Abstract: Based on the governing equation of buckling of the Euler’s column with large deflection, analytical approximate solutions to the buckling load and the largest deflection of the column have been established. First, the sine term that appears in the governing equation is replaced with a polynomial of degree 3 by means of the Maclaurin series expansion and the Chebyshev polynomial approximation. Subsequently, the resulting Duffing equation is approximately solved by combing the Newton’s method with the method of harmonic balance. The method yields simple linear algebraic equations instead of nonlinear algebraic equations without analytical solution. The new analytical approximations for the buckling load and the largest deflection of the Euler’s column show an excellent agreement with the numerically exact ones, and are valid over nearly the whole range of the independent variable.

Key words: buckling, large deflection, analytical approximation, Newtonharmonic balance method