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This paper investigates the buckling problem of a multi-scale hybrid nanocomposite shell for the first time while the cylinder is supposed to be rested on an elastic substrate. The constituent material is considered to be made from a polymeric matrix strengthened via both macro- and nano-scale reinforcements. The influence of nanofillers' agglomeration, generated due to the high surface to volume ratio in nanostructures, is included by implementing the Eshelby-Mori-Tanaka homogenization scheme. Afterwards, the equivalent material properties of the carbon nanotube-reinforced (CNTR) nanocomposite are coupled with those of carbon fibers (CFs) within the framework of a modified rule of the mixture. A cylindrical coordinate system is chosen and mixed with the infinitesimal strains of first-order shear deformation theory of shells to obtain the motion equations on the basis of the static form of principle of virtual work. Next, the achieved governing equations will be solved by Galerkin's method to obtain the buckling load of the structure for both simply supported and clamped boundary conditions. The results indicate on the fact that if the agglomeration effects are ignored, the designed nanocomposite system may fail under low static excitations. Also, it is better to avoid from the construction of a large number of small clusters to make the nanocomposite structure more powerful against buckling mode failure. [ABSTRACT FROM AUTHOR]

This article aims to investigate buckling characteristics of a functionally graded magneto-electro-thermo-elastic nanoshell based on nonlocal strain gradient theory (NSGT). Accounting for nonlocal and strain gradient size-dependency, NSGT has two scale coefficients. The nanoshell is subjected to external electric, magnetic, mechanical, and thermal fields. The temperature distributions are considered as uniform and linear thorough the nanoshell thickness. All material properties including elastic, piezoelectric, and magnetic properties are defined based on a power-law distribution type. Seven coupled governing equations are derived for the nanoshell based on Hamilton's rule and then solved applying Galerkin's approach. The dependency of the buckling behavior of the nanoshell on applied thermal load, temperature distribution, electric voltage, magnetic potential, material gradient index, scale parameters, and shear deformation will be explored. [ABSTRACT FROM AUTHOR]