A Refined Model for Analysis of Beams on Two-Parameter Foundations by Iterative Method

It is of great significance to study the interactions between structures and supporting soils for both structural engineering and geotechnical engineering. In this paper, based on the refined two-parameter elastic foundation model, the bending problem for a finite-length beam on Gibson elastic soil is solved. The effects of axial force and soil heterogeneity on the bending behaviours and stress states of beams on elastic foundations are discussed, and the parameters of the physical model are determined reasonably. The beam and elastic foundation are treated as a single system, and the complete potential energy is obtained. Based on the principle of minimum potential energy, the governing differential equations for the beam bearing axial force on the Gibson foundation are derived, and the equations for attenuation parameters are also defined. The problem of the unknown parameters in foundation models being difficult to determine is solved by an iterative method. The results demonstrate that this calculation method is feasible and accurate, and that the applied theory is universal for the analysis of interactions between beams and elastic foundations. Both axial force and soil heterogeneity have a certain effect on the deformation and internal force of beams on elastic foundations, and the vertical elastic coefficient of foundations is mainly determined by the stiffness of the surface soil. Additionally, attenuation parameters can be obtained relatively accurately by an iterative method, and then the vertical elastic coefficient and shear coefficient can be further obtained. This research lays a foundation for the popularisation and application of the two-parameter elastic foundation model.