A Three-Layer Quasi-3D Finite Element Analysis for Smart Actuation on Sandwich Plates

Background The quasi-3D finite element model includes the smart actuation on a three-layer sandwich plate with laminated composite face-sheets. In the model, the face-sheets are represented as Reissner-Mindlin plates and the core is modeled as a three-dimensional continuum. Purpose This representation allows accurate modeling for a wide range of core types. In this model, the electrical constitutive relations of piezoelectric layers are included in the formulation of the face-sheets. In previous publications, this quasi-3D finite element formulation has demonstrated some advantages in comparison with solid finite element models. The aspect ratio of three-dimensional elements can make it rather inconvenient to use on very thin faces-sheets, which makes the number of degrees of freedom very high. Methods Analytical through-thickness integration of the energy expressions is used to reduce the three-dimensional problem to two dimensions for the evaluation of mass and stiffness matrices. In the same way, the analytical integration of the electrical voltages work applied to the piezoelectric layers produces the piezoelectric actuation force vector. Result This research assesses the accuracy of the proposed model for dynamic responses of sandwich plates using a broad range of core-to-face-sheet stiffness ratio. Conclusions The numerical results show that deflections promoted by the voltage applied to piezoelectric layers of the sandwich plate are very small, even if the core is very flexible. The results also indicate that the core flexibility strongly affects the natural frequencies of the higher bending modes.