Static bending behaviors of nanoplate embedded in elastic matrix with small scale effects

In this paper, the bending behaviors of the nanoplate with small scale effects are investigated by the nonlocal continuum theory. The governing equations for the nonlocal Mindlin and Kirchhoff plate models are derived. The expressions of the bending displacement are presented analytically. The difference between the two models is discussed and bending properties of the nanoplate are illustrated. It can be observed that the small scale effects are obvious for bending properties of the nanoplate. The half wave numbers, width ratios and elastic matrix properties also have significant influence on bending behaviors.

► The governing equations and displacements for the nonlocal Mindlin and Kirchhoff plate models are derived.
► The influence of the plate models, scale coefficients, half wave numbers, width ratios and elastic matrix properties are discussed.
► The small scale effects are obvious especially for larger half wave numbers and square structures.
► The displacement ratio becomes larger with the Winkler foundation modulus and the stiffness of the shearing layer increasing.