Biannual Report - Fachbereich Mathematik - Technische Universität ...

Project: Mathematical models and algorithms for an automated product development
of branched sheet metal products
This project is part of the Collaborative Research Centre (SFB) 666 (Integral sheet metal
design with higher order bifurcations - development, production, evaluation) and addresses
the shape optimization of sheet metal products. There are two types of considered
sheet metal products: Multi-chambered profiles and hydroformed branched sheet metal
structures. For profiles, the goal is to find the optimal design of the profile-cross-sections.
For this purpose, an integrated approach combining topology and geometry optimization is
developed. Using branch and bound techniques, topological decisions are made where in
each branch and bound node a nonlinear optimization problem has to be solved. As hydroformed
parts can show arbitrary curvature, the geometry of those parts is parameterized
by cubic B-spline surfaces. The product behavior is described by the three dimensional
linear elasticity equations. To optimize the geometry optimization of the branched and hydroformed
sheet metal products, PDE constrained optimization techniques are used. The
arising nonconvex geometry optimization problem is solved with an algorithm using exact
constraints and a globalization strategy based on adaptive cubic regularization. For
decreasing the computational effort, multilevel-techniques are applied.
Partner: Collaborative Research Centre (SFB) 666: “Integral sheet metal design with
higher order bifurcations - development, production, evaluation”; speaker P. Groche (Department
of Mechanical Engineering, TU Darmstadt)
Support: German Research Foundation (DFG)
Contact: T. Göllner, H. Lüthen, M. Pfetsch, S. Ulbrich
References
[1] C. E. Ferreira, U. Günther, and A. Martin. Mathematical models and polyhedral studies for
integral sheet metal design. SIAM Journal on Optimization, 22:1493–1517, 2012.
[2] T. Göllner, U. Günther, W. Hess, A. Martin, and S. Ulbrich. Topology and geometry optimization
of branched sheet metal products. Proceedings in Applied Mathematics and Mechanics, 11:713
– 714, 2011.
[3] T. Göllner, U. Günther, W. Hess, M. Pfetsch, and S. Ulbrich. Optimierung der Geometrie und
Topologie flächiger verzweigter Blechbauteile und von Mehrkammerprofilen. Tagungsband 4.
Zwischenkolloquium Sonderforschungsbereich 666, Hrsg. Peter Groche, pages 15 – 24, 2012.
[4] T. Göllner, W. Hess, and S. Ulbrich. Geometry optimization of branched sheet metal products.
Proceedings in Applied Mathematics and Mechanics, 12:619 – 620, 2012.
[5] P. Groche, H. Birkhofer, O. Bauer, T. Göllner, S. Gramlich, V. Kaune, F. Rullmann, and O. Weitzmann.
Potenziale einer durchgängigen Produktentstehung - Nutzung technologieinduzierter
Eigenschaften zur Entwicklung von Blechstrukturen. Konstruktion, 11/12-2012, 2012.
[6] P. Groche, W. Schmitt, A. Bohn, S. Gramlich, S. Ulbrich, and U. Günther. Integration of
manufacturing-induced properties in product design. Tagungsband 4. Zwischenkolloquium Sonderforschungsbereich
666, Hrsg. Peter Groche, pages 15 – 24, 2012.
[7] W. Hess and S. Ulbrich. An inexact l1 penalty sqp algorithm for pde constrained optimization
with an application to shape optimization in linear elasticity. Optimization Methods and
Software, pages 1 – 26, 2012.
[8] O. Weitzmann, A. Schüle, T. Rollmann, R. Anderl, and T. Göllner. An object-oriented information
model for the representation of free form sheet metal parts in integral style. Tools and
Methods of Competitive Engineering, pages 725 – 738, 2012.
1.2 Research Groups 83