Example: Bifurcation analysis

Input Data

"BeamExample3_1.gif"

Nonlinear analysis

"BeamExample3_2.gif"

Buckling analysis - first 20 buckling modes
Graphics:Mode=1 γ_CR = 1.72664 Graphics:Mode=2 γ_CR = 6.90062 Graphics:Mode=3 γ_CR = 15.5042
Graphics:Mode=4 γ_CR = 27.5086 Graphics:Mode=5 γ_CR = 42.8759 Graphics:Mode=6 γ_CR = 61.5636
Graphics:Mode=7 γ_CR = 83.5315 Graphics:Mode=8 γ_CR = 108.752 Graphics:Mode=9 γ_CR = 137.222
Graphics:Mode=10 γ_CR = 167.98 Graphics:Mode=11 γ_CR = 204.198 Graphics:Mode=12 γ_CR = 242.922
Graphics:Mode=13 γ_CR = 285.46 Graphics:Mode=14 γ_CR = 332.129 Graphics:Mode=15 γ_CR = 383.292
Graphics:Mode=16 γ_CR = 439.264 Graphics:Mode=17 γ_CR = 500.012 Graphics:Mode=18 γ_CR = 564.136
Graphics:Mode=19 γ_CR = 624.763 Graphics:Mode=20 γ_CR = 894.893

"BeamExample3_23.gif"

Results

"BeamExample3_24.gif"

Results of static analysis for γ=1.
Graphics:Max[|u|]=0.4762e-2  Max[|φ|]=0 Graphics:N: Min= -0.1000e1 Max= -0.9999

"BeamExample3_27.gif"

N Euler FEM Error
1 1.72718 1.72664 -0.000311576
2 6.90872 6.90062 -0.00117326
3 15.5446 15.5042 -0.00260077
4 27.6349 27.5086 -0.00457059
5 43.1795 42.8759 -0.00703118
6 62.1785 61.5636 -0.00988971
7 84.6319 83.5315 -0.0130019
8 110.54 108.752 -0.0161684
9 139.902 137.222 -0.0191516
10 172.718 167.98 -0.0274315
11 208.989 204.198 -0.0229262
12 248.714 242.922 -0.0232886
13 291.894 285.46 -0.0220401
14 338.527 332.129 -0.0189017
15 388.616 383.292 -0.0136992
16 442.158 439.264 -0.00654508
17 499.155 500.012 0.00171634
18 559.607 564.136 0.00809415
19 623.512 624.763 0.0020053
20 690.872 894.893 0.295309
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