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In this article, the dynamic instability of the hybrid fiber/nanocomposite-reinforced toroidal shells is investigated. By using the approximation of Fourier series and applying the Galerkin method, a semi-analytical solution is achieved. The proposed method provides an accurate assessment of the dynamic stability of the shell with no computational costs in comparison to the numerical methods. By comparing the obtained results for some examples with those available in the present literature, the accuracy of present formulation is approved. In order to evaluate the effects of geometrical and mechanical specifications on the dynamic instability of the proposed shells, a comprehensive parametric study is performed, as well. [ABSTRACT FROM AUTHOR]

This paper presents an analytical solution for free-vibration and stability analyses of hybrid-composite toroidal shells. The considered hybrid material incorporates the composition of fibers and nanocomposite-reinforced matrix (NCRM) such as carbon nanotubes (CNTs) and graphene nanoplatelets (GPLs). The governing differential equations are extended based on the first-order transverse shear deformation theory (FSDT) and are solved by employing the approximation of Fourier series and Galerkin method. The considered hybrid composite material in the parametric studies are consisted of three layers in which the polymeric matrix are reinforced by CNTs in some layers and reinforced by GPLs in the other layers. [ABSTRACT FROM AUTHOR]

In the present paper, the geometrical nonlinear behaviour of the sandwich shallow spherical shells made of the functionally graded carbon nanotube-reinforced composites is assessed. In order to solve the proposed problem, the equilibrium, compatibility and constitutive equations are extended based on the first-order shear deformation theory. The obtained system of nonlinear differential equations is solved by employing an analytical approach based on the modified interactions method, which results a closed-form relationship between external load and deformation of the shell. Firstly, the obtained closed-form formula is validated by comparing the corresponding results with those obtained by other methods such as finite element method. After the validation procedure, the mentioned closed-form solution is employed to perform a comprehensive parametric study incorporating the mechanical and geometrical properties, such as the effects of CNTs agglomerating, depth and boundary conditions of the shell. The obtained results in the parametric studies show that all of the parameters can affect the buckling load, stability region and intensity of the instability (difference of upper and lower limit loads). [ABSTRACT FROM AUTHOR]