Post-buckling of a cantilever rod with variable cross-sections under combined load

Based on the geometrically nonlinear theory of axially extensible elastic rods, the governing equations of post-buckling of a clamped-free rod with variable cross-sections, subjected to a combined load, a concentrated axial load P at the free end and a non-uniformly distributed axial load q, are established. By using shooting method, the strong nonlinear boundary value problems are numerically solved. The secondary equilibrium paths and the post-buckling configurations of the rod with linearly varied cross-sections are presented.