In this article, a new higher order shear deformation theory based on trigonometric shear deformation theory is developed. In order to consider the size effects, the nonlocal elasticity theory is used. An analytical method is adopted to solve the governing equations for static analysis of simply supported nanoplates. In the present theory, the transverse shear stresses satisfy the traction free boundary conditions of the rectangular plates and these stresses can be calculated from the constitutive equations. The effects of different parameters such as nonlocal parameter and aspect ratio are investigated on both nondimensional deflections and deflection ratios. It may be important to mention that the present formulations are general and can be used for isotropic, orthotropic and anisotropic nanoplates.
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Nami et al. (2013) studied this question.
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