Nonlinear zigzag theory for electrothermomechanical buckling of piezoelectric composite and sandwich plates

A coupled geometrically nonlinear efficient zigzag theory is presented for electrothermomechanical analysis of hybrid piezoelectric plates. The geometric nonlinearity is included in Von Karman sense. The thermal and potential fields are approximated as piecewise linear across sublayers. The deflection accounts for the transverse normal strain due to thermal and electric fields. The inplane displacements are considered to have layerwise variations, but are expressed in terms of only five primary displacement variables, independent of the number of layers. The coupled nonlinear equations of equilibrium and the boundary conditions are derived from a variational principle. The nonlinear theory is used to obtain the initial buckling response of symmetrically laminated hybrid plates under inplane electrothermomechanical loading. Analytical solutions for buckling of simply-supported plates under thermoelectric load are obtained for comparing the results with the available exact three-dimensional (3D) piezothermoelasticity solution. The comparison establishes that the present results are in excellent agreement with the 3D solution, when the pre-buckling transverse normal strain is neglected in the latter solution. The present results are also compared with the third order theory with the same number of displacement variables to highlight the positive effects of the layerwise terms in the displacement field approximations of the zigzag theory.