Three
different loadings for an elastic disk, constrained on the boundary with an
isoperimetric Cosserat coating

1 marzo 2024

Badoer, aula T1

**ore 11**

conferenza di **Davide Bigoni **Instabilities
Lab, University of Trento

*organizzato da*: Scuola di Dottorato, ambito di
ricerca Innovazione per il costruire e per il patrimonio culturale

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abstract

The mechanical behaviour of a solid body is chiefly influenced by the
way the applied loads depend on the deformation. Nevertheless, loads are often
simplified as ‘dead’ or, in other cases, reduced to ‘hydrostatic
pressure’, while different loading systems are usually not introduced.

For the bifurcation problem of an elastic disk coated with an Euler-Bernulli
elastic rod, the effects of the following three different types of radial
loading is analyzed.

(i.) ‘Hydrostatic’ or ‘pressure’ load, which
always remains orthogonal to the structural element to which it is applied in
any configuration (undeformed or deformed);

(ii.) ‘Centrally directed’ load, which acts on the
structural element remaining always directed towards the initial centre of the
ring;

(iii.) ‘Dead’ load, which remains aligned parallel to the
unit normal to the structural element to which it is applied in its undeformed
configuration.

All three above loads are conservative and the difference between them
emerges in the incremental equations, holding for departures from the trivial
configuration, so that they lead to remarkably different bifurcation loads. The
latter are analyzed through complex potentials to treat the disk’s
interior and incremental Lagrangian equations to describe the prestressed
elastic rod modelling the coating. In this way, a closed-for solution for the
bifurcation problem is obtained, valid for all different loads (i.)—(iii.).

*Acknowledgements: Financial support from ERC-ADG-2021-101052956-BEYOND
is gratefully acknowledged.*

**references**

[1] Gaibotti, M.,
Mogilevskaya, S.G., Piccolroaz, A., Bigoni D. (2024) Bifurcations of an elastic
disc coated with an elastic inextensible rod. *Proceedings of the Royal
Society A*, 480: 20230491.