It is shown that, to a very good approximation, the torsional rigidity (D) of a nanosized bar differs from the prediction of standard continuum mechanics (Dc) as (D−Dc)/Dc=Ah0/a where A is a non-dimensional constant, a is the size scale of the cross-section of the bar and h0 is a material length equal to the ratio of the surface elastic constant to the bulk elastic constant.
Based on the obtained closed-form solutions, numerical examples are further presented to investigate the effects of the material length scale parameter to thickness ratio, the length to thickness ratio, the power law index and the elastic foundation on the nonlinear bending and free vibration responses of the microplate.
Numerical examples are presented and discussed, in which the effects of material inhomogeneity, length to thickness ratio and boundary conditions on natural frequencies and critical buckling loads are investigated.
A detailed parametric study is performed to investigate the effects of the material length scale parameters-to-thickness ratio l/h, material property gradient index k, slenderness ratio L/h, Winkler modulus kw and shear correction factor on the bending behavior of embedded functionally graded microbeams.
A detailed parametric study is performed to investigate the influences of shear deformation, material length scale parameter-to-outer radius ratio, aspect ratio and shear modulus ratio on mechanical responses of microtubules.
Furthermore, the effects of the material length scale parameter to thickness ratio, the power law index and the radial load to axial load ratio on the pre-buckling and buckling behaviors of the FG microshell are discussed in detail.
Besides, the present model contains three material length scale parameters to capture the size effect.
The adopted model also can degenerate to the beam model based on the modified couple stress theory (MCST) or the classical beam theory (CBT) by setting two or all material length scale parameters to be zero.
Furthermore, the effects of the material length scale parameter to thickness ratio, the applied electric field and in-plane boundary conditions on the buckling and post-buckling behavior of the piezoelectric hybrid microplate are discussed in detail.
