Saint-Venant's problem and semi-inverse solutions in linear viscoelasticity

Abstract

This paper gives a treatment of Saint-Venant's problem for viscoelastic cylinders by reformulating the quasi-static equilibrium equations as a formal integro-differential operator over the cross section of the cylinder, with the axial variable playing the role of a parameter. Then, the conditions are established that the solution of Saint-Venant's problem may be treated as a generalized plane strain problem. Further, two classes of semi-inverse solutions to Saint-Venant's problem are described. These classes are used in order to obtain a solution for the relaxed Saint-Venant's problem.