Nonlinear thermal buckling instability analysis of a rotating nanocomposite beam reinforced with graphene platelet via the Chebyshev–Ritz scheme

Abstract

Resorting to the Chebyshev–Ritz scheme instability as well as post-instability response as a consequence of the buckling occurrence for a rotating nanocomposite beam in a uniform thermal environment is studied. The beam has been reinforced with graphene platelet. The Halpin–Tsai theory is utilized for the sake of specifying the elasticity modulus of the reinforced nanocomposite beam. The Chebyshev set of polynomial functions has been used to serve as a required independent set for the Ritz method. The static displacement field owing to the rotation of the beam and the thermal load is acquired by employing a potent algorithm. The outcomes indicate that for nanocomposite beams with the graphene platelet patterns in the model of O- and U-patterns rotating, respectively, below 9,326, and 7,420 rpm, the graphene reinforcing phase should not be used since it leads to a thermal buckling stiffness for the nanocomposite rotating beam smaller than the thermal buckling stiffness of the associated original rotating beam that just made of a host matrix. Moreover, developing the weight fraction of the graphene platelet for a U-type beam rotating below 9,628 rpm lessens the corresponding thermal buckling stiffness while an X-type beam always strengthens in a similar conditions.