A tale of two nested elastic rings
Elastic rods in contact provide a rich paradigm for understanding shape and deformation in interacting elastic bodies. Here, we consider the problem of determining the static solutions of two nested elastic rings in the plane. If the inner ring is longer than the outer ring, it will buckle creating...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Published: |
Royal Society
2017
|
| _version_ | 1826259732194656256 |
|---|---|
| author | Napoli, G Goriely, A |
| author_facet | Napoli, G Goriely, A |
| author_sort | Napoli, G |
| collection | OXFORD |
| description | Elastic rods in contact provide a rich paradigm for understanding shape and deformation in interacting elastic bodies. Here, we consider the problem of determining the static solutions of two nested elastic rings in the plane. If the inner ring is longer than the outer ring, it will buckle creating a space between the two rings. This deformation can be further influenced by either adhesion between the rings or if pressure is applied externally or internally. We obtain an exact solution of this problem when both rings are assumed inextensible and unshearable. Through a variational formulation of the problem, we identify the boundary conditions at the contact point and use the Kirchhoff analogy to give exact solutions of the problems in terms of elliptic functions. The role of both adhesion and pressure is explored. |
| first_indexed | 2024-03-06T18:54:27Z |
| format | Journal article |
| id | oxford-uuid:1153de6c-e08f-442e-b6af-23164f006631 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:54:27Z |
| publishDate | 2017 |
| publisher | Royal Society |
| record_format | dspace |
| spelling | oxford-uuid:1153de6c-e08f-442e-b6af-23164f0066312022-03-26T10:01:48ZA tale of two nested elastic ringsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1153de6c-e08f-442e-b6af-23164f006631Symplectic Elements at OxfordRoyal Society2017Napoli, GGoriely, AElastic rods in contact provide a rich paradigm for understanding shape and deformation in interacting elastic bodies. Here, we consider the problem of determining the static solutions of two nested elastic rings in the plane. If the inner ring is longer than the outer ring, it will buckle creating a space between the two rings. This deformation can be further influenced by either adhesion between the rings or if pressure is applied externally or internally. We obtain an exact solution of this problem when both rings are assumed inextensible and unshearable. Through a variational formulation of the problem, we identify the boundary conditions at the contact point and use the Kirchhoff analogy to give exact solutions of the problems in terms of elliptic functions. The role of both adhesion and pressure is explored. |
| spellingShingle | Napoli, G Goriely, A A tale of two nested elastic rings |
| title | A tale of two nested elastic rings |
| title_full | A tale of two nested elastic rings |
| title_fullStr | A tale of two nested elastic rings |
| title_full_unstemmed | A tale of two nested elastic rings |
| title_short | A tale of two nested elastic rings |
| title_sort | tale of two nested elastic rings |
| work_keys_str_mv | AT napolig ataleoftwonestedelasticrings AT gorielya ataleoftwonestedelasticrings AT napolig taleoftwonestedelasticrings AT gorielya taleoftwonestedelasticrings |