Nonlinear Post-Buckling of Axially Functionally Graded Nonuniform Columns

A novel approach was proposed using a trial-and-error iteration method for analyzing the nonlinear post-buckling of simply supported columns subjected to a compressive force. Buckled columns have two unknowns: the initial rotation at one hinged end and the axial displacement at the other end, which are directly computed to determine the post-buckling solutions. This scheme was applied to axially functionally graded columns with nonuniform cross-sections. Based on the large-deflection theory, a set of first-order nonlinear differential equations for the problem with boundary conditions was derived and solved. Numerical experiments were performed to elucidate the effects of the material and geometric parameters on the buckled elastica, equilibrium path, and internal stress of the columns. The approach proposed exhibited fast convergence and provided accurate solutions for the post-buckling of slender columns.