[an error occurred while processing this directive]
The paper presents a concise
framework investigating the stability of curved beams. The governing equations used
are both geometrically exact and fully intrinsic; that is, they have no displacement
and rotation variables, with a maximum degree of nonlinearity equal to two. The
equations of motion are linearized about either the reference state or an equilibrium
state. A central difference spatial discretization scheme is applied, and the resulting
linearized ordinary differential equations are cast as an eigenvalue problem. The
scheme is validated by comparing predicted numerical results for prebuckling
deformation and buckling loads for high arches under uniform pressure with
published analytical solutions. This is a conservative system of forces despite
their being modeled as distributed follower forces. The results show that the
stretch-bending coupling term must be included in order to accurately calculate the
prebuckling curvature and bending moment of high arches. In addition, the
lateral-torsional buckling instability of curved beams under tip moments is
investigated. Finally, when a curved beam is loaded with nonconservative
forces, resulting dynamic instabilities may be found through the current
framework.
