Abstract:
Euler buckling is a classical problem in mechanics of materials. Linear theory can determine the Euler critical load and the corresponding buckling mode, but it cannot determine the finite post-buckling amplitude. Using a pinned–pinned rod as an example, we revisit this problem from an energy perspective. By retaining higher-order terms arising from geometric nonlinearity, we show that the Euler critical point corresponds to a degeneration of the quadratic term in the potential energy, while the quartic term determines the near-critical post-buckling branches and their stability. Euler buckling can therefore be understood intuitively as a transition of the energy landscape from a single well to a double well, naturally connecting the classical buckling problem to a Landau-type potential and a supercritical pitchfork bifurcation.