NON LINEAR BUCKLING OF COLUMNS

Abstract:The geometric non-linear total potential energy equation is developed andextended to study the behavior of buckling and deflection beyond the bifurcationpoint and showing columns resistance beyond the Euler load.Three types of boundary conditions are studied (pin ended, fixed ended andcantilever). The equation of non-linear total potential energy is solved by exactmethod (closed form solution) and compared with other approximated methods(Rayleigh- Ritz, Koiters theory and non-linear finite difference method). Theagreement is found quite enough and satisfactory for most situations of practicalcases.Key words:Bifurcation, Buckling, Columns, Finite difference method, Koiters theory,nonlinear buckling and Rayleigh- Ritz method