Civil Engineering Reference
In-Depth Information
TABLE 5.1
Number of Optimization Iterations for the Different Starting Points
7
Case number
1
2
3
4
5
6
Number of extrusion
simulations
37
21
39
23
41
19
1
FIGURE 5.42
Initial mesh and the extrusio
n
die defined by a four points spline—Final mesh when a quasi steady-
state has been reached and the iso-values of
˙
.
FIGURE 5.43
Plot of the objective function for the
quasi steady-state extrusion problem.
The maximum gap between the different values of the objective function is less than 3 percent, which is
close to the finite element discretization error for such a problem.
This shows the robustness of the optimization method, as well as its computational cost in terms of
number of process simulations. However, as has just been mentioned, from the convergence rate stand-
point, these examples are more severe than the forthcoming industrial applications.
Preform Shape Optimization for a Two-Step Forging Sequence
When the forging problem is not too different from problems handled in the past or when the shape of
the final part is simple, experienced designers can find the appropriate general outline of the preforming
dies. In these cases, the computer contribution will be to improve the proposed design, according to
selected optimization criteria. In the present example, it is applied to the minimization of the total
forming energy.
