3D capability of refined GDQ models for the bending analysis of composite and sandwich plates, spherical and doubly-curved shells. (August 2018) - Tornabene, Francesco; Brischetto, Salvatore
Abstract: The paper proposes a comparative study between different analytical and numerical three-dimensional (3D) and two-dimensional (2D) shell models for the bending analysis of composite and sandwich plates, spherical and doubly-curved shells subjected to a transverse normal load applied at the top surface. 3D shell models, based on the equilibrium equations written in mixed orthogonal curvilinear coordinates, are proposed in closed form considering harmonic forms for displacements, stresses and loads and simply supported boundary conditions. The partial differential equations in the normal direction are solved in analytical form using the Exponential Matrix (EM) method and in numerical form by means of the Generalized Differential Quadrature (GDQ) method. The first 3D model is here defined as 3D EM model and the second one is here defined as 3D GDQ model. Two-dimensional shell solutions are based on the unified formulation which allows to obtain several refined and classical 2D shell theories in both Equivalent Single Layer (ESL) and Layer Wise (LW) form. Classical theories such as the First order Shear Deformation Theory (FSDT), the Third order Shear Deformation Theory (TSDT) and the Kirchhoff-Love (KL) theory are obtained as particular cases of refined 2D ESL models. 2D shell solutions are proposed by means of a complete generic numerical method such as the GDQ method which allows the investigation of complicated geometries, lamination schemes, materials, loading conditions and boundary conditions. The analyses and comparisons are proposed in terms of displacements, stresses and strains. In 2D GDQ models the transverse shear and transverse normal stresses are recovered from the 3D equilibrium equations allowing results in accordance with the 3D shell solutions. After these validations, the refined 2D GDQ shell models are used for the investigations of new cases which cannot be analyzed by means of closed form solutions. In the present work, the static analysis of an elliptic pseudo-sphere is proposed. Considerations about the typical zigzag form of displacements for multilayered structures are given. The interlaminar continuity in terms of compatibility and equilibrium conditions are also discussed for all the proposed assessments and benchmarks. Highlights: Generalized Differential Quadrature Method (GDQ) and Exponential matrix method. 3D exact and 3D GDQ shell models. Refined equivalent single layer and layer wise 2D GDQ shell models. Sandwich and laminated composite plates, spherical shells and double-curved shells. Interlaminar continuity and zigzag effects.