Shape Parametrization & Morphing in Sheet-Metal Forming

• Published in: Procedia manufacturing Vol. 47; pp. 702 - 706
• Main Authors: Thomas, Anoop Ebey, Guevelou, Simon, Pasquale, Edmondo Di, Chambard, Anne, Duval, Jean-Louis, Chinesta, Francisco, Limousin, Victor, Delgerie, Xavier, Leroy, Emmanuel
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 2020
• Subjects: 3D surface morphing; Conformal Mapping; Ricci flow; s-PGD; Shape parametrization; SSL-PGD; Yamabe flow; SSL-PGD; Yamabe flow; Ricci flow; Shape parametrization; s-PGD; Conformal Mapping; 3D surface morphing
• ISSN: 2351-9789; 2351-9789
• DOI: 10.1016/j.promfg.2020.04.216

Numerical simulations have long been used in many engineering process industries for the virtual evaluation of responses from an accurate solution of the physics/mathematical models describing it. However, in most industrial cases, these simulations tend to be time-consuming, especially in studies involving parameter optimization studies/inverse analysis where a multitude of direct computations are necessary. Non-intrusive Model Order Reduction techniques (SSL-PGD, s-PGD) enable the construction of parametric solution spaces to ensure almost instantaneous responses to changes in input parameters. These parametrized solutions are built from snapshots generated from simulations using commercially available software, but the process parameters and re-meshing rules add a condition that the different snapshots be suitably parametrized for being able to compute and represent the parametric solutions using the MOR techniques. The snapshots generated in the case of sheet-metal forming simulations are 3D surfaces. Even though surface parametrization is a fairly easy process in the case of planar surfaces, the problem ceases to be trivial in the case of 3D surfaces. In this work, we present a conformal mapping procedure based on the Riemannian surface parametrization using the Yamabe-flow for the parametrization of 3D surfaces into planar 2D surfaces. These parametrized surfaces can then be interpolated to create parametric solution configurations for the full range of input parameters and hence allows the application of non-intrusive model order reduction techniques to simulations which include adaptive mesh refinement.