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

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.