Stability of a compressible elastic rod with imperfections

Stability of a compressible elastic rod, axially loaded by two concentrated forces of arbitrary intensity is studied. It is assumed that imperfections in shape and loading are present. The shape imperfections are characterized by an initial deformation of the rod axis, while the load imperfections are characterized by a small distributed force acting perpendicular to the action line of the compressive forces. A number of solutions and their local behaviour is analyzed.