A quasi-3D hyperbolic formulation for the buckling study of metal foam microplates layered with graphene nanoplatelets-embedded nanocomposite patches with temperature fluctuations

Abstract

The work analyzes the buckling behavior of size-dependent microplates with a metal foam core, covered by graphene nanoplatelets (GNPs)-embedded nanocomposite patches. Microplates rest on a bi-parameter elastic substrate, and they are immersed in a thermal environment to observe the effect of temperature fluctuations on their elastic buckling performance. All material properties for each layer of the microstructure are thickness-dependent. A novel quasi-3D shear and normal (Q-3D S-N) hyperbolic theory is here proposed to describe the kinematic relations, accounting for the transverse normal strain. At the same time, a modified couple stress theory (MCST) is employed to account for the size dependence of the mechanical behavior due to the presence of a material length-scale parameter. Using the energy method and virtual work principle, the differential equilibrium equations are derived and solved analytically, where solutions are verified against the existing literature. The study focuses on the impact of different parameters on the normalized critical buckling load (NCBL). Based on the results from the systematic investigation, it is found that the addition of GNPs to the microplate enhances its stiffness, leading to increased values of NCBL, which in turn reduce for an increased imperfection ratio.