Moving least squares response surface approximation: Formulation and metal forming applications

Authors:
Piotr Breitkopf;Hakim Naceur;Alain Rassineux;Pierre Villon
Affiliations:
Laboratoire de Mécanique Roberval UMR 6066 UTC-CNRS, Université de Technologie de Compiègne, BP 20529, Compiègne 60206, France;Laboratoire de Mécanique Roberval UMR 6066 UTC-CNRS, Université de Technologie de Compiègne, BP 20529, Compiègne 60206, France;Laboratoire de Mécanique Roberval UMR 6066 UTC-CNRS, Université de Technologie de Compiègne, BP 20529, Compiègne 60206, France;Laboratoire de Mécanique Roberval UMR 6066 UTC-CNRS, Université de Technologie de Compiègne, BP 20529, Compiègne 60206, France
Venue:
Computers and Structures
Year:
2005

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Abstract

We focus on a successive response surface method for the optimization problems. The response surfaces are built using Moving Least Squares approximations constructed within a moving region of interest. Our first approach is an extension of pattern search algorithms with a fixed pattern panned and zoomed in a continuous manner across the design space. In the second one, the region of interest moves across a predefined discrete grid of authorized experimental designs. Two examples of the sheet metal forming process are used to demonstrate the robustness of the method. We use the one-step Inverse Approach as a surrogate model during the optimization. The final designs is validated with Stampack commercial code based on Explicit Dynamics Approach.