Abstract

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.

摘要

本文首次研究了多尺度混合纳米复合材料壳的屈曲问题，而圆柱体应该放在弹性基板上。构成材料被认为是由通过宏观和纳米级增强材料增强的聚合物基体制成的。由于纳米结构中的高表面积与体积比而产生的纳米填料团聚的影响，通过实施 Eshelby-Mori-Tanaka 均质化方案包括在内。之后，碳纳米管增强 (CNTR) 纳米复合材料的等效材料特性与碳纤维 (CF) 的材料特性在混合物的修改规则的框架内耦合。根据虚功原理的静态形式，选择圆柱坐标系，混合壳一阶剪切变形理论的无穷小应变，得到运动方程。接下来，将获得的控制方程通过 Galerkin 方法求解，以获得结构在简支和夹紧边界条件下的屈曲载荷。结果表明，如果忽略团聚效应，所设计的纳米复合材料系统可能会在低静态激发下失效。此外，最好避免构建大量小团簇，以使纳米复合结构更有效地抵抗屈曲模式失效。获得的控制方程将通过 Galerkin 方法求解，以获得结构在简支和夹紧边界条件下的屈曲载荷。结果表明，如果忽略团聚效应，所设计的纳米复合材料系统可能会在低静态激发下失效。此外，最好避免构建大量小团簇，以使纳米复合结构更有效地抵抗屈曲模式失效。获得的控制方程将通过 Galerkin 方法求解，以获得结构在简支和夹紧边界条件下的屈曲载荷。结果表明，如果忽略团聚效应，所设计的纳米复合材料系统可能会在低静态激发下失效。此外，最好避免构建大量小团簇，以使纳米复合结构更有效地抵抗屈曲模式失效。