Behaviour of the extensible elastica solution

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, i t turns out that a linear relation between Biot's stress tensor and the (Bi ot) nominal strain tensor forms the differential equation used to derive th e elastica solution. Moreover, in the differential equation one additional term enters which is related to the extensibility of the beam axis. As a sp ecial application, the well-known problem of an axially loaded beam is anal ysed. Due to the extensibility of the beam axis, it is shown that the buckl ing load of the extensible elastica solution depends on the slenderness, an d it is of interest that for small slenderness the bifurcation point become s unstable. This means the bifurcation point changes from being supercritic al, which always hold for the inextensible case, i.e. the classical elastic a solution, to being a subcritical point. In addition, higher order singula rities are found as well as nonbifurcating (isolated) branches. (C) 2001 El sevier Science Ltd. All rights reserved.