Abstract
This paper presents an analytical study on the multiple equilibria and buckling of pinned-fixed functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) arches under central point load. It is assumed that graphene nanoplatelets (GPLs) in each GPLRC layer are uniformly distributed and randomly oriented with its concentration varying layer-wise along the thickness direction. The Halpin–Tsai micromechanics-based model is used to estimate the effective elastic modulus of GPLRC. The non-linear equilibrium path and buckling load of the pinned-fixed FG-GPLRC arch are subsequently derived by employing the principle of virtual work. The effects of GPLs distribution, weight fraction, size and geometry on the buckling load are examined comprehensively. It is found that the buckling performances of FG-GPLRC arches can be significantly improved by using GPLs as reinforcing nanofillers. It is also found that the non-linear equilibrium path of the pinned-fixed FG-GPLRC arch have multiple limit points and non-linear equilibrium branches when the arch is with a special geometric parameter.
Highlights
The development of carbonaceous nanomaterials, such as graphene and carbon nanotubes, has been greatly advanced by rapidly developing material science and manufacturing techniques over the last decade [1,2,3,4]
When the applied point load reaches a maximum load, namely limit point load, the limit point buckling may occur to the FG-GPLRC arch, and the limit point buckling load is the local maximum point on the non-linear equilibrium path defined in Equation (25)
The multiple equilibria and buckling of the pinned-fixed FG-GPLRC arch under central point has been comprehensively studied in this paper
Summary
The development of carbonaceous nanomaterials, such as graphene and carbon nanotubes, has been greatly advanced by rapidly developing material science and manufacturing techniques over the last decade [1,2,3,4]. Except for the study on the material properties of the GPL-reinforced nanocomposite, the mechanical behaviors of structures made of these composites have been investigated widely. Yang and co-workers [11,12,13,14,15] carried out a series of studies on the vibration, dynamic stability, buckling and postbuckling of functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC). Structures, which revealed that the performances of the FG-GPLRC structures can be remarkably improved by adding a low concentration of GPLs. Dong et al [16,17,18] analytically investigated the non-linear dynamic behavior of graded graphene-reinforced composite cylindrical shells subjected to thermal loading, impact loading and harmonic loading. Liu et al [32] presented an analytical solution for non-linear static responses and buckling of functionally graded porous (FGP) arches with GPLs reinforcements. The effects of GPLs distribution, weight fraction, size and geometry on the limit point buckling load are examined comprehensively
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