Flexure of beams resting on hyperbolic elastic foundations

Abstract This article examines the static problem of the flexure of a Bernoulli-Euler beam resting on a nonlinear Winkler-type foundation. A perturbation technique is used to solve the nonlinear differential equation associated with the problem. Using this technique, the initially nonlinear problem is reduced to the solution of a set of linearised equations. For the successive solution of these equations, some analytical methods are outlined. These methods are applicable to either finite or infinite beams. As an example of the applications of the proposed analysis, the problem of the flexure of a finite beam subjected to a concentrated line load, applied at an arbitrary point of the beam, is solved. In a second example, the solution of the problem of the flexure of a finite beam having free edges and subjected to an initial displacement at its middle point is presented.