Variable Kinematic Shell Elements for the Analysis of Electro-Mechanical Problems

The present article considers the linear static analysis of both composite plate and shell structures embedding piezoelectric layers by means of a shell finite element with variable through-the-thickness kinematic. The refined models used are grouped in the Unified Formulation by Carrera (CUF) and they permit to accurately describe the distribution of displacements and stresses along the thickness of the multilayered shell. The shell element has nine nodes and the mixed interpolation of tensorial components (MITC) method is employed to contrast the membrane and shear locking phenomenon. The governing equations are derived from the principle of virtual displacement (PVD) and the finite element method (FEM) is employed to solve them. Cross-ply multilayered plates and cylindrical shells embedding piezoelectric layers are analyzed with simply-supported boundary conditions and subjected to sensor and actuator configurations. Various thickness ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in literature and the analytical solutions obtained using the CUF and the Navier’s method. From the analysis, one can conclude that the shell element based on the CUF is very efficient and its use is mandatory with respect to the classical models in the study of multilayered structures embedding piezo-layers.