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Acta Mechanica

, Volume 227, Issue 4, pp 1157–1179 | Cite as

Analytical solution for the elastic bending of beams lying on a variable Winkler support

  • Diego Froio
  • Egidio RizziEmail author
Original Paper

Abstract

The interaction between structures and supporting media is crucial for several engineering applications. Among existing models, the elastic one originally attributed to Emil Winkler is rather well-known to both researchers and engineers, with main reference to a constant foundation modulus. The present paper reviews first the state of the art on this model and then considers, analytically, the little-explored case of a space-dependent stiffness coefficient. The analytical solution of the ordinary differential equation describing the static deflection of a simply-supported Euler–Bernoulli elastic beam lying on a variable Winkler elastic foundation is sought. Specifically, the case of a nonlinear, minus four power variation of the stiffness coefficient is considered, allowing for closed-form representations. These are derived and examined in view of interpreting their parametric variations due to changes in the mechanical properties of the beam-foundation system. In the end, a consistent validation comparison between analytical solution and alternative reimplemented numerical treatments is produced.

Keywords

Elastic Foundation Railway Track Elastic Support Uniform Beam Subgrade Reaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 2015

Authors and Affiliations

  1. 1.Department of Engineering and Applied SciencesUniversity of BergamoDalmineItaly

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