The track geometry is a critical factor that affects the running safety and riding comfort of trains moving on a high-speed railway bridge.This study addresses the mapping relationship between the track deformation an...The track geometry is a critical factor that affects the running safety and riding comfort of trains moving on a high-speed railway bridge.This study addresses the mapping relationship between the track deformation and lateral deformations of bridges.Equilibrium equations and natural boundary conditions of the track-bridge system are established based on the energy variational principle,and an analytical solution is derived for the track deformation accounting for lateral bridge deformations.A five-span simply-supported bridge with continuous welded rail has been selected as the case study.The mapping rail deformations are compared to the finite element results,and both results agree well with each other,validating the analytical method proposed in this paper.The influence factors on the mapping rail deformation are further evaluated.Results show that the mapping rail deformation is consistent with the girder displacement at the area that is away from the girder ends when the flexural stiffness ratio between the track and the bridge girder is low.The interlayer stiffness has a significant effect on the mapping rail deformation when the track flexural stiffness is of a high value.展开更多
From the viewpoint of continuous systems, optimal control problem is proposed for a class of controlled Hybrid dynamical systems. Then a mathematical method- HDS minimum principle is put forward, which can solve the a...From the viewpoint of continuous systems, optimal control problem is proposed for a class of controlled Hybrid dynamical systems. Then a mathematical method- HDS minimum principle is put forward, which can solve the above problem. The HDS minimum principle is proved by means of Ekeland＇ s variational principle.展开更多
A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forwar...A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forward modeling was derived from Maxwell's equations using general variation principle. The divergence condition was added forcedly to the electric field boundary value problem, which made the solution correct. The system of equation of the finite element algorithm was a large sparse, banded, symmetric, ill-conditioned, non-Hermitian complex matrix equation, which can be solved using the Bi-CGSTAB method. In order to prove correctness of the three-dimensional magnetotelluric forward algorithm, the computed results and analytic results of one-dimensional geo-electrical model were compared. In addition, the three-dimensional magnetotelluric forward algorithm is given a further evaluation by computing COMMEMI model. The forward modeling results show that the algorithm is very efficient, and it has a lot of advantages, such as the high precision, the canonical process of solving problem, meeting the internal boundary condition automatically and adapting to all kinds of distribution of multi-substances.展开更多
基金Project(2021RC2011)supported by the Science and Technology Innovation Program of Hunan Province,ChinaProjects(U1934207,52178180)supported by the National Natural Science Foundation of ChinaProject(2021M703648)supported by the China Postdoctoral Science Foundation。
文摘The track geometry is a critical factor that affects the running safety and riding comfort of trains moving on a high-speed railway bridge.This study addresses the mapping relationship between the track deformation and lateral deformations of bridges.Equilibrium equations and natural boundary conditions of the track-bridge system are established based on the energy variational principle,and an analytical solution is derived for the track deformation accounting for lateral bridge deformations.A five-span simply-supported bridge with continuous welded rail has been selected as the case study.The mapping rail deformations are compared to the finite element results,and both results agree well with each other,validating the analytical method proposed in this paper.The influence factors on the mapping rail deformation are further evaluated.Results show that the mapping rail deformation is consistent with the girder displacement at the area that is away from the girder ends when the flexural stiffness ratio between the track and the bridge girder is low.The interlayer stiffness has a significant effect on the mapping rail deformation when the track flexural stiffness is of a high value.
文摘From the viewpoint of continuous systems, optimal control problem is proposed for a class of controlled Hybrid dynamical systems. Then a mathematical method- HDS minimum principle is put forward, which can solve the above problem. The HDS minimum principle is proved by means of Ekeland＇ s variational principle.
基金Project(60672042) supported by the National Natural Science Foundation of China
文摘A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forward modeling was derived from Maxwell's equations using general variation principle. The divergence condition was added forcedly to the electric field boundary value problem, which made the solution correct. The system of equation of the finite element algorithm was a large sparse, banded, symmetric, ill-conditioned, non-Hermitian complex matrix equation, which can be solved using the Bi-CGSTAB method. In order to prove correctness of the three-dimensional magnetotelluric forward algorithm, the computed results and analytic results of one-dimensional geo-electrical model were compared. In addition, the three-dimensional magnetotelluric forward algorithm is given a further evaluation by computing COMMEMI model. The forward modeling results show that the algorithm is very efficient, and it has a lot of advantages, such as the high precision, the canonical process of solving problem, meeting the internal boundary condition automatically and adapting to all kinds of distribution of multi-substances.
