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1.	magnusson, Anders, et al. (author) Behaviour of the extensible elastica solution 2001 In: International Journal of Solids and Structures. - 0020-7683. ; 38:46-47, s. 8441-8457 Journal article (peer-reviewed)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.

magnusson, Anders, et al. (author)
Behaviour of the extensible elastica solution
2001
In: International Journal of Solids and Structures. - 0020-7683. ; 38:46-47, s. 8441-8457
Journal article (peer-reviewed)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.

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