A 2ND-ORDER SOLUTION OF SAINT-VENANT PROBLEM FOR AN ELASTIC PRETWISTED BAR USING SIGNORINI PERTURBATION METHOD

We use Signorini's expansion to analyse deformations of a straight, pr ismatic, isotropic, stress free, homogeneous body made of a second-ord er elastic material and loaded as follows. II is first twisted by an i nfinitesimal amount and then loaded by applying surface tractions, wit h 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 se mi-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 infini tesimal twist. It is shown that the Clebsch hypothesis is not valid fo r this problem. A second-order Poisson's effect, no of the Saint-Venan t type, and generalized Poynting effects may also occur in these probl ems.