Parameter-Free Shape Optimization: Various Shape Updates for Engineering Applications
Lars Radtke,
Georgios Bletsos,
Niklas Kühl,
Tim Suchan,
Thomas Rung,
Alexander Düster,
Kathrin Welker
Affiliations
Lars Radtke
Institute for Ship Structural Design and Analysis (M-10), Numerical Structural Analysis with Application in Ship Technology, Hamburg University of Technology, 21073 Hamburg, Germany
Georgios Bletsos
Institute for Fluid Dynamics and Ship Theory (M-8), Hamburg University of Technology, 21073 Hamburg, Germany
Niklas Kühl
Institute for Fluid Dynamics and Ship Theory (M-8), Hamburg University of Technology, 21073 Hamburg, Germany
Tim Suchan
Faculty for Mechanical and Civil Engineering, Helmut Schmidt University, 22008 Hamburg, Germany
Thomas Rung
Institute for Fluid Dynamics and Ship Theory (M-8), Hamburg University of Technology, 21073 Hamburg, Germany
Alexander Düster
Institute for Ship Structural Design and Analysis (M-10), Numerical Structural Analysis with Application in Ship Technology, Hamburg University of Technology, 21073 Hamburg, Germany
Kathrin Welker
Institute of Numerical Mathematics and Optimization, Technische Universität Bergakademie Freiberg, 09599 Freiberg, Germany
In the last decade, parameter-free approaches to shape optimization problems have matured to a state where they provide a versatile tool for complex engineering applications. However, sensitivity distributions obtained from shape derivatives in this context cannot be directly used as a shape update in gradient-based optimization strategies. Instead, an auxiliary problem has to be solved to obtain a gradient from the sensitivity. While several choices for these auxiliary problems were investigated mathematically, the complexity of the concepts behind their derivation has often prevented their application in engineering. This work aims to explain several approaches to compute shape updates from an engineering perspective. We introduce the corresponding auxiliary problems in a formal way and compare the choices by means of numerical examples. To this end, a test case and exemplary applications from computational fluid dynamics are considered.
