On the buckling of a column in an elastic medium

Abstract

One deals with the buckling of a cantilever column in an elastic medium by the aid of the differential eqns (2), (2′) with bilocal conditions (3), (3′). Introducing the conventional load (4), one considers the three cases P cr < P 0, P cr = P 0 and P cr > P 0 and one determines the corresponding characteristics eqns (8″), (12), (15″). The reduced critical load P cr P ) and the reduced critical length l cr l are listed in a table and plotted into diagrams for various values of an adimensional magnitude bl. One obtains also the asymptotic formulae (16), (16′).