A closed-form 3D shell solution for multilayered structures subjected to different load combinations

Abstract

Multilayered composite and sandwich plates and shells are typical aerospace structures. They introduce complicating effects such as in-plane and transverse anisotropy which lead to zigzag forms of displacement and interlaminar continuity problems. The present closed-form 3D shell solution allows the static analysis of simply-supported cross-ply laminated and sandwich plates, cylinders and cylindrical/spherical shell panels subjected to different harmonic load types. It is possible to consider transverse normal and transverse shear loads simultaneously or separately applied at the top and at the bottom of the considered structure. The present work extends the previous exact 3D shell model developed for the static analysis of plates and shells in the case of transverse normal load applied at the top or at the bottom of the investigated structure. This new extension is still based on the 3D equilibrium equations written in general orthogonal curvilinear coordinates. The obtained system is solved using simply supported boundary conditions, harmonic forms for loads and displacements, a general layer wise approach and the exponential matrix method for the solution of the differential equations in z. However, the load boundary conditions introduced in the proposed shell model have been opportunely modified in order to allow the combination of different transverse normal and transverse shear loads applied at the external surfaces. The new proposed benchmarks fill the gap present in the literature where the proposed 3D exact models always use a transverse normal load applied at the external surfaces. The present paper investigates the zigzag effects, the interlaminar continuity, the equilibrium and compatibility conditions, the load boundary conditions, the symmetry characteristics, the thickness ratio effect and the 3D behavior in laminated and sandwich plates and shells in the case of different load applications. The new proposed benchmarks will be fundamental for the validation of those new refined 2D shell models which want to capture all these features for different load types.