A size-dependent isogeometric analysis of laminated composite plates based on the nonlocal strain gradient theory

The paper presents a size-dependent high-order shear deformation theory (HSDT) model for static and free vibration and analyses of laminated composite and sandwich nanoplates based on the nonlocal strain gradient theory. To consider the size effect of nanostructures, two scale parameters having relationship with the nonlocal and strain gradient effects are introduced into the classical HSDT model. Due to these parameters, the increase and decrease in the stiffness of nanostructures are confirmed by adjusting these two ones. The virtual work principle is used in order to perform the weak forms, and the size-dependent bending and free vibration isogeometric analysis model are developed using the weak form. As observed numerical results, bending and free vibration characteristics of laminated composite and sandwich nanoplates are changed by the geometry, boundary condition, length-to-thickness ratio, strain gradient parameter and nonlocal parameter. In addition, the pure nonlocal, strain gradient and classical HSDT models can be retrieved from the present model when the strain gradient parameter, nonlocal parameter and these two parameters are taken equal to zero.