The two-dimensional electroelasticity problems for multiconnected bodies situated under electric potential difference action

Solutions of the two-dimensional electroelasticity problems for infinitely long piezoelectric cylinders with cavities and cracks under electrical potential difference action are obtained using the Lekhnitskii’s generalized complex potentials. Herewith, piezoelectric bodies under consideration are free from mechanical loads, some (or all) openings and maybe the exterior boundary of the cylinders are fully covered by thin electrodes. Voltage differences are supplied on the electroded surfaces, the rest boundary surfaces are charge-free. In this case, the complex potentials are investigated. Boundary conditions are satisfied by the least-squares method. There are carried out numerical investigations of behaviour of some basic electroelastic characteristics in a circular hollow cylinder and in an infinite body with two longitudinal cavities and a charge-free plane crack. New electromechanical regularities of influence of material properties, geometrical characteristics of considered regions on values of electroelastic state characteristics and the stress, electric displacements and tensions intensity factor k1k1 are determined.