Electro-mechanical analysis of laminated anisotropic doubly-curved shells of arbitrary shape using higher-order theories

Abstract In this work, a two-dimensional (2D) Equivalent Single Layer (ESL) model, based on unified formulation with higher-order shear deformation theories, is developed for the coupled electro-mechanical analysis of doubly-curved shell structures of arbitrary shape, defined on irregular physical domains. The formulation is derived with curvilinear principal coordinates, considering a higher-order Lagrange interpolation of the unknown variables with respect to a 2D rectangular discrete grid. Each layer of the laminate is modeled as generally anisotropic material with an arbitrary three-dimensional (3D) orientation relative to the geometric reference system. The governing equations are derived from the Master Balance principle in weak form, and isogeometric mapping is used for arbitrarily-shaped structures. For singly-connected domains, a numerical solution is obtained using the Generalized Differential Quadrature (GDQ) and the Generalized Integral Quadrature (GIQ) methods. In addition, a finite element implementation based on 2D Lagrange and Hermite shape functions is presented for arbitrarily-shaped bi-connected structures. In the post-processing phase, an efficient reconstruction of mechanical and electric variables is introduced, based on the 3D balance equations. The model is applied to several numerical examples to study the coupled electro-mechanical response of laminated panels with single and double curvature under various loading and boundary conditions. A systematic comparison with 3D reference solutions demonstrates the accuracy and computational efficiency of the proposed approach. It is shown that the refined 2D ESL model, based on higher-order theories, along with the recovery procedure, can accurately predict not only the classical mechanical response of laminated anisotropic shells of arbitrary shape, but also their coupled electrical response. As a consequence, the proposed methodology is suitable for analyzing a wide range of piezoelectric structural components in advanced engineering applications.