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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 104
PROCEEDINGS OF THE SECOND INTERNATIONAL CONFERENCE ON RAILWAY TECHNOLOGY: RESEARCH, DEVELOPMENT AND MAINTENANCE
Edited by: J. Pombo
Paper 222

The Analysis of Beams subject to Moving Loads using: Coiflets, the Wavelet Finite Element Method and the Finite Element Method

M. Musuva1, P. Koziol2, C. Mares1 and M.M. Neves3

1School of Engineering and Design, Brunel University, London, UK
2Department of Civil and Environmental Engineering, Koszalin University of Technology, Koszalin, Poland
3IDMEC, IST, Institute of Mechanical Engineering, Instituto Superior Técnico, University of Lisbon, Portugal

Full Bibliographic Reference for this paper
M. Musuva, P. Koziol, C. Mares, M.M. Neves, "The Analysis of Beams subject to Moving Loads using: Coiflets, the Wavelet Finite Element Method and the Finite Element Method", in J. Pombo, (Editor), "Proceedings of the Second International Conference on Railway Technology: Research, Development and Maintenance", Civil-Comp Press, Stirlingshire, UK, Paper 222, 2014. doi:10.4203/ccp.104.222
Keywords: wavelet finite element method, moving load, finite element, infinite beam, wavelet expansion, viscoelastic foundation.

Summary
Recent railway engineering underlines the necessity of finding new methods enabling parametrical analysis of dynamic systems associated with rail-track modelling, especially those linked to moving load analysis. A fundamental comparative study on the application of some conventional and wavelet based approaches to moving load analysis is presented in this paper: the classical finite element analysis (FEM), the modified wavelet finite element method (WFEM) and the semi-analytical formulation based on coiflet expansion. The properties of wavelets allow for the function approximations to rapidly converge to the exact solution. Hence, it is for this reason that research of the WFEM in the analysis of structural problems is ongoing and has demonstrated its ability to overcome some difficulties and limitations of the FEM, particularly for problems with regions of the solution domain where the gradient of the field variables is expected to vary rapidly or suddenly, leading to higher computational costs or possible inaccurate results. Another approach, based on an analytical formulation for structures that can be described in terms of the Fourier transforms, uses the coiflet expansion of functions. This provides an alternative approach to classical methods, such as numerical integration or residue theorem. It provides the possibility of avoiding numerical instabilities near critical regions and it is applicable to more complex cases with strong variations such as nonlinear or stochastic systems. Numerical examples are presented for the theoretical model of uniformly distributed and harmonically varying in time load moving with a constant velocity along the beam resting on Winkler foundation, which simulates the response of railway under the moving load of a locomotive.

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