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Behaviour of the extensible elastica solution

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Author

Summary, in English

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.

Department/s

Publishing year

2001

Language

English

Pages

8441-8457

Publication/Series

International Journal of Solids and Structures

Volume

38

Issue

46-47

Document type

Journal article

Publisher

Elsevier

Topic

  • Mechanical Engineering

Keywords

  • Stability
  • Elastica
  • Bifurcation

Status

Published

ISBN/ISSN/Other

  • ISSN: 0020-7683