Analysis of laminated composite structures with embedded piezoelectric sheets by variable kinematic shell elements

Abstract

In this article, the static analysis of multilayered shell structure embedding piezoelectric layers is performed using some advanced theories, obtained by expanding the unknown variables along the thickness direction using equivalent single-layer models, layer-wise models, and variable kinematic models. The variable kinematic models permit to reduce the computational cost of the analyses by grouping some layers of the multilayered structure with equivalent single-layer models and keeping the layer-wise models in other zones of the multilayer. This model is here extended to the static analysis of electro-mechanical problems. The used refined models are grouped in the Carrera Unified Formulation, and they accurately describe the displacement field, the stress distributions, and the electric potential along the thickness of the multilayered shell. The shell element has nine nodes, and the mixed interpolation of tensorial components method is used to contrast the membrane and shear locking phenomenon. The governing equations are derived from the principle of virtual displacement, and the finite element method is employed to solve them. Cross-ply plates and shells, with piezoelectric skins and simply supported edges, subjected to bi-sinusoidal mechanical or electrical load are analyzed. Various aspect ratios and radius-to-thickness ratios are considered. The results, obtained with different theories within Carrera Unified Formulation context, are compared with the elasticity solutions given in the literature. From the results, it is possible to conclude that the shell element based on Carrera Unified Formulation is very efficient in the study of electro-mechanical problems of composite structures. The variable kinematic models combining the equivalent single-layer with the layer-wise models permit to have a reduction of the computational costs, with respect to the full layer-wise theories, preserving the accuracy of the results in localized layers.