A Modified Analysis Method Of Beam Foundation On The Elastic Ground And Beam On Multilayer Foundation Using Finite Element Method

In recent years,with the development of railway engineering,civil and industrial buildings,the analysis of beam foundation on elastic ground is more thorough.Beam on elastic foundation is a classic topic. However, due to the complexity of the ground and diversity of the structure and load, new foundation model, analysis method and calculation means appeared in succession, the subject is still under development. It is difficult to analyze the interaction of foundation model considering all the characteristics of soil,so the foundation model has experienced the development from the Winkler model,the elastic continuum model,the double parameter foundation model and so on.The corresponding calculation methods were also widely applied to the analysis of the model of the foundation,such as the analytical method,the energy variational method and the numerical analysis method.In fact,with the increasing precision of engineering calculation, the theoretical analysis and calculation method of elastic foundation beam is an important topic in the construction project, which still need to be solved. So based on currently theoretical research results and situation of engineering application,a modified analysis method of beams foundation on the elastic ground was put,the main results and theoretical analysis are as follows:Firstly,the calculation model of elastic foundation and common analysis methods were systematically summarized and analyzed.The development status of elastic foundation beam at abroad and home was summarized, and the mechanism and advantages and disadvantages of the calculation model of elastic foundation beam were discussed.Secondly,a modified analysis method of beam on the elastic ground was proposed by using the variational method. The main innovation of this paper is that an exact closed-form solution for beam foundation resting on the modified Vlasov elastic ground that the modulus of foundation soil exponentially increases with the increase of thickness was developed.The governing differential equation of the beam foundation was derived by using variational principle, and a dimensionless parameter that could be refined by iteration was introduced as a function of the modulus of the beam. Then, the deformation and the shear force and bending moments of the beam were determined by solving the boundary value problem.Then,interaction among the parameters was discussed in the practical analysis example, and the results werecompared with more sophisticated finite element solutions.Finally,using the finite element method, considering the characteristics of layered soil, the modified Vlasov elastic foundation that the modulus of foundation soil increases with the increase of thickness was calculated by stratified summation method. Stiffness matrix of foundation was formed according to vertical deformation of foundation soil at beam nod.then,system total stiffness matrix was formed combined with beam deformation compatibility conditions and equilibrium conditions.The results of layered foundation were compared with the modified Vlasov foundation.