Functionally graded curved Timoshenko microbeams: A numerical study using IGA and modified couple stress theory

Abstract

Studies on functionally graded (FG) curved microbeam structures are rather rare in the literature, and we thus present an effective computational approach on the basic combination of isogeometric analysis (IGA) and modified couple stress theory (MCST) for mechanical behavior analysis of such FG curved microbeams. The proposed method can cope with simultaneous complexities in material properties and geometries of the FG curved microbeams. The material properties of microbeams vary continuously along the thickness direction. The non-uniform rational B-spline (NURBS) basis functions are used to describe exactly geometries of the curved beams and displacement approximation. The MCST is adopted to capture the small-scale effects. Several examples of static bending and free vibration behaviors are presented to demonstrate the effectiveness and accuracy of the developed method. The effects of some factors (e.g., material gradient, size effect, boundary conditions, curvature, and aspect ratio of the beams) on mechanical behaviors of FG curved microbeams are investigated. The numerical results reveal that the small-scale effects decrease the deflection and increase the natural frequency because of increasing the stiffness.