Reflection waves from high speed trains - adaptive FE solutions

Other conference contribution, 2003

Wave propagation in solid materials is of great interest in many engineering applications. The fact that the area of interest changes with time gives a number of computational problems like the need of time and place dependent mesh density. This means that the mesh must be continuously updated and controlled, leading to a large demand of computer effort. In some applications like in railway mechanics loads are moving which gives rise to certain problems like shock waves when the speed of the moving load is close to the natural speed in the underlying soil material[1]. Related to such problems the wave has to leave the defined finite element domain without reflection, which demands certain methods. The paper will deal with quality controlled FE-procedures for wave propagation including error estimation[2] and mesh refinement/coarsening. As the problems are large (3D) and need many steps in time and iteration processes to handle nonlinearities direct solvers are out of question, and iterative techniques based on multigrid[3] have to be used. As an application an important problem from railway mechanics is considered. When a high speed train approaches an area with decreasing thickness of underlying soft soil on a stiff rock, a reflection of the wave will increase the total height of the wave, in a similar way as when sea waves approaches a shallow shore; it becomes much higher and brakes. We will study this problem with the procedures described above in 2D as well as in full 3D with partly absorbing boundaries. References: [1] T. Ekevid, Computational Solid Wave Propagation – Numerical Techniques and Industrial Applications, Ph. D. thesis, Department of Structural Mechanics, Chalmers University of Technology, Publication 02:10, 2002. [2] K. Eriksson, D. Estep, P. Hansbo, C. Johnson, Computational Differential Equations, Studentlitteratur, Lund, Sweden, (1996). [3] U. Trottenberg, C. Oosterlee and A. Schüller, Multigrid, Academic Press, London (2001).