Mechanical Analysis of Three Kinds of Beams on Non-Linear Elastic Foundation Materials

Abstract:

The deformation and internal forces of beams on non-linear elastic foundation materials were studied. The reaction force between the beam and the foundation was fitted as a cubic polynomial about the deflection of beams by experimental data, and the corresponding control equations were derived by the finite difference method. MATLAB program with the Newton iteration method was used to obtain numerical results. Results of the numerical example show the deformation and internal force of short non-linear and linear elastic Winkler beams are same, but the relative errors can reach 10%-20% for moderate and long beams, so the non-linear foundation effect on the settlement of beams should be considered in engineering; the relative errors of the deformation and internal force between moderate non-linear and linear elastic Winkler beams vary with the length of beams, but keep invariant for long beams.

• Periodical: Materials Science Forum (Volume 867)
• Pages: 147-151
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.867.147
• Online since: August 2016
• Authors: Xiao Liang Chen*, Zuan Tian, Jian Ping Ding
• Keywords: Beam, Deformation, Finite Difference Method, Force, Non-Linear Foundation Material

References

[1] Y. Zhong, A.M. Sun, F.L. Zhou, Y.S. Zhang. Dynamic response of beam on elastic foundation caused by variable speed moving load. Journal of Shenyang Jianzhu University (Natural Science Edition), 23(2007)776-779.

[2] X. Li, H.Z. Wang, S.P. Li, X.R. Fu, X.G. Jiang. Element for beam on Winkler elastic foundation based on analytical trail functions. Engineering Mechanics, 32(2015)66-72.

[3] W.D. Zhao, Y.P. Yang, X. Wang, S.W. Gao. Nonlinear response of a beam resting on elastic foundation subjected to thermal-mechanical load. Journal of Qinghai University (Nature Science Edition), 32(2014)41-44.

[4] B.W. Sun, M.W. Liu. Brief introduction to the elastic foundation beam model and calculation method. Industrial Construction, 44(2014)818-820.

[5] K. Frydrysek, S. Michenkova, M. Nikodym. Straight beams rested on nonlinear elastic foundations-Part 1 (theory, experiments, numerical approach). Applied Mechanics and Materials, 684(2014)11-20.

DOI: 10.4028/www.scientific.net/amm.684.11

[6] Y.Q. Long. Computation on the Elastic Foundation Beams. Higher Education Press, Beijing, (1981).

[7] Q.Y. Li, N.C. Wang, D.Y. Yi. Numerical Analysis. Tsinghua University Press, Beijing, (2008).

[8] S. Michenkova, K. Frydrysek, M. Nikodym. Straight beams rested on nonlinear elastic foundations-Part 2 (numerical solutions, results and evaluation). Applied Mechanics and Materials, 684(2014)21-29.

DOI: 10.4028/www.scientific.net/amm.684.21