6.4 Answers for Problems from Chap. 4
147
Fig. 6.13 Convergence rate of the finite difference approximation for a cantilevered Timoshenko
beam with distributed or point load; dim. = 2 × (domain nodes − 1)
u Z (L) = −
3072E
2 I
2
Y + 1024E I Y k s AG L
2
+ 11k
2
s A
2 G
2 L
4
L F 0
32k s AG E I Y
64E I Y + k s AG L 2
(5 nodes) .
(6.195)
6.5 Answers for Problems from Chap. 5
5.1 Comparison between analytical and layer-wise integration of the bending
stiffness
The relative error as a function of the layer number for different size of the plastic
zone is shown in Fig. 6.14.
5.2 Investigation of the proportions of the relative bending stiffness
The absolute and relative difference between the proportions of the relative bending
stiffness in the elastic range within the layered approach is shown in Fig. 6.15.
5.3 Elasto-plastic finite difference solution: influence of layer number
The numerical results for the deformed shape and a comparison with the analytical
solution is presented in Table 6.3.
5.4 Elasto-plastic finite difference solution: influence of load increment