Higher Order Theories for Laminated Doubly-Curved Shells with Arbitrary Loads and General Boundary Conditions

An innovative modelling strategy is presented in this contribution to study the mechanical response of laminated doubly-curved shells with arbitrary shapes and advanced materials. The structure is described through differential geometry principles, allowing for an arbitrary variable thickness. Furthermore, a generalized isogeometric technique is adopted for the mapping procedure of the physical domain. The kinematic field variable is described according to the Equivalent Single Layer (ESL) and the Layer-Wise (LW) assumptions. The study also provides homogenization procedures for advanced materials like anisogrid, honeycomb, functionally graded materials, and carbon nanotubes, taking into account also the porosity effects. The Hamilton Principle is applied to determine the governing equations of the problem, accounting for arbitrary loading and boundary conditions, modelled with linear elastic springs. The Generalized Differential Quadrature (GDQ) method is used to determine the numerical solution, whereas an analytical approach is adopted in some multifield applications involving electric, thermal, and magnetic fields. Validation examples show the accuracy of the formulation for the prediction, with a reduced computational effort, of the static and vibrational response of the selected structures. A parametric investigation focuses on different geometries and materials. The higher-order theory-based two-dimensional formulation here proposed, is an efficient and valid alternative to widespread tools for accurately predicting the three-dimensional structural response of complex structural elements.