تحلیل استاتیکی ورق‌های چندلایه کامپوزیتی با لایه‌های پیزوالکتریک

The Levy-type analytical solution is employed for the problem of bending of cross-ply and antisymmetric angle-ply piezoelectric hybrid laminated plates with at least two simply supported opposite edges. The governing equations of equilibrium are derived in the framework of the first-order shear deformation plate theory. The equations are classified according to the crystallography type of piezoelectric layers and a comprehensive discussion on limitations of the method for the analysis of this kind of structures is performs. Finally, the governing equations of equilibrium are solved analytically with the aid of the state-space approach. We concluded that during the analysis of piezoelectric hybrid laminated plates with Levy-type method, simultaneous applying of all electrical forces and moments is not possible (depending on type of lay-up, crystallography of piezoelectric layers, and expansion of electrical potential, some of electrical forces and moments may not be considered). In order to study the accuracy and convergence rate of the proposed method, several numerical examples are examined. The numerical results are compared with those obtained by the Navier method and those presented in the other published articles. It is found that the present results have very good agreements with those obtained by other methods.