Improvements on a non-invasive, parameter-free approach to inverse form finding

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autor(en): Landkammer P, Caspari M, Steinmann P
Zeitschrift: Computational Mechanics
Jahr der Veröffentlichung: 2017
Seitenbereich: 1-15
ISSN: 0178-7675
Sprache: Englisch


Abstract


Our objective is to determine the optimal undeformed workpiece geometry (material configuration) within forming processes when the prescribed deformed geometry (spatial configuration) is given. For solving the resulting shape optimization problem—also denoted as inverse form finding—we use a novel parameter-free approach, which relocates in each iteration the material nodal positions as design variables. The spatial nodal positions computed by an elasto-plastic finite element (FE) forming simulation are compared with their prescribed values. The objective function expresses a least-squares summation of the differences between the computed and the prescribed nodal positions. Here, a recently developed shape optimization approach (Landkammer and Steinmann in Comput Mech 57(2):169–191, 2016) is investigated with a view to enhance its stability and efficiency. Motivated by nonlinear optimization theory a detailed justification of the algorithm is given. Furthermore, a classification according to shape changing design, fixed and controlled nodal coordinates is introduced. Two examples with large elasto-plastic strains demonstrate that using a superconvergent patch recovery technique instead of a least-squares (L2)-smoothing improves the efficiency. Updating the interior discretization nodes by solving a fictitious elastic problem also reduces the number of required FE iterations and avoids severe mesh distortions. Furthermore, the impact of the inclusion of the second deformation gradient in the Hessian of the Quasi-Newton approach is analyzed. Inverse form finding is a crucial issue in metal forming applications. As a special feature, the approach is designed to be coupled in a non-invasive fashion to arbitrary FE software.



FAU-Autoren / FAU-Herausgeber

Caspari, Michael
Sonderforschungsbereich/Transregio 73 Umformtechnische Herstellung von komplexen Funktionsbauteilen mit Nebenformelementen aus Feinblechen - Blechmassivumformung
Landkammer, Philipp
Sonderforschungsbereich/Transregio 73 Umformtechnische Herstellung von komplexen Funktionsbauteilen mit Nebenformelementen aus Feinblechen - Blechmassivumformung
Steinmann, Paul Prof. Dr.-Ing.
Lehrstuhl für Technische Mechanik


Zitierweisen

APA:
Landkammer, P., Caspari, M., & Steinmann, P. (2017). Improvements on a non-invasive, parameter-free approach to inverse form finding. Computational Mechanics, 1-15. https://dx.doi.org/10.1007/s00466-017-1468-2

MLA:
Landkammer, Philipp, Michael Caspari, and Paul Steinmann. "Improvements on a non-invasive, parameter-free approach to inverse form finding." Computational Mechanics (2017): 1-15.

BibTeX: 

Zuletzt aktualisiert 2018-17-10 um 05:40