Exact 3D piezothermoelasticity solution for buckling of hybrid cross-ply plates using state space approach

Abstract

A three dimensional exact piezothermoelasticity solution is presented for buckling of simply-supported symmetrically laminated hybrid plates with elastic substrate and piezoelectric layers. Buckling is considered under thermal load in open as well as closed circuit conditions of the piezolayers. A mixed formulation is used to form the governing equations for buckling mode in terms of eight primary variables: Three displacements, electric potential, three transverse stresses and the transverse electric displacement. Using double Fourier series expansion of the entities, which satisfy the end conditions, the governing equations is reduced to a z-invariant state equation with the state vector consisting of the the above eight variables. The state vector at the bottom of the laminate is related to that at its top through a global transfer matrix using continuity/jump conditions at the layer interfaces. The eight homogenous boundary conditions at the top and the bottom of the plate are used to set up four homogeneous equations for the three displacements and electric potential/electric displacement at the bottom. The determinant of their coefficient matrix is set to zero to obtain the buckling temperature/potential. Benchmark results are presented for hybrid highly inhomogeneous test plate, cross-ply composite plate and sandwich plates. The effect of the exclusion of the prebuckling strains in the formulation on the buckling temperature is investigated. The effects of thickness parameter, aspect ratio and the electric boundary conditions on the buckling loads are illustrated. The enhancement of buckling temperature by the application of actuation potential is discussed.