Ships and Offshore Structures, Vol.15(1), page 19-28, published : Jan 2020

Numerical investigation of non-linear deflections of an infinite beam on non-linear and discontinuous elastic foundation

Author(s) : Hyoungsu Baek, Jinsoo Park, T.S. Jang, H.G. Sung & Jeom Kee Paik

Abstract : The analysis of static deflections of an infinite beam resting on a non-linear and discontinuous foundation is not trivial. We apply a recently proposed iterative non-linear procedure to the analysis. Mathematical models of the elastic foundation are incorporated into the governing non-linear fourth-order differential equation of the system and then the differential equation is transformed into an equivalent non-linear integral equation using Green’s functions. Numerical solutions of the integral equation clearly demonstrate herein that our non-linear iterative numerical method is simple and straightforward for approximate solutions of the static deflection of an infinite beam on a non-linear elastic foundation. Iterative numerical solutions converge fast to corresponding analytic solutions. However, numerical errors are observed in a narrow neighbourhood of material discontinuities of foundations.