Large deflections of buckled bars under distributed axial load

An analysis of the strongly non-linear differential equations governing the elastica configuration of a flexible straight bar due to a longitudinal compressive force continuously distributed along its length, is presented in this paper. For the derivation of a straightforward closed-form solution of this complicated problem several functional transformations are used and a quantitative analysis is developed yielding reliable results in conformity with the physical problem. The functional transformations introduced in this paper though simple are original and useful in solving, without the use of numerical procedures, problems of non-linear elasticity.