Buckling Analysis of Graphene-Nanoplatelet-Reinforced Functionally Graded Porous Microbeams Based on Modified Strain Gradient Theory

The buckling of functionally graded graphene-nanoplatelets reinforced porous composite (FG-GRPC) microbeams is analyzed using the modified strain gradient theory (MSGT) and refined beam theory, incorporating two types of pore distribution and three patterns of graphene nanoplatelets (GNPL) dispersion. Firstly, the effective Poisson's ratio and elastic modulus of GNPL-reinforced porous nanocomposites are calculated on the basis of the Halpin-Tsai model and closed-cell Gaussian random field model. Then, governing equations for buckling of the microbeams are derived according to the refined beam theory and the principle of minimum potential energy, and solved by Ritz method to acquire the critical buckling loads. Finally, a detailed parametric study is conducted to analyze the effects of GNPL mass fraction, dispersion patterns, geometry, porosity, pore distribution types, and intrinsic material length scale on the critical loads of the FG-GRPC microbeams. The results show that significant enhancement of the stability of the FG-GRPC microbeams can be achieved by adjusting the distribution patterns of pores and GNPL, which provides a novel design dimension for the performance optimization of microstructures. And under the synergistic regulation of GNPL and porosity, an increase in the GNPL mass fraction can effectively reduce the effect of porosity on the buckling.