Universität Karlsruhe (TH) - am Institut für Baustatik

4.4 L–shaped beam
In the next geometrical nonlinear example we investigate the post–critical behaviour of a
clamped L–shaped beam, origionally proposed in [39], see Fig. 7. The geometrical data are:
length l = 240 mm, widthb =30mm and thickness h =0.6 mm. The elastic constants are
E = 71240 N/mm 2 and ν =0.31. A buckling load of P c =1.09 has been determined in [39]
using beam elements, see also [40]. However with a width to height ratio 1/50 the beam is
rather a thin plate. Thus a discretisation with shell elements leads to slightly different results.
The post–critical path can be reached for the perfect structure using a branch switching
procedure or with the introduction of imperfections, for example a small perturbation load
P 3 = P/1000 in thickness direction. Nonlinear buckling loads are presented in Tab. 3 for
different FE–meshes. Here the loading position has a significant influence on the buckling
load. The complete load–deflection curve is computed using an arc–length scheme on the
68 element mesh. It is nearly identical to results obtained with the EAS–shell [17] andis
depicted in Fig. 8. The robustness of the present element in comparison to the element
[17] is demonstrated by the equilibrium iteration for a large step (from u 3 =19.540 mm to
u 3 =35.614 mm), see Fig. 8. Furthermore the initial mesh and the deformed mesh (for a
displacement u 3 =56.1 mm) are plotted in Fig. 7.
l
P
b
l
b
Figure 7: Geometry, initial and deformed mesh at displacement u 3 = 56.1 mm
Table 3: Nonlinear buckling loads
mesh for elements Simo et al. [9] EAS-shell [17] present
one leg center bottom center top
16×2 68 1.137 1.200 1.137 1.198 1.258
32×4 272 1.191 1.128 1.190 1.248
64×8 1088 1.186 1.125 1.186 1.244
’converged solution’ [9] 1.128
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