Energy Minimizers of the Coupling of a Cosserat Rod to an Elastic Continuum
Please always quote using this URN:urn:nbn:de:0296-matheon-10389
- We formulate the static mechanical coupling of a geometrically exact Cosserat rod to an elastic continuum. The coupling conditions accommodate for the difference in dimension between the two models. Also, the Cosserat rod model incorporates director variables, which are not present in the elastic continuum model. Two alternative coupling conditions are proposed, which correspond to two different configuration trace spaces. For both we show existence of solutions of the coupled problems. We also derive the corresponding conditions for the dual variables and interpret them in mechanical terms.
| Author: | Oliver Sander, Anton Schiela |
|---|---|
| URN: | urn:nbn:de:0296-matheon-10389 |
| Referee: | Peter Deuflhard |
| Document Type: | Preprint, Research Center Matheon |
| Language: | English |
| Date of first Publication: | 2012/01/30 |
| Release Date: | 2012/01/30 |
| Tag: | |
| Institute: | Freie Universität Berlin |
| Technische Universität Berlin | |
| MSC-Classification: | 74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Bxx Elastic materials / 74B20 Nonlinear elasticity |
| 74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Gxx Equilibrium (steady-state) problems / 74G65 Energy minimization | |
| 74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Kxx Thin bodies, structures / 74K10 Rods (beams, columns, shafts, arches, rings, etc.) | |
| Preprint Number: | 903 |
