A nonlocal strain gradient isogeometric model for free vibration and bending analyses of functionally graded plates

Abstract

In this paper, a novel nonlocal strain gradient isogeometric model using the nonlocal strain gradient theory (NSGT) and isogeometric analysis (IGA) is developed to analyze free vibration and bending behaviors of functionally graded (FG) plates. Based on the higher-order shear deformation theory (HSDT) and NSGT, the weak form of the governing equation motion of the plates is presented. To homogenize material properties, the Mori-Tanaka scheme is used. The proposed model is capable of capturing both nonlocal effects and strain gradient effects in nanoplate structures due to adding two parameters, i.e. nonlocal and strain gradient parameters, into the elastic constants of FG materials. Thanks to those two parameters, both stiffness reduction and stiffness enhancement mechanism of FG plates are observed. The principle of virtual work is used to derive governing equations, subsequently, the natural frequencies and deflections of the FG plates are determined. Numerical results are presented to evaluate effects of the geometry, boundary condition, length-to-thickness ratio, exponential factor, nonlocal parameter and strain gradient parameter on the natural frequency and deflection of FG plates. In addition, the pure nonlocal and strain gradient models can be restored from the proposed model when taking the zero of the strain gradient and nonlocal parameters, respectively.