Spatially curved functionally graded Timoshenko microbeams: A numerical study using IGA

Abstract In this paper, we present numerical investigations on static bending and free vibration behaviors of spatially curved functionally graded (FG) microbeam using isogeometric analysis (IGA). The material properties change continuously along the thickness direction. The small scale effects are captured using the modified couple stress theory while microbeam kinematics are described by Timoshenko beam theory, and the spatially curved microbeam is represented by the Frenet–Serret bases. The geometries of curved microbeams are exactly represented with the non-uniform rational B-spline (NURBS) basis functions, and the same basis functions are applied to obtain displacement field approximation. Numerical examples are presented and computed results are then compared with reference methods to show the accuracy of the developed method. The effects of some factors including material gradient factor, material length scale parameter, and boundary conditions on the mechanical behaviors of spatially curved FG Timoshenko microbeams are investigated.