Civil Engineering Reference
In-Depth Information
preforming tools of a complex forging sequence, making it possible either to remove folding defects, to
obtain the right forged part at the end of the process, or to minimize the forging energy. The proposed
new design methodologies introduce new ideas and may allow standardization of the design procedures.
Prospect
The future of the optimization techniques is rich. First, more complex constitutive equations, more
complex metal forming problems, and more complex objective functions can be handled with the same
approach. It requires some additional efforts for their developments but does not present any theoretical
difficulty. The multi-objective optimization has not been much studied till now but several strategies can
be developed in order to answer more precisely the actual design problem, which is always a compromise
between several objectives. Our presentation has been limited to axisymmetrical problems, mainly for
computational time reasons. However, three-dimensional non-steady-state metal forming softwares are
available, exhibiting the same level of accuracy as two-dimensional softwares. It is then possible to extend
these techniques to three-dimensional processes. Moreover, it can be noticed that several forging preforms
are axisymmetrical while the final part is three-dimensional. These problems provide an intermediate
step before handling a complete three-dimensional optimization procedure and the related computational
costs. Finally, we have seen that these methods can be applied to a wide range of metal forming processes,
but they can also be extended to other materials such as polymers, glass, etc. For instance, they could be
applied to the thermal regulation of the extrusion dies of polymer profiles, or to the pressure cycle
optimization of the glass bottle blowing process.
Regarding the development these techniques, two different costs have been emphasized: the computa-
tional cost of the simulation and the human cost required by the differentiation of the finite element
softwares. For the first issue, the generalization of parallel computer offers an easy answer. The optimization
method based on the approximation of the objective functions is easy to parallelize with a high efficiency.
For the methods based on the gradients calculations, the parallelization is tougher. It requires the paral-
lelization of the metal forming softwares. However, this is already available for some. Regarding the second
source of costs, a lot of potentials are offered by the automatic differentiation softwares. In fact, they make
it possible to carry out a fast and reliable sensitivity analysis. The generated code is rather inefficient in
terms of computational time and it is too memory requiring. Consequently, it has to be improved and
optimized by hand. This is, however, much easier and much faster than carrying out the entire differen-
tiation by hand. So, an important reduction of the development time is expected from this technique.
For the closure, we believe that in a near future optimization methods will be as popular in metal
forming applications as they are now in structural mechanics.
References
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