Dynamic and Static Analysis of Laminated Doubly-Curved Shells and Panels Using Layer-Wise and Equivalent-Single-Layer Theories via GDQ Method

The present study uses the fundamental nuclei developed by the authors [1] in order to carry out Equivalent-Single-Layer (ESL) and Layer-Wise (LW) solutions for doubly-curved multi-layered shells. These differential operators are based on a generalized version of Carrera's Unified Formulation (CUF) with curvature effect included. In addition the shell geometry is described using Differential Geometry [1-3]. The shell formulation is presented in its strong form, and it is solved directly through Generalized Differential Quadrature (GDQ) method. This numerical technique allows to discretize each derivative directly. So, once the solution is found, the generalized strains and stress resultants can be evaluated by applying the GDQ method too. As a post-processing application, the stress profiles through the shell thickness of the transverse shear and normal stresses are computed by solving numerically the local 3D equilibrium equations in each point of the doubly-curved shell [4]. In order to verify the accuracy and stability of the procedure, GDQ results are compared with the ones obtained using analytical and numerical solutions, where very good agreement is observed in all the examples.