Size effects of functionally graded moderately thick microplates: A novel non-classical simple-FSDT isogeometric analysis

This paper presents an effective plate formulation coupling the merits of isogeometric analysis (IGA) and a new non-classical simple first-order shear deformation theory (SFSDT) for static bending, free vibration, and buckling of functionally graded (FG) moderately thick microplates. In contrast to the conventional first-order shear deformation theory (FSDT), the new SFSDT adopted here inherently owns several advantages such as free from shear-locking, capturing the shear-deformation effect, and fewer unknowns. In order to capture the small scale effects, we thus introduce a non-classical SFSDT based on a modified couple stress theory. The requirement for C2-continuity in terms of the non-classical SFSDT is straightforwardly treated with the aid of inherent high-order continuity of non-uniform rational B-spline (NURBS), which serves as basis functions in our IGA framework. Numerical examples are presented and the obtained numerical results reveal that the deflection decreases while the frequency and buckling load increase with decreasing the plate thickness. Results also show that the small size effect can lead to an increase of microplate stiffness.