A novel size-dependent nonlocal strain gradient isogeometric model for functionally graded carbon nanotube-reinforced composite nanoplates

Abstract

The paper presents a novel nonlocal strain gradient isogeometric model for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates. To observe the length scale and size-dependency effects of nanostructures, the nonlocal strain gradient theory (NSGT) is considered. The present model is efficient to capture both nonlocal effects and strain gradient effects in nanoplate structures. In addition, the material properties of the FG-CNTRC are assumed to be graded in the plate thickness direction. Based on the higher order shear deformation theory (HSDT), the weak form of the governing equations of motion of the nanoplates is presented using the principle of virtual work. Afterward, the natural frequency and deflection of the nanoplates are made out of isogeometric analysis (IGA). Thanks to higher order derivatives and continuity of NURBS basic function, IGA is suitable for the weak form of NSGT which requires at least the third-order derivatives in approximate formulations. Effects of nonlocal parameter, strain gradient parameter, carbon nanotube (CNT) volume fraction, distributions of CNTs and length-to-thickness ratios on deflection and natural frequency of the nanoplates are examined and discussed in detail. Numerical results are developed to show the phenomenon of stiffness-softening and stiffness-hardening mechanisms of the present model.