Behaviour of the extensible elastica solution
(2001) In International Journal of Solids and Structures 38(4647). p.84418457 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 wellknown 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 wellknown 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:
http://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
 4647
 pages
 8441  8457
 publisher
 Elsevier
 external identifiers

 scopus:0035834460
 ISSN
 00207683
 DOI
 10.1016/S00207683(01)000890
 language
 English
 LU publication?
 yes
 id
 44c46e416c394f068ab20819d91d8bad (old id 2223709)
 date added to LUP
 20111206 13:19:53
 date last changed
 20180708 04:12:57
@article{44c46e416c394f068ab20819d91d8bad, 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 wellknown 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 = {00207683}, keyword = {Stability,Elastica,Bifurcation}, language = {eng}, number = {4647}, pages = {84418457}, publisher = {Elsevier}, series = {International Journal of Solids and Structures}, title = {Behaviour of the extensible elastica solution}, url = {http://dx.doi.org/10.1016/S00207683(01)000890}, volume = {38}, year = {2001}, }