We consider the geometry optimization of branched sheet metal structures which may exhibit an arbitrary curvature. With the new technologies linear flow splitting and linear bend splitting, developed within the framework of the Collaborative Research Centre 666, such structures can be produced continuously and in integral style. For an appropriate description of the free form geometry, a parameterization by tensor products of cubic B-splines is used, and the mechanical behaviour of the structure under load is given by the three dimensional linear elasticity equations. We formulate the resulting PDE-constrained problem for optimizing the stiffness of the considered structure. Then, an algorithm for solving these shape optimization problems is presented. Its globalization strategy is based on cubic regularization and the exact constraints of the problem are used. We conclude by showing numerical results for an engineering application.