Exact three-dimensional shell model, shell structures, free vibrations, vibration modes, composites, functionally graded materials, carbon nanotubes
This work proposes an exact general three-dimensional shell model for the free vibration analysis of advanced structures. The equilibrium equations are written in general orthogonal curvilinear coordinate system valid for plates and shells with constant radii of curvature. The model is developed in layer-wise form in the case of multilayered structures, and a closed form solution is provided supposing simply supported edges. The partial differential equations in z are solved by means of the exponential matrix method which is stable and not expansive from the computational point of view. The equilibrium equations are written for the general case of spherical shells and they automatically degenerate in the cylindrical and flat panel cases considering one or both radii of curvature equals zero, respectively. Results are proposed for single- and multi-layered isotropic, orthotropic, composite and functionally graded structures, and for single- and multi-walled carbon nanotubes.
Cite this paper
Salvatore Brischetto. (2016) A General Elastic Shell Model for Advanced Structures. International Journal of Theoretical and Applied Mechanics, 1, 239-246