Two-dimensional benchmark solution for buckling and vibration of simply supported hybrid piezoelectric angle-ply flat panels

Abstract

A benchmark 2D piezothermoelasticity exact solution is presented, based on state space approach for buckling and free vibration response of simply supported laminated hybrid angle-ply panels in cylindrical bending under initial in-plane thermo-electromechanical loads. A mixed formulation of governing equations for the incremental problem of buckling/vibration is presented in terms of eight primary variables: three displacements, electric potential, three transverse stresses, and transverse electric displacement. The entities are expanded in Fourier series that satisfy the end conditions. The governing equations reduce to a z-invariant state equation with the state vector of 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 angle-ply panel are used to set up four homogeneous equations for u, v, w, and Φ/Dz at the bottom. The determinant of their coefficient matrix is set to zero to obtain the buckling parameter or natural frequency. Benchmark results are presented for hybrid highly inhomogeneous test panel, composite panel, and sandwich panel. The effect of exclusion of the pre-buckling strains in the formulation on the buckling temperature is investigated. The effects of thickness parameter, and the electric boundary conditions on the buckling loads are illustrated. The enhancement of buckling temperature by the application of actuation potential is discussed. The present benchmark solution would help assess 1D theories for buckling of hybrid angle-ply panel.