A new semi-analytical approach to large deflections of Bernoulli–Euler-v. Karman beams on a linear elastic foundation: Nonlinear analysis of infinite beams

A new method is proposed for the analysis of a moderately large deflection of an infinite nonlinear beam resting on an elastic foundation under localized external loads. For that, based on the v. Karman approximation of geometrical non-linearity, the system of nonlinear integral equations is first formulated, which is equivalent to the original differential equation of the nonlinear beam. Thereby, we can develop an iterative procedure which completely solves the present nonlinear problem. Our results demonstrate that the method proposed is not only simple and straightforward but achieves an accurate solution with just a few iterations. The method also covers a wide range of applications in practical design solutions.

► A new method is proposed for analyzing large deflections of a nonlinear beam. ► The v. Karman's geometrically non-linear beam is considered for the analysis. ► The proposed method, simple but straightforward, is a new iterative procedure. ► It achieves an accurate nonlinear solution with just a few iterations. ► It covers a wide range of applications in practical design solutions.