Dynamic Analysis of Doubly-Curved Shells Made of Advanced Materials with Higher Order Theories and Generalized Differential Quadrature

In the present work, a refined theory with three-dimensional capabilities is proposed for the structural analysis of shell structures made of smart materials for advanced engineering applications. Principal curvilinear coordinates are used for the geometry definition of the structure. The kinematic description of the configuration variables is performed according to the Equivalent Single Layer (ESL) approach with higher order theories. A constitutive relation for elastic anisotropic laminates is considered. The fundamental equations, written in the strong form, are derived from the Hamilton principle together with the boundary conditions, and they are numerically solved by means of the Generalized Differential Quadrature (GDQ) method. The accuracy and the computational efficiency of the present theory is shown by means of different applicative examples. The numerical predictions of the present ESL model are compared to refined solutions coming from three-dimensional Finite-Element-based simulations. Furthermore, some parametric investigations are performed on a doubly-curved panel made of Variable Angle Tow (VAT) anisotropic materials in order to show the sensitivity of the VAT distribution on the dynamic response of the shell under consideration. The present formulation is very accurate if compared to refined models, despite its reduced computational demand, and it can be useful for design purposes of doubly-curved elements made of advanced materials.