Acta Mechanica

, Volume 230, Issue 10, pp 3511–3523 | Cite as

A homogenized theory for functionally graded Euler–Bernoulli and Timoshenko beams

  • Giovanni FalsoneEmail author
  • Gabriele La Valle
Original Paper


A new theoretical approach to resolve functionally graded beams is the subject of the present work. In particular, it is shown how the definition of some particular generalized quantities allows to simplify the form of the differential equations governing the response of both Euler–Bernoulli and Timoshenko functionally graded beams. Indeed, they take the same form as the differential equations governing the axial and the bending equilibrium in the Euler–Bernoulli theory. This result is obtained in both the cases of material variation in transversal and axial direction.



This study was funded by MIUR (PRIN 2015 \(\hbox {n}^{\circ }\) B82F16005920005), Grant/Award Number: 2015JW9NJT and 2017J4EAYB.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria CivileUniversità di MessinaMessinaItaly

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