Non linear buckling of columns

Abstract EN

The geometric non-linear total potential energy equation is developed and extended to study the behavior of buckling and deflection beyond the bifurcation point and showing columns resistance beyond the Euler load.

Three types of boundary conditions are studied (pin ended, fixed ended and cantilever).

The equation of non-linear total potential energy is solved by exact method (closed form solution) and compared with other approximated methods Rayleigh-Ritz, Koiter’s theory and non-linear finite difference method.

The agreement is found quite enough and satisfactory for most situations of practical cases.