Bending analysis of ultra-thin functionally graded Mindlin plates incorporating surface energy effects

• A size-dependent continuum model incorporating surface energy effects is investigated for ultra-thin functionally graded Mindlin plates.
• Classical continuum models are adopted, accounting for surface effects and considering the exact neutral plane position for FG plates.
• A series of continuum governing differential equations which include surface energy and neutral plane position effects are derived.
• An analytical solution is provided to study the bending behavior of ultra-thin simply supported FG films.
• A parametric study is provided to study the effect of surface parameters on the FG plate response.

In this paper, an analytical solution for Mindlin plate theory accounting for the position of the neutral plane for continuum incorporating surface effects is investigated to study the bending behavior of ultra-thin simply supported functionally graded (FG) plates. The size-dependent mechanical response is very important while the plate thickness reduces to micro/nano scales. Bulk stresses on the surfaces are required to satisfy the surface balance conditions involving surface stresses. Therefore, unlike the classical continuum plate models, the bulk transverse normal stress is preserved here. Moreover, unlike most of previous studies in the literature, the neutral plane position effects are considered for FG plates. A series of continuum governing differential equations which include surface energy and neutral plane position effects are derived. The proposed analytical solution is then used for a comparison between the continuum analysis of simply supported FG ultra-thin plates with and without incorporating surface effects. Also, a parametric study is provided to study the effect of surface parameters and the effect of aspect ratio on the behavior of the simply supported FG plate. The proposed model is verified by previous work.