Shape optimization of the time-harmonic response of vibroacoustic devices using cut elements

Sumer B. Dilgen*, Jakob S. Jensen, Niels Aage

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

This article presents a method for generalized shape optimization of time-harmonic vibroacoustic problems. The modeling approach utilizes an immersed boundary cut element method in conjunction with a level set representation of the geometry. The cut element method utilizes a fixed background mesh, a dimensionless contrast parameter and an integration scheme to realize complex geometries and obtain accurate physical solutions to the governing problem. The design parameterization is obtained using a nodal level set description, directly linked to the mathematical design variables, and the gradients of the objective and the constraints are obtained with the discrete adjoint approach. The framework is applied to the optimization of three 2D examples. A study on the effect of initial guess for the proposed optimization procedure is presented on a benchmark example of the design of an acoustic partitioner. Further optimization examples include design of a wave splitter to realize prescribed frequency dependent directivity for emitted acoustic waves and a suspension structure design to improve the performance of a simplified 2D model of a hearing instrument. The results demonstrate that, even though the final topology is strongly dictated by the initial design, modifying the shape allows for a significant improvement of the system behavior.

Original languageEnglish
Article number103608
JournalFinite Elements in Analysis and Design
Volume196
Number of pages19
ISSN0168-874X
DOIs
Publication statusPublished - 2021

Keywords

  • Cut finite elements
  • Immersed boundary methods
  • Level set methods
  • Shape optimization
  • Vibroacoustics

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