A new method for the non-linear analysis of an infinite beam on a non-linear elastic foundation: a general approach to a variable beam cross-section

Abstract

We propose a new nonlinear method for analyzing an infinite non-uniform beam resting on a nonlinear elastic foundation under localized external loads. To this end, an integral operator equation is newly formulated, which is equivalent to the original differential equation of non- uniform beam. By using the integral operator equation, we propose a new functional iterative method for beam analysis as a general approach to a variable beam cross-section. The method proposed is fairly simple as well as straightforward to apply. An illustrative example is presented to examine the validity of the proposed method. It shows that just a few iterations are required for an accurate solution.o the original differential equation of non- uniform beam. By using the integral operator equation, we propose a new functional iterative method for beam analysis as a general approach to a variable beam cross-section. The method proposed is fairly simple as well as straightforward to apply. An illustrative example is presented to examine the validity of the proposed method. It shows that just a few iterations are required for an accurate solution.