Accurate variational formulation for the static analysis of functionally graded quadrilateral nanoplates with surface effects
Paper ID : 1542-ICNS
Abolfazl Shahabodini *
Department of mechanical engineering, Vali-e-Asr university of Rafsanjan, Rafsanjan , Iran
Described in the current paper is the bending behavior of functionally graded (FG) arbitrary straight-sided quadrilateral nanoplates using a continuum-based variational approach. The surface stresses and shear deformation effects are accounted for through incorporation of Gurtin-Murdoch’s surface theory into the Mindlin plate theory. The solution method named variational deferential quadrature (VDQ) does the discretization in a variational framework. By the VDQ, the transformation and discretization processes of the high-order derivatives of displacement field appeared in the strong form solution of the equations are bypassed. Numerical examples are firstly given to verify the accuracy and fast convergence rate of the present model. Afterward, the surface influences on the static deflection of the FG quadrilateral nanoplate are investigated. It is discerned that skew and quadrilateral nanoplates are of higher flexural stiffness and less affected by the surface stresses influence than rectangular ones.
Variational formulation; Static analysis; FG quadrilateral nanoplates; Surface effects; Differential quadrature
Status : Abstract Accepted (Poster Presentation)