Conservative Static Systems

Static perturbation methods are used to analyze a linear beam on nonlinear elastic soil, namely: (i) the elastostatic response to transverse forces, and (ii) the buckling and postbuckling induced by a compression force. The general case of non-symmetric soil is first addressed for both problems, and then specialized to symmetric soil. Concerning the elastostatic problem, a series expansion of the displacement field, as a function of the transverse load multiplier, is obtained. Regarding the buckling problem, the branched path and the displacement field are drawn as power expansions of the axial load multiplier. Moreover, the effect of imperfections, represented by small transverse forces, is investigated.