problem of identification of constitutive coefficients for rods of uniform cross-section is dealt with at some length.