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
Key words:
Bifurcation, Buckling, Columns, Finite difference method, Koiter’s theory,
nonlinear buckling and Rayleigh- Ritz method