In-plane and out-of-plane dynamics and buckling of functionally graded circular curved beams

In this paper the dynamic and buckling features of slender structures with curved axis are addressed. A survey on the literature concerning mechanics of beams constructed with non-homogeneous materials or with functionally graded materials reveals only a few papers devoted to the dynamics and buckling of curved beams constructed with such materials. This problem was tackled mainly through 2D or 3D numerical formulations, but comprehensive beam theories on the matter are scarce. In the present paper a model of non-homogeneous and/or FGM curved beams is developed. The model is deduced by adopting a consistent displacement field which incorporates second order rotational terms based on the semi-tangential rule. The model also incorporates the shear flexibility due to bending and warping due to twisting effects. Arbitrary initial stresses and initial off-axis loads are taken into account in the linearized principle of virtual works. The finite element method is employed to discretize the motion equations with the objective to solve problems of dynamics, statics and buckling. The model contains, as particular cases, several straight beam theories as well as curved beam theories. Some comparisons with the available experimental data of the open literature are performed in order to illustrate the predictive features of the model, and comparisons with 2D and 3D finite element approaches are also performed.