Buckling enhancement of laminated composite structures partially covered by piezoelectric actuators

The buckling (eigenvalue) problem of biaxially compressed laminated plates and shallow cylindrical panels having two symmetric piezoelectrical (PZT) patches on the top and the bottom of laminates is considered. The analysis is carried out with the use of the classical laminate theory and of the first order shear deformation theory. The variable thickness of structures (the local positions of PZT patches) is described by piecewise constant step functions in one direction or in both directions due. Three different methods of the solution of the linear eigenvalue problem are proposed: the exact analytical solution, the approximate solution based on the definition of the Rayleigh quotient and the numerical 3D finite element analysis. For the approximate Donnell's theory of shallow panels two variational formulations of the eigenvalue problem are derived in the form of the Hu-Washizu functional (the Airy stress functions and transverse normal displacements) and in the form of the Legendre functional (displacements). The influence of geometric parameters of composite panels and PZT patches, piezoelectric effect, external electric voltage and laminate configurations (symmetric angle-ply and cross ply laminates) on buckling characteristics are discussed in detail. The analysis demonstrates evidently that the use of the local piezopatches should be considered as the buckling problem for structures with the non-uniform thickness distribution. The appropriate use of the local PZT patches should be always combined with the appropriate choice of the best (optimal) laminate configuration. The formulation system developed is suitable to other shell theories and to account for the analysis of thermal effects or the imperfection sensitivity.