150
6 Answers to Supplementary Problems
Table 6.3 Numerical results for deformed shape and comparison with analytical solution: influence
of k max
k max = 11
k max = 101
k max = 1001
k max = 10001
Displacement u Z (X )
X
L = 0.0
0.0
0.0
0.0
0.0
X
L = 0.25
−0.110762
−0.120338
−0.121357
−0.121390
X
L = 0.5
−0.147682
−0.160451
−0.161810
−0.161853
Relative Error in %
X
L = 0.0
−
−
−
−
X
L = 0.25
2.933360
5.459040
6.352147
6.380597
X
L = 0.5
2.933148
5.459271
6.352380
6.380830
Table 6.4 Numerical results for deformed shape and comparison with analytical solution: influence
of load increment
M = 1/5
M = 1/8
M = 1/10
Displacement u Z (X )
X
L = 0.0
0.0
0.0
0.0
X
L = 0.25
−0.128549
−0.119502
−0.120338
X
L = 0.5
−0.171399
−0.159336
−0.160451
Relative Error in %
X
L = 0.0
−
−
−
X
L = 0.25
12.654530
4.726031
5.459040
X
L = 0.5
12.654777
4.726261
5.459271
References
1. Öchsner A (2014) Elasto-plasticity of frame structure elements: modeling and simulation of
rods and beams. Springer, Berlin
2. Öchsner A (2020) Computational statics and dynamics: an introduction based on the finite
element method. Springer, Singapore