Stability of the bifurcation point and the initial post-buckling of an elastic column with a flexible support. (1st June 2020) - Yan-Ping, ZHAO; Lin, LI; Ming, JIN
Abstract: For the investigation of the initial post-buckling of a column built in at one end, clamped in rotation with a flexible support at the other, the stability of the bifurcation point is studied using the Fourier series. The second-order variation of the potential energy is proved to be semi-positive-definite at the bifurcation point. When the disturbance matches the buckling mode, the fourth-order variation is positive for some flexible support stiffness, and negative for other flexible support stiffness. Based on the Koiter's initial post-buckling theory, the condition on the flexible support stiffness conducive to the unstable branch path is derived. The unstable branch paths indicate that the buckling load of the column will be sensitive to the imperfections