ABSTRACT
In this chapter, the author investigates thin-walled bodies, i.e., shells made of polarized ceramics. A polarized ceramic is an electroelastic material in which the link between deformation fields and internal electric fields is rather strong. The author assumes that displacements are small compared to the body thickness and the deformations, the mechanical stresses, and the electric field are directly proportional. A complete system of equations in electroelasticity theory consists of the equilibrium equations, the geometrical relationships between the components of the deformation tensor and those of the displacement vector, the constitutive relations, and the electrostatic equations. In electroelasticity theory, mechanical boundary conditions are formulated just like in the classical elasticity theory: the stresses, displacements, or mixed boundary conditions are specified at the boundary of the body. When the general theorems are fulfilled, problems on electroelasticity can be solved by variational methods. The variational methods and extremal estimates used in elasticity theory can be generalized to electroelasticity.
