Three-dimensional analysis of some symmetric hybrid piezoelectric laminates

The present paper studies 3D responses of a kind of hybrid laminates. The l aminates consist of a nonpiezoelectric layer with a number, of symmetricall y covered piezoelectric layers possessing 6mm material symmetry. The top an d bottom surfaces of the laminates are traction free, and the edge boundary is free of any transverse shear forces. In the first place, an approximate 2D model including the charge equation of electrostatics is proposed on th e basis of the classical Kirchhoff hypothesis. Then, it is shown that the c orresponding SD solution can be generated immediately, provided the solutio n of the 2D model is obtained. The 3D solution, satisfies all field equatio ns and surface or interlayer conditions;: the only restriction is that the mechanical and electric edge boundary conditions are generally fulfilled in an average manner. As examples, explicit solutions are given Sor infinite long laminated strips and for arbitrarily shaped laminates with free bounda ries. In both cases, however, the electric boundary condition is satisfied exactly, and therefore, the solutions are exact in Saint Venant's sense. MS C (1991): 73C02, 73K12, 73R05.