POD Surrogates for Real-Time Multi-Parametric Sheet Metal Forming Problems
Résumé
Our approach aims at coupling the ever increasing off-line computing power of mainframe computers with the interactive on-line possibilities of ubiquitous low computing power devices at the early design stages in order to provide insight into the design problems and to search for candidate optimal design points. In the off-line phase, the method under investigation relies on combining an optimized space-filling sampling plan on the design parameter space with extensive finite elements (FE) simulations yielding a learning set of displacement fields. The objective of this paper is the on-line phase. We provide a rigorous mathematical presentation of a family of non-intrusive, bi-level surrogates. We focus on displacement field approximation by Proper Orthogonal Decomposition (POD) combined with kriging interpolation of coefficients. The method is illustrated with two simple, easily reproduced numerical examples of quality assessment of deep-drawing process of a cylindrical cup by on-the-fly plotting forming limit diagrams (FLDs) and related quantities enabling thus to spot improved design points.