4. Deterministic and reliable optimization of a tube with two expansion zones

The second example discussed in this article involves hydroforming a tube with two expansion zones of different heights. The problem is solved using a classical deterministic method and a probabilistic approach, in order to compare the two. To simplify the problem, only the loading parameters are considered to be uncertain.

The finite element model is composed of a matrix with two expansion zones, and two punches that supply material to the expanded zone modeled by rigid bodies. The tube has a diameter of 45 mm and an initial thickness of 1.5 mm. The model is shown in figure 27 .