Bending, buckling and free vibration analyses of functionally graded curved beams with variable curvatures using isogeometric approach

A study on the bending, buckling and free vibration of functionally graded curved beams with variable curvatures using isogeometric analysis is presented here. Non-uniform rational B-splines, known from computer aided geometric design, are employed to describe the exact geometry and approximate the unknown fields of a curved beam element based on Timoshenko model. Material properties of the beam are assumed to vary continuously through the thickness direction according to the power law form. The numerical examples investigated in this paper deal with circular, elliptic, parabolic and cycloid curved beams. Results have been verified with the previously published works in both cases of straight functionally graded beam and isotropic curved beam. The effects of material distribution, aspect ratio and slenderness ratio on the response of the beam with different boundary conditions are numerically studied. Furthermore, an interesting phenomenon of changing mode shapes for both buckling and free vibration characteristics corresponding to the variation in the parameters mentioned above is also examined.