Deterministic and robust optimization of a square plate
Optimization and reliability of the Hydroforming process

In this example, we solve the problem of optimizing the shaping of a square plate in two different ways: a classical deterministic optimization and a robust optimization in order to compare the two.

The process involves applying an internal pressure (P) and a clamping force to prevent the sheet from wrinkling. This back pressure, set at 9 MPa, is assumed to be deterministic. This process remains sensitive to fluctuations in pressure, as well as to variations in material parameters, and in the geometric parameters of the plate, notably its initial thickness. Taking these variabilities into account during the optimization phase can make the process more robust.

These parameters are subject to considerable randomness and variation, which affects process stability and leads to significant deviations in final mechanical properties. This can also...