Bending, buckling and vibration of shear deformable beams made of three-dimensional graphene foam material

Abstract

This paper studies bending, buckling and vibration of three-dimensional graphene foam (3D-GrF) beams in the framework of the sinusoidal shear deformation theory. Graphene foams can distribute along the thickness of beams in different patterns. The material properties of three-dimensional graphene foams are described by the scaling laws of open-cell foams. Based on Hamilton's principle, the governing equations together with boundary conditions are derived. Then, Navier's method and Rayleigh-Ritz method are used to calculate natural frequencies, critical buckling loads and center deflections of the 3D-GrF beams. Results show that the graphene foam distribution, the foam coefficient and the slenderness ratio have significant effect on buckling, bending and vibration behaviors of 3D-GrF beams. In addition, the present results are verified by the comparison with published ones in the literature.

Finite element formulation of metal foam microbeams via modified strain gradient theory

“…A normal and shear deformation theory is used to investigate the vibration and elastic bending of the metal foam beams based on iso-geometric analysis (IGA) [13]. Mechanical behaviours of graphene foam beams are presented by implementing Rayleigh-Ritz method [14]. An optimization study is performed for the stability response of beams having functionally graded faces and metal foam core [15].…”