Stability of elastic column with spring supports at both clamped ends

Abstract

This paper analyzes the large deflections and stability of an elastic column. The column is supported by a spring at each of its clamped ends, and is also subject to a conservative compressive terminal force. The equilibrium equation is derived from the principle of the minimum total potential energy, and its solution is expressed using Jacobian elliptic functions. The stability is determined with the help of the Jacobi criterion, and the resulting bifurcation diagrams are also determined.