Static Analysis of a Nano Plate by Using Generalized Differential Quadrature Method

Abstract

In this paper, static analysis of a nano rectangular plate subjected to uniform distributed load is studied based on modified couple stress theory (MSCT) by using Generalized Differential Quadrature (GDQ) Method. The inclusion of an additional material parameter enables the new plate model to capture the size effect. The new non-classical plate model reduces to the classical plate model when the length scale parameter is set to zero. In deriving of the governing equations, the minimum total potential energy principle is used. In the solution of the governing equations, the DQM method is used for simply-supported nano plate within the Kirchhoff-Love plate theory. In the numerical results, the influences the material length scale parameter and the dimension parameters of the plate on the static deflection of the nano plate is presented. Also, the difference between the classical theory (CT) and MSCT is investigated for static responses of nano plate.

A Levy solution for bending, buckling, and vibration of Mindlin micro plates with a modified couple stress theory

“…Roque et al [23] carried out the bending analysis of an isotropic Mindlin micro plate using both the Navier method and a meshless method and presented the results for clamped and simply supported plates. Akbaş [24] studied the bending behavior of a Kirchhoff-Love rectangular nano plate using the differential quadrature method. They reported the results for simply supported nano plates.…”

Static Analysis of a Fiber Reinforced Composite Beam Resting on Winkler-Pasternak Foundation

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Free Vibration Analysis of a Cross-Ply Laminated Plate in Thermal Environment

“…Li and Qiao [41,42] examined thermal postbuckling analysis of laminated composite beams under thermal loading. Akbaş [43] examined a nano-plate by using generalized differential quadrature method. Ramos et al [44] investigated thermoelastic static analysis of composite plates by using a new combined trigonometric equation.…”