A Second-Order Solution of Saint-Venant's Problem for an Elastic Pretwisted Bar Using Signorini's Perturbation Method

We use Signorini's expansion to analyse deformations of a straight, prismatic, isotropic, stress free, homogeneous body made of a second-order elastic material and loaded as follows. It is first twisted by an infinitesimal amount and then loaded by applying surface tractions, with nonzero resultant forces and/or moments, only at its end faces. The centroid of one end face is taken to be rigidly clamped. By using a semi-inverse method, the problem is reduced to that of solving two plane elliptic problems involving six arbitrary constants that characterize flexure, bending, extension, and torsion superimposed upon the infinitesimal twist. It is shown that the Clebsch hypothesis is not valid for this problem. A second-order Poisson's effect, not of the Saint-Venant type, and generalized Poynting effects may also occur in these problems. This revised version was published online in August 2006 with corrections to the Cover Date.