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Structural and Multidisciplinary Optimization

, Volume 59, Issue 5, pp 1567–1580 | Cite as

A simple method for coupled acoustic-mechanical analysis with application to gradient-based topology optimization

  • Jakob S. JensenEmail author
Research Paper
  • 258 Downloads

Abstract

A simple computational framework for analysis of acoustic-mechanical coupling is proposed. The method is based on extended finite element models for structural vibrations and acoustic pressure fluctuations using artificial mechanical and acoustic parameters in the non-structural and non-acoustic domains, respectively. The acoustic-mechanical interaction is created using a self-coupling matrix assembled in the entire computational domain, effectively generating coupling at acoustic-mechanical interface boundaries. The simple analysis tool circumvents the need for explicit interface tracking with accuracy controlled explicitly using a contrast parameter between the physical and artificial material parameters. Furthermore, the method’s direct applicability to gradient-based topology optimization, where elements can turn from mechanical to acoustic and vice versa, is demonstrated and illustrated using a simple example.

Keywords

Acoustic-mechanical coupling Extended models Topology optimization 

Notes

References

  1. Akl W, El-Sabbagh A, Al-Mitani K, Baz A (2009) Topology optimization of a plate coupled with acoustic cavity. Int J Solids Struct 46(10):2060–2074CrossRefzbMATHGoogle Scholar
  2. Allaire G, Jouve F, Toader A (2002) A level-set method for shape optimization. C R Math 334 (12):1125–1130MathSciNetCrossRefzbMATHGoogle Scholar
  3. Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2011) Efficient topology optimization in matlab using 88 lines of code. Struct Multidisc Optim 43(1):1–16CrossRefzbMATHGoogle Scholar
  4. Bendsøe M, Sigmund O (2003) Topology optimization. Theory, methods and applications. Springer, BerlinzbMATHGoogle Scholar
  5. Chen N, Yu D, Xia B, Liu J, Ma Z (2017) Microstructural topology optimization of structural-acoustic coupled systems for minimizing sound pressure level. Struct Multidiscip Optim 56(6):1259–1270MathSciNetCrossRefGoogle Scholar
  6. Christiansen RE, Lazarov BS, Jensen JS, Sigmund O (2015) Creating geometrically robust designs for highly sensitive problems using topology optimization. Struct Multidiscip Optim 52(4):737–754MathSciNetCrossRefGoogle Scholar
  7. Cook RD, Malkus DS, Plesha ME, Witt RJ (2002) Concepts and applications of finite element analysis, 4th edn. Wiley, New YorkGoogle Scholar
  8. Desai J, Faure A, Michailidis G, Parry G, Estevez R (2018) Topology optimization in acoustics and elasto-acoustics via a level-set method. J Sound Vib 420:73–103CrossRefGoogle Scholar
  9. Du J, Olhoff N (2010) Topological design of vibrating structures with respect to optimum sound pressure characteristics in a surrounding acoustic medium. Struct Multidiscip Optim 42(1):43–54MathSciNetCrossRefzbMATHGoogle Scholar
  10. Kasolis F, Wadbro E, Berggren M (2015) Analysis of fictitious domain approximations of hard scatterers. SIAM J Numer Anal 53(5):2347–2362.  https://doi.org/10.1137/140981630 MathSciNetCrossRefzbMATHGoogle Scholar
  11. Kook J (2017) Evolutionary topology optimization for acoustic-structure interaction problems using a mixed u/p formulation. SubmittedGoogle Scholar
  12. Kook J, Jensen JS (2017) Topology optimization of periodic microstructures for enhanced loss factor using acoustic-structure interaction. Int J Solids Struct 122:59–68CrossRefGoogle Scholar
  13. Lee JS, Kang YJ, Kim YY (2012) Unified multiphase modeling for evolving, acoustically coupled systems consisting of acoustic, elastic, poroelastic media and septa. J Sound Vib 331(25):5518–5536CrossRefGoogle Scholar
