Abstract
In this study, static analysis of the two-dimensional rectangular nanoplates are investigated by the Differential Quadrature Method (DQM). Numerical solution procedures are proposed for deflection of an embedded nanoplate under distributed nanoparticles based on the DQM within the framework of Kirchhoff and Mindlin plate theories. The governing equations and the related boundary conditions are derived by using nonlocal elasticity theory. The difference between the two models is discussed and bending properties of the nanoplate are illustrated. Consequently, the DQM has been successfully applied to analyze nanoplates with discontinuous loading and various boundary conditions for solving Kirchhoff and Mindlin plates with small-scale effect, which are not solvable directly. The results show that the above mentioned effects play an important role on the static behavior of the nanoplates.
Highlights
Nanostructures have significant mechanical, electrical and thermal performances that are superior to the conventional structural materials
1710 Hassan Kananipour / Static analysis of nanoplates based on the nonlocal Kirchhoff and Mindlin plate theories using Differential Quadrature Method (DQM)
Hassan Kananipour / Static analysis of nanoplates based on the nonlocal Kirchhoff and Mindlin plate theories using DQM 1711 (1− (e0a)2∇2 )σij = Cijklεkl, (1)
Summary
Nanostructures have significant mechanical, electrical and thermal performances that are superior to the conventional structural materials. 1710 Hassan Kananipour / Static analysis of nanoplates based on the nonlocal Kirchhoff and Mindlin plate theories using DQM. It is found that the effect of nonlocal elasticity on the static behavior of nano-scale plates has been investigated. Both Kirchhoff and Mindlin plate theories will be discussed. The effects of nonlocal parameter and transverse shear deformation of the plate on the bending deflection of the plate are studied for different values of the plate size. E0a is nonlocal parameter or distinctive length that means the scale coefficient which denotes the small-scale effect on the mechanical characteristics.
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