Abstract :
In the relaxed Saint-Venant’s elastic problem, in virtue of Saint-Venant’s Postulate, the pointwise assignments of tractions
at cylinder plane ends are replaced by the assignments of the corresponding resultant forces and moments. The solution
indeterminacy so introduced is traditionally overcome by postulating that some specific features characterize the
elastic state. In this work a relaxed incremental equilibrium problem is posed for a heterogenous anisotropic cylinder,
whose tangent elasticity tensor field possesses the usual major and minor symmetries, is positive definite, independent from
the axial coordinate and endowed with a plane of elastic symmetry orthogonal to the cylinder axis. Symmetry has been
consistently employed to formulate the basic problems of extension, bending, torsion and flexure as symmetric and antisymmetric
problems respectively. It is shown that Saint-Venant’s postulate, momentum balance and symmetry are sufficient,
without resorting to any a priori assumption, to determine the general form of the displacement field and to
remove the solution indeterminacy.
