A size dependent meshfree model for functionally graded plates based on the nonlocal strain gradient theory

Abstract

A nonlocal strain gradient meshfree model based on the nonlocal strain gradient theory (NSGT) and higher-order shear deformation theory (HSDT) is presented and developed to examine the bending and free vibration behaviors of functionally graded (FG) nanoplates. Regarding two scale parameters, nonlocal and strain gradient effects in nanostructures are appeared in the current model. The power index and Mori-Tanaka schemes are utilized to compute material properties. A weak form of governing equations of motion for NSGT can be obtained by using the principle of virtual displacements. Later, the deflections and natural frequencies of the FG nanoplates are resolved by using the moving Kriging (MK) meshfree method. A detailed study to assess effects of exponential factor, length-to-thickness ratio, geometry, boundary condition, strain gradient parameter and nonlocal parameter on the deflections and natural frequencies of the FG nanoplates is revealed by numerical results. It is shown that large different results of deflections and natural frequencies between NSGT and classical theory are indicated through numerical examples.