ON THE ASYMPTOTIC ANALYSIS OF THE STATIC BUCKLING OF INFINITELY LONG AND HARMONICALLY IMPERFECT COLUMN LYING ON QUADRATIC – CUBIC ELASTIC FOUNDATIONS

The analysis here is aimed at determining the static buckling load of some harmonically imperfect infinitely long columns lying on a quadratic – cubic nonlinear elastic foundation by using two slightly different perturbation schemes. In the first scheme, the perturbation parameter is given in terms of the displacement component while in the second scheme, the perturbation parameter is given in terms of the load component. Using both schemes, the static buckling load and the displacement are asymptotically obtained and the mathematical relationship between the static buckling load and imperfection amplitude is deduced.