An Improved Reissner-Mindlin-Type Model for the Electromechanical Analysis of Multilayered Plates Including Piezo-Layers

Abstract

Dealing with multilayered plates including piezo-layers, this paper presents a mechanical model which allows an accurate description of both the in-plane displacement (zig-zag effect is included) and the transverse shear stress fields (interlaminar equilibrium is fulfilled). Moreover, it preserves the computational advantages of the standard Reissner-Mindlin finite element formulation. The electrical stiffnesses are taken into account through assuming a quadratic distribution along the thickness for the voltage field. Von K'ármán-type nonlinearities are considered. The weak form of the coupled system of governing equations, in the dynamic case, has been written by employing the principle of the virtual displacements. Approximate governing equations in the form of nonlinear systems of algebraic equations have been obtained for the particular case of finite element applications. Newton-Raphson linearization technique has been applied and the consistent tangent matrix has been derived. Explicit forms of the derived electromechanical arrays have been quoted in the form of an Appendix. Some numerical results are given to furnish a preliminary assessment of the novel model.