Nonlocal strain gradient IGA numerical solution for static bending, free vibration and buckling of sigmoid FG sandwich nanoplate

For the first time, a numerical isogeometric numerical solution based on the nonlocal strain gradient elasticity theory for static bending, free vibration, and buckling of sigmoid functionally graded (S-FG) nanoplate is presented. Two configurations of S-FG sandwich material, including isotropic core and FG core, are considered. A parameter is proposed to define the location of the neutral axis through the cross-section. The simple ReissnerMindlin plate theory, the nonlocal strain gradient theory, and Hamilton's principle are employed to establish the general equilibrium of S-FG nanoplate that contains two small size coefficients, including nonlocal and strain gradient parameters. The static bending, free vibration, and buckling responses of S-FG nanoplate are explored using isogeometric analysis with a NURBS basic function. The accuracy of the presented model is verified through the comparison with other solutions for nanoplate. As a result of numerical investigation studies, the static bending, free vibration, and buckling responses of S-FG are significantly affected by the material variation along the thickness direction, the neutral axis location, nonlocal parameter, strain gradient parameter, and material index