Behaviour of the extensible elastica solution
(2001) In International Journal of Solids and Structures 38(46-47). p.8441-8457- Abstract
- The general form of the virtual work expression for the large strain Euler–Bernoulli beam theory is derived using the nominal strain (Biot's) tensor. From the equilibrium equations, derived from the virtual work expression, it turns out that a linear relation between Biot's stress tensor and the (Biot) nominal strain tensor forms the differential equation used to derive the elastica solution. Moreover, in the differential equation one additional term enters which is related to the extensibility of the beam axis. As a special application, the well-known problem of an axially loaded beam is analysed. Due to the extensibility of the beam axis, it is shown that the buckling load of the extensible elastica solution depends on the slenderness,... (More)
- The general form of the virtual work expression for the large strain Euler–Bernoulli beam theory is derived using the nominal strain (Biot's) tensor. From the equilibrium equations, derived from the virtual work expression, it turns out that a linear relation between Biot's stress tensor and the (Biot) nominal strain tensor forms the differential equation used to derive the elastica solution. Moreover, in the differential equation one additional term enters which is related to the extensibility of the beam axis. As a special application, the well-known problem of an axially loaded beam is analysed. Due to the extensibility of the beam axis, it is shown that the buckling load of the extensible elastica solution depends on the slenderness, and it is of interest that for small slenderness the bifurcation point becomes unstable. This means the bifurcation point changes from being supercritical, which always hold for the inextensible case, i.e. the classical elastica solution, to being a subcritical point. In addition, higher order singularities are found as well as nonbifurcating (isolated) branches. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2223709
- author
- magnusson, Anders ; Ristinmaa, Matti LU and Ljung, Christer
- organization
- publishing date
- 2001
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Stability, Elastica, Bifurcation
- in
- International Journal of Solids and Structures
- volume
- 38
- issue
- 46-47
- pages
- 8441 - 8457
- publisher
- Elsevier
- external identifiers
-
- scopus:0035834460
- ISSN
- 0020-7683
- DOI
- 10.1016/S0020-7683(01)00089-0
- language
- English
- LU publication?
- yes
- id
- 44c46e41-6c39-4f06-8ab2-0819d91d8bad (old id 2223709)
- date added to LUP
- 2016-04-04 13:41:05
- date last changed
- 2022-02-21 07:30:15
@article{44c46e41-6c39-4f06-8ab2-0819d91d8bad, abstract = {{The general form of the virtual work expression for the large strain Euler–Bernoulli beam theory is derived using the nominal strain (Biot's) tensor. From the equilibrium equations, derived from the virtual work expression, it turns out that a linear relation between Biot's stress tensor and the (Biot) nominal strain tensor forms the differential equation used to derive the elastica solution. Moreover, in the differential equation one additional term enters which is related to the extensibility of the beam axis. As a special application, the well-known problem of an axially loaded beam is analysed. Due to the extensibility of the beam axis, it is shown that the buckling load of the extensible elastica solution depends on the slenderness, and it is of interest that for small slenderness the bifurcation point becomes unstable. This means the bifurcation point changes from being supercritical, which always hold for the inextensible case, i.e. the classical elastica solution, to being a subcritical point. In addition, higher order singularities are found as well as nonbifurcating (isolated) branches.}}, author = {{magnusson, Anders and Ristinmaa, Matti and Ljung, Christer}}, issn = {{0020-7683}}, keywords = {{Stability; Elastica; Bifurcation}}, language = {{eng}}, number = {{46-47}}, pages = {{8441--8457}}, publisher = {{Elsevier}}, series = {{International Journal of Solids and Structures}}, title = {{Behaviour of the extensible elastica solution}}, url = {{http://dx.doi.org/10.1016/S0020-7683(01)00089-0}}, doi = {{10.1016/S0020-7683(01)00089-0}}, volume = {{38}}, year = {{2001}}, }