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.

(2016). Analytical solution for the elastic bending of beams lying on a variable Winkler support [journal article - articolo]. In ACTA MECHANICA. Retrieved from http://hdl.handle.net/10446/57964

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

FROIO, Diego;RIZZI, Egidio
2016

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.
articolo
Froio, Diego; Rizzi, Egidio
(2016). Analytical solution for the elastic bending of beams lying on a variable Winkler support [journal article - articolo]. In ACTA MECHANICA. Retrieved from http://hdl.handle.net/10446/57964
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/57964
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