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Geometry Optimization of Branched Sheet Metal Products
Author(s) -
Göllner Thea,
Hess Wolfgang,
Ulbrich Stefan
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210298
Subject(s) - parameterized complexity , sheet metal , stiffness , mathematical optimization , geometry , linear elasticity , mathematics , elasticity (physics) , optimization problem , mechanical engineering , materials science , algorithm , finite element method , engineering , structural engineering , composite material
We consider the geometry optimization of branched sheet metal products, which can be produced continuously and in integral style using the new technologies of linear flow splitting and linear bend splitting. These are explored within the framework of the Collaborative Research Centre (CRC) 666. The geometry of such products can be parameterized by means of free form surfaces whereas their mechanical behaviour is described by the three dimensional linear elasticity equations. The associated PDE‐constrained problem for optimizing the stiffness of the structure is formulated and an algorithm for solving this problem using exact constraints and a globalization strategy based on adaptive cubic regularization is presented. Numerical results for an example are given. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)