Modified nonlocal couple stress isogeometric approach for bending and free vibration analysis of functionally graded nanoplates

In this article, isogeometric analysis (IGA) based on the modified nonlocal couple stress theory (MNCST) is introduced to study bending and free vibration characteristics of functionally graded (FG) nanoplates placed on an elastic foundation (EF). The MNCST is a combination of nonlocal elasticity theory and modified couple stress theory to capture the small-size effects most accurately, hence this theory considers both softening and stiffening effects on responses of FG nanoplates. A higher order refined plate theory is adapted, because it satisfies parabolic distributions of transverse shear stresses across the nanoplate thickness and equals zero at the top and bottom surfaces without requiring shear correction factors. The governing equations are obtained using Hamilton's principle from which deduce the equations determining the natural frequency and displacement of the FG nanoplates. Several comparison studies are conducted to verify the proposed model with other results in the literature. Furthermore, the influence of nonlocal parameters, material length parameters, boundary conditions, material volume exponent on the bending, and free vibration response of FG nanoplates are fully studied.