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978-3-8439-1911-1, Reihe Mathematik

Thea Göllner
Geometry Optimization of Branched Sheet Metal Structures with a Globalization Strategy by Adaptive Cubic Regularization

147 Seiten, Dissertation Technische Universität Darmstadt (2014), Softcover, B5

Zusammenfassung / Abstract

The topic of this work is the geometry optimization of branched and possibly curved sheet metal parts, that are considered in the framework of Collaborative Research Centre 666, in order to further improve their stiffness under load. This leads to a shape optimization problem with partial differential equations as constraints.

The PDE constraints arise from the description of the physical behaviour of the considered structure. Here, the three-dimensional linear elasticity equations are applied. Further, (potentially nonlinear) constraints on the geometry are posed, for example bounds on the size of the part or on the curvature of the webs. For a suitable, and CAD-compatible, description of the sheet metal geometries methods of free form surfaces are employed.

To solve the resulting shape optimization problems, an algorithm with a globalization strategy based on adaptive cubic regularization techniques is developed. This algorithm is then extended to a version which allows inexact evaluations of the objective function and its gradient. For both versions, we show global convergence of the method.

Following this, we apply the presented algorithm to geometry optimization problems for branched sheet metal structures and give numerical results for different examples.