Zigzag theory for buckling of hybrid piezoelectric beams under electromechanical loads

Abstract

A new efficient coupled one-dimensional (1D) geometrically nonlinear zigzag theory is developed for buckling analysis of hybrid piezoelectric beams, under electromechanical loads. The potential field is approximated layerwise as piecewise linear. The deflection is approximated to account for the normal strain due to electric field. The axial displacement is approximated as a combination of a global third-order variation and layerwise linear variation. It is expressed in terms of three primary displacement variables and a set of electric potential variables by enforcing exactly the conditions of zero transverse shear stress at the top and bottom and the conditions of its continuity at the layer interfaces. The governing coupled nonlinear field equations and boundary conditions are derived using a variational principle. Analytical solutions for buckling of simply supported beams under electromechanical loads are presented. Comparisons with the exact 2D piezoelasticity solution establish that the present zigzag theory is very accurate for buckling analysis.