Here, we address a dimension-reduction problem in the context of nonlinear elasticity where the applied external surface forces induce bending-torsion moments. The underlying body is a multi-structure in R3 consisting of a thin tube-shaped domain placed upon a thin plate-shaped domain. The problem involves two small parameters, the radius of the cross-section of the tube-shaped domain and the thickness of the plate-shaped domain. We characterize the different limit models, including the limit junction condition, in the membrane-string regime according to the ratio between these two parameters as they converge to zero.
|Original language||English (US)|
|Number of pages||47|
|Journal||Communications on Pure and Applied Analysis|
|State||Published - Dec 12 2019|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors thank Professors F. Murat for having suggested to target the model proposed in Section 6.2 and R. Alicandro and M.G. Mora for insights on the double-well case. E. Zappale is a member of GNAMPA- INdAM whose support is gratefully acknowledged.