A Nonlocal IGA Numerical Solution for Free Vibration and Buckling Analysis of Porous Sigmoid Functionally Graded (P-SFGM) Nanoplate

The aim of this work is to investigate the free vibration and buckling characteristics of sigmoid functionally graded (FG) nanoplate with the influence of porosity. The modified rule of the mixture is utilized to calculate the effective material properties of porous sigmoid functionally graded (P-SFGM) nanoplate. Three schemes of porosity distribution, including uniform, symmetric and nonsymmetric are investigated. The first-order shear deformation theory is utilized to simulate the displacement fields of P-SFGM nanoplate. Eringen's nonlocal elastic theory and isogeometric analysis (IGA) are used to establish the governing equations for free vibration and buckling analysis of nanoplate structure with small size effect. By using NURBS as a basic function, IGA can fulfill the higher-order derivative requirement of governing equations. The accuracy of the presented solution is verified. By taking the nonlocal parameter into account, the stiffness of the plate is softened. Also, the effects of porosity distribution across the plate's thickness, porosity parameter, material power index, boundary conditions (BCs) and aspect ratio on the frequency response of P-SFGM nanoplate are presented.

Automated summary

The aim of this work is to investigate the influence of porosity on the free vibration and buckling characteristics of sigmoid functionally graded nanoplate. Modified rule of the mixture is used to calculate the effective material properties of porous sigmoid functionally graded nanoplate. Three schemes of porosity distribution are investigated. The governing equations for free vibration and buckling analysis are established using Eringen's nonlocal elastic theory and isogeometric analysis. The effects of porosity distribution, porosity parameter, material power index, boundary conditions, and aspect ratio on the frequency response of nanoplate are presented.