Static and dynamic response of sector-shaped graphene sheets

Abstract

Nonlocal elasticity theory is presented for the free vibration and bending analysis of nano scaled graphene sheets having sector shape. An eight-node curvilinear domain is used for transformation of the governing equation of motion of sector graphene from physical region to computational region in conjunctions with the Kirchhoff plate theory. The discrete singular convolution (DSC) method is employed for numerical solution of resulting nonlocal governing differential equation and related boundary conditions. Then, the effects of nonlocal parameter, mode numbers, sector angle and radius ratio on the static and vibration results of nano-scaled sector shaped graphene sheets are discussed.

Comparison of small scale effect theories for buckling analysis of nanobeams

“…Armchair, zigzag, and chiral structure Graphene is one of the most futuristic material founded in present century. Within its discovery in 2004 (13 years after the foundation of carbon nanotube) graphene sheets attracted huge attention with its superior material properties [4,[15][16][17][18][19]. Graphene sheets consist of six carbon atoms.…”

New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method

“…Necira 22 developed the hierarchical finite element method for size-dependent free vibration analysis of Mindlin nano-plates with curvilinear plan-forms. Akgöz and Civalek 23 employed the discrete singular convolution method for the free vibration and bending analysis of nano-scaled graphene sheets having sector shape. Babaei and Shahidi 24 investigated the buckling behavior of quadrilateral SLGS under bi-axial compression by the Galerkin method, where the buckling loads of nanoplates with different geometrical parameters were obtained.…”