Higher order theories for the vibration study of doubly-curved anisotropic shells with a variable thickness and isogeometric mapped geometry

Anisotropic materials are widely used in many complex structures and panels, whose modelling can represent a challenging issue for engineers, especially when variable geometries are involved. In the present work we propose a novel strategy, based on the Equivalent Single Layer (ESL) approach, to analyze doubly-curved shells with constant and/or varying thicknesses made of completely anisotropic materials. An isogeometric mapping procedure is applied to define the reference surface, thus enabling to study a wide range of structural shapes. Different higher order theories are here applied in a unified setting to describe the kinematic field, where the governing equations of the problem are realized applying the Hamiltonian Principle, and solved numerically in a strong form with the 2D Generalized Differential Quadrature (GDQ) method. Several examples are illustrated for validation purposes of the proposed method, whose results are compared with predictions from 3D finite elements. A large parametric investigation is also performed to assess the sensitivity of the vibration response of generally-curved shell structures to different stacking sequences, material typologies, and boundary conditions.