This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...

The axially compressed buckling of a double-walled carbon nanotabe surrounded by an elastic medium using the energy and the Rayleigh-Ritz methods is investigated in this paper. In this research, based on the elastic shell models at nano scale, the effects of the van der Waals forces between the inner and the outer tubes, the small scale and the surrounding elastic medium on the critical bucklin...

Modified couple stress theory is applied to study of temperature effects on free vibration of Timoshenko functionally graded microbeams. Due to the interatomic and microstructural reactions of the structures in micro scale, the dynamic behavior of the microbeam is predicted more accurate applying the couple stress theory. Both of the simply supported and clamped boundary conditions are assumed ...

In this article, the free vibration behavior of nanoscale FG rectangular plates is studied within the framework of the refined plate theory (RPT) and small-scale effects are taken into account. Using the nonlocal elasticity theory, the governing equations are derived for single-layered FG nanoplate. The Navier’s method is employed to obtain closed-form solutions for rectangular nanoplates assum...

The covarying scale effect in the observational relativistic measurement found a few years ago is that the Lorentz factor is a scale conversion ratio between the virtual covarying scale of measurement in relative motion and the real invariant scale at rest with respect to the observer. We find this scale conversion ratio being the bridge between two relative frames, and a logical symmetry for t...

In this research, the bending analysis of rectangular nanoplates subjected to mechanical loading is investigated. For this purpose, the strain gradient elasticity theory with one gradient parameter is presented to study the nanoplates. From the best knowledge of authors, it is the first time that the exponential shear deformation formulation based on strain gradient elasticity theory is carried...

It has been suggested that the mass-to-light (M/L) ratio of gravitationally clustering objects is scale-independent on scales beyond galaxy clusters, and may also be independent of the mass of the objects. In this paper, we show that the scale behavior of M/L ratio is closely related to the scaling of cosmic structures larger than clusters. The scale dependence of the M/L ratio can be determine...

this paper aims to evaluate the impact of several indices of market structure including entry to barrier, economies of scale and concentration degree on 140 active industries using the digit. accordingly, we apply three methods including cost disadvantages ratio ( ), herfindahl–hirschman concentration index ( ) and comanor and willson criterion in order to assess the economies of scale and usin...