| In recent years,the railway infrastructure has been under great pressure due to the increasing demand for rail transport.There is a considerable amount of railway track around the world consisting of seamless tracks,which have the potential to reduce maintenance costs,increase the service life of track and train components,increase passenger comfort,and reduce energy consumption and noise emissions.The advantages are many,but there is also the risk of derailment of the train due to track buckling in the transverse plane.Because the present nonlinear finite element method can not deal with the high-order variational,it can only solve the critical load and buckling mode,and can not judge the stability of the critical equilibrium state,so it can not give the range of the relative foundation stiffness when the critical equilibrium state is stable or unstable.On this basis,this paper proposes a theoretical analysis method for the stability of critical equilibrium state of axial compression bar and track on Winkler elastic foundation.In this paper,the stability of critical equilibrium state of hinged supports column on Winkler elastic foundation is studied by using Koiter’s theory.The exact expression of curvature is introduced into the potential energy.The perturbation is expanded by Fourier series,and the second-order variation of the potential energy is semi-positive definite at critical equilibrium.Then,the stability of critical equilibrium state is analyzed by judging the sign of high-order variation.The critical load and buckling mode are compared with the ANSYS simulation results,the previous theoretical and experimental results.On this basis,the stability of the critical equilibrium state of hinged supports column on Winkler elastic foundation under uniform torsional restraint is studied.It is found that with the increase of relative torsional stiffness,the range of relative support stiffness under stable critical equilibrium state also increases gradually.A mechanical model is established to simulate the local instability of railway track.The stability of the critical equilibrium state of the hinged supports column on Winkler elastic foundation with imperfects at the left end is analyzed.Euler’s equation is obtained by the second-order variation of the potential energy equation.According to the range of the critical load factor,the solution of the characteristic equation is discussed and the buckling mode function is obtained.The theoretical results are in agreement with the results of critical load and buckling mode obtained by ANSYS simulation.When antisymmetric buckling occurs in the railway track,the buckling modes are stable and can appear in actual situations. |
