Two kinds of C0-type elements for buckling analysis of thin-walled curved beams Original Research Article

This paper deals with the spatial buckling analysis of curved beams. First, a second-order expansion for the finite rigid-rotations in nonlinear strain expressions is derived and employed to produce the geometric stiffness matrix. This second-order accurate geometric stiffness matrix can ensure that all significant instability modes can be predicted. Furthermore, Timoshenkoʹs and Vlasovʹs beam theories are combined to develop two kinds of the C0-type finite element formulations for arbitrary cross-section thin-walled curved beams, which include the isoparametric curved beam element and the strain curved beam element. These two kinds of elements include both shear and warping deformations caused by bending moments and bimoments. In numerical examples, the effect of the second-order terms in the nonlinear strains on the buckling load is investigated. Furthermore, efficiencies of the proposed two kinds of elements are studied in the buckling analysis of curved beam structures.