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Topology optimization of two-dimensional wave barriers
Topology optimization is an efficient tool to optimally distribute material in a design domain. It simultaneously optimizes not only the size and the shape of the design, but also the topology, making it possible to discover novel, improved design geometries. Topology optimization was originally developed for static mechanical problems, but is now used for many other applications. In this contribution, topology optimization is used to design two-dimensional wave barriers embedded in an elastic domain. Stiffened material is inserted into a design domain such that it optimally reflects and guides incoming waves by maximizing the insertion loss in an output point.When considering harmonic waves, the resulting designs significantly improve the performance as compared to classical design geometries, especially at high frequencies where interference patterns occur. In many practical applications, the response should be minimized not for a single frequency, but for a certain frequency range. For broadband sources, the frequency averaged insertion loss is maximized. This maximizes the insertion loss mainly at high frequencies. This is desired for broadband sources, but is less suited for narrowband sources, where a good performance is needed for the entire frequency range. When the minimal insertion loss over the frequency range is maximized, a more uniform performance over the frequency range of interest is obtained.
The interference patterns that provide the good performance at high frequencies make the performance sensitive to uncertainties such as geometric imperfections, the position of the source, the design domain and the receiver, the material properties, etc. As a consequence, the performance of the actual wave barrier may be far from optimal. A worst case approach is therefore used to obtain a robust design, where the worst performance of some (extreme) cases is maximized. This proves to be effective, resulting in designs that are less sensitive to variations.
Author(s):
Cédric Van hoorickx
KU Leuven, Department of Civil Engineering, Structural Mechanics Section, Kasteelpark Arenberg 40, 3001 Leuven
Belgium
Mattias Schevenels
KU Leuven, Department of Architecture, Architectural Engineering, Kasteelpark Arenberg 1, 3001 Leuven
Belgium
Geert Lombaert
KU Leuven, Department of Civil Engineering, Structural Mechanics Section, Kasteelpark Arenberg 40, 3001 Leuven
Belgium