Linear Analysis of Planar Curved Bi-directional Functionally Graded Microbeams Using the Modified Couple Stress Theory

This paper presents an efficient formulation for linear analysis of planar curved microbeams made of bi-directional functionally graded materials. The formulation is derived using the modified couple stress theory in conjunction with the kinematic assumptions of the Euler-Bernoulli beam theory. Univariate non-uniform rational B-spline (NURBS) basis functions are used to discretize the kinematic unknowns. In addition, the volume fraction of materials is described by a NURBS surface to enable the consideration of arbitrary variations of material properties in two directions, i.e., the directions of the beam axis and cross-sectional height. To validate the presented formulation, linear static and vibration analyses of a semi-circular microbeam are performed. Since the exact solutions of the considered problems do not exist, the reference solutions are obtained with significantly many isogeometric plane elements, and the accuracy and efficiency of the proposed formulation are assessed.