Civil Engineering Reference
In-Depth Information
50
5
T4
T10
T20
0.5
100
1000
10,000
100,000
Number of degrees of freedom, N
Figure 8.153
Rate of convergence for example 1.
50
5
T4
T10
T20
0.5
50
500 5000 50,000 500,000
Number of degrees of freedom, N
Figure 8.154
Rate of convergence for example 2.
From the graphs shown in Figures 8.153 and 8.154, it is observed that in spite of line
singularities in Examples 1 and 2, the FE solution converges with the optimal rate of conver-
gence as predicted by Equation 8.7 for the adaptive refinement analysis based on the element
size computed using Equation 8.9. Although T20 can achieve a higher convergence rate, for
the same target relative error η
o
of 1%, T10 element is the most efficient in terms of both
memory requirement and computational cost.
