Adaptive Solid Wave Propagation - Influences of Boundary Conditions in High-Speed Train Applications

Wave propagation in solid materials is of great interest in many engineering applications. The fact that the area of interest changes with time creates a number of computational problems such as the need for a mesh density varying in space and time. This means that the mesh must be continuously updated and controlled, rendering a large demand of computer effort. In certain applications like railway mechanics there are mobile loads. A load speed close to the natural speed in the underlying soil causes specific problems, shock waves being one of them. The mechanism behind high velocity wave propagation is described in Ekevid and Wibergi. Furthermore, the wave has to leave the defined finite element domain without reflection, which imposes a need for certain modeling methods. The paper will deal with quality controlled FE-procedures for wave propagation including error estimation 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 ruled out. Iterative techniques based on multigrid are preferred. 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 way resembling to sea waves approaching a shallow shore; it becomes much higher and brakes. We will study this problem with the procedures described above in full 3D with partly absorbing boundaries