Saint-Venant's principles for anti-plane shear deformations of linear piezoelectric materials

This paper is concerned with investigation of the effect of mechanical/electrical coupling on the decay of Saint-Venant end effects in linear piezoelectricity. Saint-Venant's principle and related results for elasticity theory have received considerable attention in the literature but relatively little is known about analogous issues in piezoelectricity. The current rapidly developing smart structures technology provides motivation for the investigation of such problems. We examine the decay of Saint-Venant end effects in the context of antiplane shear deformations for linear homogeneous piezoelectric solids. For a rather general class of anisotropic piezoelectric materials, the governing partial differential equations of equilibrium are shown to be a coupled system of second-order partial differential equations for the mechanical displacement u and electric potential φ. The traction boundary-value problem with prescribed surface charge is formulated as an oblique derivative boundary-v...