Buckling analysis of orthotropic nanoplates based on nonlocal strain gradient theory using the higher-order finite strip method (H-FSM)

Abstract

In this paper, a semi-analytical higher-order finite strip method is developed based on the nonlocal strain gradient theory (NSGT) for buckling analysis of orthotropic nanoplates. NSGT contains two material length scale parameters related to the nonlocal and strain gradient effects. To consider the effect of the strain gradient in the governing equation of the plate in the transverse direction, the higher-order polynomial shape functions (higher-order Hermitian shape functions) are utilized to assess the second derivatives, in addition to the displacement and first derivatives. Also, some numerical study is presented on the effects of different factors such as boundary conditions, nonlocal and strain gradient parameters, aspect ratio, and different types of in-plane loading for the isotropic and orthotropic rectangular nanoplate to verify the proposed formulation. In the following, a relation for the nanoplates based on the nonlocal strain gradient theory using the Navier method is extracted and presented for preliminary comparisons. According to the proposed relation, it is shown that in simply supported nanoplates, if the non-local parameter is equal to the second power of the strain gradient parameter, the responses obtained for the nanoplates are equal to the locally available responses.