Geometry Optimization of Branched Sheet Metal Products

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)