Local and global shape functions in a boundary element formulation for the calculation of traffic induced vibrations

This paper compares the use of local and global shape functions in a boundary element method that is used in a prediction model for traffic induced vibrations. The boundary element formulation describes the interaction problem between a linear elastic layered half-space and a longitudinally invariant structure representing a road or a railway track. The boundary element formulation in the frequency–wavenumber domain is obtained by means of a weighted residual method. Constant element shape functions, as well as Legendre and Chebyshev shape functions are considered. Their effect on both accuracy and computational effort is investigated. The presence of a singularity in the Chebyshev based shape functions allows to obtain a better approximation for the soil tractions. The theory is applied to road traffic induced vibrations where the response is calculated in a large number of output points.