Abstract
In this study, considering surface and bulk residual stresses, size- and orientation-dependent nonlinear bending, large amplitude vibration and postbuckling of single-crystalline nanoplates with cubic anisotropy are studied. Based on the first-order shear deformation plate theory, von-Karman geometrical nonlinearity and Gurtin-Murdoch theory, the model is formulated. In order to discretize the governing equations along with different combinations of boundary conditions, the generalized differential quadrature method is used and then a direct iterative method (Picard) is employed to solve the nonlinear system of equations. The presented results reveal that when thickness of the nanoplate increases, especially at high orientation and anisotropicity, ignoring shear deformation could cause some noticeable errors in the response of nonlinear bending, large amplitude vibration and postbuckling of nanoplates. Moreover, although orientation has a very direct effect on large amplitude vibration of nanoplates, it is observed that at a specific amplitude, the natural frequencies are independent from the orientation. The results of this study show that geometrical nonlinearity could be ignored in analyzing large amplitude vibration and postbuckling of highly anisotropic nanoplates in the [110] direction.
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