A comparison of methods for the stability analysis of beams with varying cross sections under nonconservative loading

Four methods for the stability analysis of beams, including the variational-differential and the sagittary function methods, are considered. The dependence of solutions on the discretization parameters of these numerical methods is investigated. It is shown, that mathematical models, accurate enough for the stability analysis of columns with constant cross sections, can lead to fundamentally erroneous results in the case of varying cross sections. This is especially important for widely applied Bubnov-Galerkin and the finite element methods. The procedure for the accuracy estimation, based on the sagittary function method is given.