Fourier p-elements for dynamic stability of columns

Abstract

Using Fourier series as shape functions practically eliminates the ill-conditioning problem associated with high-order polynomials in structural analyses as confirmed by the newly constructed condition number diagram. This paper extends the Fourier p-elements to study the dynamic stability of frame structures. Both conservative and follower forces are considered. The results compare very well to the exact method of dynamic stiffness. It is found that the Fourier p-elements outperform the dynamic stiffness method in terms of versatility in applications and numerical stability at the very low and high ends of the frequency spectrum. New results of follower tension are given. Follower tension buckling under uniformly distributed follower tension is originally reported.