Post-buckling of linearly tapered column made of nonlinear elastic materials obeying the generalized Ludwick constitutive law

This paper aims to present the post-buckling behavior of a linearly tapered column with pinned ends made of nonlinear elastic materials and subjected to an axial compressive force. The stress–strain relationship of such materials is represented by the generalized Ludwick constitutive law. The column has a rectangular cross-section with a constant width and linearly varying depth along the length of the column. The governing equations are derived by considering the geometrical and material nonlinearities. Up to this point, a set of strongly nonlinear simultaneous first-order differential equations with boundary conditions is established and numerically solved by using the shooting method. The effects of material nonlinearity parameter n   and depth ratio h¯B/h¯A on the equilibrium configurations and the equilibrium paths are investigated and thoroughly discussed herein. As a result, many interesting features found in the nonlinear hardening column exhibit the nonlinear phenomena such as a non-monotonic bifurcation curve, the limit load point, snap-through phenomenon and hysteresis loop.

► Column's stress–strain relationship obeys the generalized Ludwick constitutive law.
► This elastica problem is concerned with the geometric and material nonlinearities.
► Governing equations are strongly nonlinear differential equations.
► The stability is reported with any degree of material nonlinearity and depth ratio.
► Post-buckling behavior of the hardening column exhibits nonlinear phenomena.