Nonlinear coupled zigzag theory for buckling of hybrid piezoelectric plates

Abstract

A coupled zigzag theory for hybrid piezoelectric plates, recently developed by the first author, is extended to include geometric nonlinearity in the Von Karman sense. In this theory, the potential field is approximated as piecewise linear across sublayers. The deflection approximation accounts for the transverse normal strain due to an electric field. The inplane displacements are assumed to follow a global third order variation across the thickness with a layerwise linear variation. The shear continuity conditions at the layer interfaces and the shear traction-free conditions at the top and bottom are enforced to formulate the theory 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 electromechanical loading. Analytical solutions for buckling of simply supported plates under uniaxial and bi-axial inplane strains and electric potential are obtained for comparing the results with the available exact three-dimensional piezoelasticity solution. The comparison establishes that the present theory is very accurate for buckling response of hybrid plates even for highly inhomogeneous lay-ups.