Spectral assessment of mesh adaptations for the analysis of the dynamical longitudinal behavior of railway bridges

Abstract

Extensive studies, [1], concerning the longitudinal behavior of long railway bridges due to braking forces have been done by measurements in situ, [2], and by statical, [3, 4], as well as dynamical simulations. Thereby, the only consistent numerical realization with respect to the measured data was the dynamical one. However, the consecutive discretizations in space and time with time-dependent system matrices are extremely time consuming due to the moving loads and varying stiffness of the ballast under, and in front of, the moving train. Therefore, every effort should be made to optimize the discretization in the space domain. This paper presents a strategy for assessing the quality of finite elements in space and for applying an adaptive mesh-refinement for this special engineering problem. The method is characterized by a spectral assessment, comparing a certain set of eigenvalues of the actual discretization with those of a very fine and rather exact numerical model. The error estimator introduced in this paper controls a whole set of global eigenvalues with corresponding natural vibration modes in order to assess certain types of shape functions. Thus, the procedure estimates local modifications on the one hand and p-properties on the other by means of global indication.