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

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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.

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  1. Department of Engineering and Applied Sciences, University of Bergamo, Viale G. Marconi 5, 24044, Dalmine, BG, Italy

    Diego Froio & Egidio Rizzi

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  1. Diego Froio
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  2. Egidio Rizzi
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Froio, D., Rizzi, E. Analytical solution for the elastic bending of beams lying on a variable Winkler support. Acta Mech 227, 1157–1179 (2016). https://doi.org/10.1007/s00707-015-1508-y

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