On the robustness of the volumetric shrinkage method in the context of variation simulation

Welding induces high temperatures that cause residual stresses and strains in the welded structure. With a welding simulation, these stresses and strains may be predicted. A full simulation implies performing a transient thermal and a quasi-static mechanical analysis. These analyses usually involve a large number of time steps that leads to long simulation times. For welding distortions, there are approximate methods that require considerably less time. This is useful when simulating large structures or for analyses that use an iterative approach common in optimization or variation simulation. One of these methods is volumetric shrinkage, which has been shown to give reasonable results. Here it is assumed that the driving force in welding distortion is the contraction of the region that has been melted by the weld. In volumetric shrinkage, the nodes that are inside the melted region are assigned a uniform temperature and the distortion is calculated using elastic volumetric shrinkage. Although this method has been shown to give reasonable predictions, we will show that it is sensitive to small perturbations, which is an essential part in variation simulation. We also propose a modification of the volumetric shrinkage method that addresses this lack of robustness; instead of defining the melted region by applying a uniform temperature to the nodes inside the zone, we formulate an optimization problem that finds a temperature distribution such that the local melted volume is preserved. A case study with application to variation simulation has been used to elicit the proposed method