THE SAINT-VENANT PROBLEM FOR MONOCLINIC PIEZOELECTRIC CYLINDERS

The Saint-Venant problem is formulated in the framework of the linear theory of piezoelectricity for homogeneous, monoclinic. piezoelectric cylinders. A relaxed version of this problem is stated and is proved t o be well-posed under Clebsch- type assumptions. The general solution of the related problem is explicitly given. up to the solution of a tw o-dimensional Dirichlet-type problem involving two scalar fields, and is decomposed into five ''fundamental'' solutions. Finally, a Saint-Ve nant principle, related to the present relaxed formulation of the piez oelectric Saint-Venant problem, is established. In particular, the exp onential decay along the cylinder asis of the free energy stored into a piezoelectric cylinder, subject to self-equilibrated loads on one ba se only, is proved.