Finite elements in Fourier transformed domain for the simulation of trains in tunnels
Résumé
For the simulation of railway tunnels in an anisotropic horizontally layered medium a combined approach with boundary and finite elements is presented. To reduce the numerical efforts it is assumed that the structure is straight and infinitely long. In this case, a Fourier transformation about the longitudinal coordinate reduces the dimensionality. In the 2.5D approach, a sequence of 2D simulations is needed instead of one large simulation in 3D. The soil is simulated by the boundary element method. The structure is divided into finite elements in 2.5D. The derivation of a plane triangular element for an isotropic medium for the super structure and the tunnel wall, and a point element for the rail in the 2.5D domain are derived. The derivation is based on a modified Plancherel?s theorem. This theorem leads to a coupling of the positive and negative wave numbers. A derivation with respect to the negative wave number side leads to a set of linear equations that depend on the unknowns at the positive wave number side.
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