A Finite Elements with Continue Transverse Electric Displacement for the Electro-Mechanical Analysis of Shell Structures

Because of their capability to adapt and/or sense to the external environment, so-called smart structures have attracted considerable research over the past few years. This capability leads to a wide range of applications, in particular in the aerospace field. Among materials that can be used, only piezoelectric ones have shown the capability to perform effectively both as actuators and sensors, and the possibility of a simple integration with composite structures. The present work deals with the analysis of multilayered plates and shells embedding piezoelectric layers as actuators and sensors, see Fig. 1. Finite elements with layer-wise capabilities are employed to ensure an accurate description of the mechanical and electric fields in the layers. It is essential to take into account the discontinuity of the mechanical and electrical properties at the layer interfaces. For these reasons, the use of classical plate theories based on Kirchhoff and Reissner-Mindlin hypotheses can lead to inaccurate results. Even if analytical models are available, the solution of practical problems often demand the use of computational methods such as the finite element method. To this aim, the refined shell elements, recently formulated by the authors on the basis of Carrera Unified Formulation (CUF), have been extended to the electro-mechanical problem. The governing equations are derived using the Reissner’s Mixed Varational Theorem (RMVT) extended to the electro-mechanical case, the original RMVT has been modified to account for ”only” interlaminar continous D3. Continuity of mechanical variables, such as transverse shear and normal stress components, has been discarded to provide a simple ”electrical” modified RMVT, here called (RMV T −D3) . ∗Research Assistant, Aerospace Department, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy, e-mail: maria.cinefra@polito.it, website: www.mul2.com. †Aerospace Department, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy, e-mail: stefano.valvano@polito.it, website: www.mul2.com. ‡Professor, Aerospace Department, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy, e-mail: erasmo.carrera@polito.it, website: www.mul2.com. §currently at School of Aerospace, Mechanical and Manufacturing Engineering College, RMIT University, Melbourne, Australia.