  14. Lee JS, Göransson P, Kim YY (2015) Topology optimization for three-phase materials distribution in a dissipative expansion chamber by unified multiphase modeling-approach. Comput Methods Appl Mech Eng 287:191–211MathSciNetCrossRefzbMATHGoogle Scholar
  15. Marburg S (2002) Developments in structural-acoustic optimization for passive noise control. Arch Comput Meth Eng 9(4):291–370CrossRefzbMATHGoogle Scholar
  16. Miyata K, Noguchi Y, Yamada T, Izui K, Nishiwaki S (2018) Optimum design of a multi-functional acoustic metasurface using topology optimization based on Zwicker’s loudness model. Comput Methods Appl Mech Eng 331:116–137MathSciNetCrossRefGoogle Scholar
  17. Noguchi Y, Yamada T, Otomori M, Izui K, Nishiwaki S (2015) An acoustic metasurface design for wave motion conversion of longitudinal waves to transverse waves using topology optimization. Appl Phys Lett 221 (22):909Google Scholar
  18. Noguchi Y, Yamada T, Yamamoto T, Izui K, Nishiwaki S (2016) Topological derivative for an acoustic-elastic coupled system based on two-phase material model. Mech Eng Lett 2:16–00,246–16–00,246CrossRefGoogle Scholar
  19. Noguchi Y, Yamamoto T, Yamada T, Izui K, Nishiwaki S (2017) A level set-based topology optimization method for simultaneous design of elastic structure and coupled acoustic cavity using a two-phase material model. J Sound Vib 404:15–30CrossRefGoogle Scholar
  20. Osher S, Santosa F (2001) Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum. J Comput Phys 171(1):272–288MathSciNetCrossRefzbMATHGoogle Scholar
  21. Osher S, Sethian J (1988) Fronts propagating with curvature-dependent speed—algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79(1):12–49MathSciNetCrossRefzbMATHGoogle Scholar
  22. Sethian J, Wiegmann A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163(2):489–528MathSciNetCrossRefzbMATHGoogle Scholar
  23. Shu L, Wang MY, Ma Z (2014) Level set based topology optimization of vibrating structures for coupled acoustic-structural dynamics. Compos Struct 132:34–42CrossRefGoogle Scholar
  24. Sigmund O, Clausen PM (2007) Topology optimization using a mixed formulation: An alternative way to solve pressure load problems. Comput Methods Appl Mech Eng 196(13-16):1874–1889MathSciNetCrossRefzbMATHGoogle Scholar
  25. Søndergaard MB, Pedersen CB (2014) Applied topology optimization of vibro-acoustic hearing instrument models. J Sound Vib 333(3):683–692CrossRefGoogle Scholar
  26. Stolpe M, Svanberg K (2001) An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidiscip Optim 22(2):116–124CrossRefGoogle Scholar
  27. Svanberg K (1987) Method of moving asymptotes—a new method for structural optimization. Int J Numer Meth Eng 24(2):359–373MathSciNetCrossRefzbMATHGoogle Scholar
  28. Vicente W, Picelli R, Pavanello R, Xie Y (2015) Topology optimization of frequency responses of fluid–structure interaction systems. Finite Elem Anal Des 98(Supplement C):1–13CrossRefGoogle Scholar
  29. Wang X, Bathe K (1997) Displacement pressure based mixed finite element formulations for acoustic fluid-structure interaction problems. Int J Numer Methods Eng 40(11):2001–2017CrossRefzbMATHGoogle Scholar
  30. Wang M, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1–2):227–246MathSciNetCrossRefzbMATHGoogle Scholar
  31. Yoon GH, Sigmund O (2008) A monolithic approach for topology optimization of electrostatically actuated devices. Comput Methods Appl Mech Eng 197(45–48):4062–4075MathSciNetCrossRefzbMATHGoogle Scholar
  32. Yoon GH, Jensen JS, Sigmund O (2007) Topology optimization of acoustic-structure interaction problems using a mixed finite element formulation. Int J Numer Methods Eng 70(9):1049–1075MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringTechnical University of DenmarkLyngbyDenmark

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