Stability of the critical equilibrium of a compressed column on a Winkler foundation

Abstract

In this paper, the critical equilibrium of a simply supported compressed column on a Winkler foundation is analyzed based on Koiter’s theory. The exact expression of the potential energy functional is presented. By the Fourier series of the disturbance deflection, the second-order variation of the potential energy is expressed as a quadratic form. At critical equilibrium, the second-order variation of the potential energy is semi-positive definite, so that the stability of the critical equilibrium is determined by the sign of the fourth-order variation or sixth-order variation. It can be seen that only in two small ranges of elastic-foundation stiffness is the corresponding critical state stable and the bifurcation equilibrium upward. Then, the theoretical results of this paper are compared with previous experimental and theoretical results.