Abstract
In this paper using the modified couple stress theory, to study the bending, buckling and vibration characteristics of the rectangular Mindlin's nanoplates with graphene material was investigated. With the aim of considering the effects of small scales, the modified couple stress theory, which has only one parameter of length scale and also was presented by Yang in 2002, was used. In the modified couple stress theory; the strain energy density is a function of the components of the strain tensor, curvature tensor, stress tensor and the symmetric part of the couple stress tensor. After obtaining the strain energy, external work, and buckling equation and placing them in the Hamilton's equation, the basic and auxiliary equations of the nanoplates were obtained. Then, by applying boundary and force conditions in the governing equations, the bending, buckling and vibration of the rectangular graphene nanoplates with thickness h and simply-supported conditions were explored. Also, the solution method was the Navier's solution.
Highlights
Introduction whereThe atomic and molecular scale test is known as the safest method for the study of materials in small-scales
As observed in the tables and figures, the Mindlin's nanoplate bending rate under sinusoidal load, decreases with an increase in length to thickness ratio of the nanoplate, but, this value increases with an increase in the aspect ratio of the nanoplate
By comparing different nanoplates under uniform surface traction it was found that the Kirchhoff's nanoplate yields the lowest and the third-order nanoplate yields the highest values for bending
Summary
The atomic and molecular scale test is known as the safest method for the study of materials in small-scales. In this method, the nanostructures are studied in real dimensions. It is used only to validate other simple and low-cost methods Atomic simulation is another solution for studying small-scale structures. In this method, the behavior of atoms and molecules is examined by considering the intermolecular and interatomic effects on their motions, which eventually involves the total deformation of the body. In the case of large deformations and multi atomic scale the computational costs is too high, so this method is only used for small deformation problems. From Eqs. (3) and (6) it can be seen that ij and mij are symmetric
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