Adaptive FEA of Wave Propagation Induced by High-Speed Trains

Abstract The analysis of wave propagation in a solid under moving dynamic loads is a topic of great interest in railway engineering. On actual lines, high-level vibrations identified to be similar to supersonic booms in fluid dynamics has been observed when trains run at speeds close to or exceeding the surface wave velocities in the surrounding ground. The objective of the present paper is devoted to develop effective numerical procedures for solving problems associated with wave propagation in the track–ground system. Our approach is based on the discontinuous Galerkin space–time method, by which the finite element discretization is applied not only in space but also in time. For adaptivity, the Zienkiewicz–Zhu error estimate as well as a very simple refinement indicator based on the gradients of effective stresses (or other variables of interest) are used.

[1]  Victor V. Krylov,et al.  Generation of Ground Vibrations by Superfast Trains , 1995 .

[2]  Nils-Erik Wiberg,et al.  Error estimation and adaptive procedures based on superconvergent patch recovery (SPR) techniques , 1997 .

[3]  Nils-Erik Wiberg,et al.  Adaptive finite element procedures for linear and non‐linear dynamics , 1999 .

[4]  Nils-Erik Wiberg,et al.  STRUCTURAL DYNAMIC ANALYSIS BY A TIME‐DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD , 1996 .

[5]  O. C. Zienkiewicz,et al.  The finite element method, fourth edition; volume 2: solid and fluid mechanics, dynamics and non-linearity , 1991 .

[6]  Claes Johnson,et al.  Discontinuous Galerkin finite element methods for second order hyperbolic problems , 1993 .

[7]  Xiangdong Li.  Adaptive Finite Element Procedures in Structural Dynamics , 1996 .

[8]  Chris Jones,et al.  Ground vibration generated by a load moving along a railway track , 1999 .

[9]  Karl Popp,et al.  Vehicle-Track Dynamics in the Mid-Frequency Range , 1999 .

[10]  Klaus Knothe,et al.  Receptance behaviour of railway track and subgrade , 1998 .

[11]  T. Hughes,et al.  Space-time finite element methods for elastodynamics: formulations and error estimates , 1988 .

[12]  Chris Jones,et al.  Ground vibration generated by a harmonic load acting on a railway track , 1999 .

[13]  J. Z. Zhu,et al.  The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique , 1992 .

[14]  Nils-Erik Wiberg,et al.  Wave Propagation in Solids by Adaptive DG-FE-Procedure , 1999 .

[15]  Thomas J. R. Hughes,et al.  Space-time finite element methods for second-order hyperbolic equations , 1990 .

[16]  Klaus Knothe,et al.  Modelling of Railway Track and Vehicle/Track Interaction at High Frequencies , 1993 .

[17]  J. Neumann,et al.  Analysis of Shell Structures under Transient Loading Using Adaptivity in Time and Space , 2001 .

[18]  L Fryba,et al.  VIBRATION OF SOLIDS AND STRUCTURES UNDER MOVING LOADS (3RD EDITION) , 1999 .

[19]  J. Z. Zhu,et al.  The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity , 1992 .

[20]  Claes Johnson,et al.  Introduction to Adaptive Methods for Differential Equations , 1995, Acta Numerica.

[21]  Victor V. Krylov,et al.  Effects of track properties on ground vibrations generated by high-speed trains , 1998 .