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

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.

KEYWORDS:

• Infinite beam
• discontinuous non-linear elastic foundation
• Green's function
• iterative method

Additional information

Funding

The second and the corresponding author (Jinsoo Park and T.S. Jang) were supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education [grant number NRF-2011-0010090]. The corresponding author (T.S. Jang) was supported by the Financial Supporting Project of Long-term Overseas Dispatch of PNU's Tenure-track Faculty, 2013. The fourth author (H.G. Sung) acknowledges the financial support by a research program of KRISO granted by KIMST: ``Establishment of Research Infrastructure for Deepsea Offshore Engineering Basin and Development of Offshore Structure Pre-FEED Technologies''. Finally, the last co-author (Jeom Kee Paik) was supported by Leading Foreign Research Institute Recruitment Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (MSIP) [grant number 2013044761]. Jeom Kee Paik acknowledges the support of the Lloyd's Register Foundation Research Centre of Excellence at Pusan National University.