Advertisement

Optimization of Electro-mechanical Smart Structures

  • Eberhard BänschEmail author
  • Manfred Kaltenbacher
  • Günter Leugering
  • Fabian Schury
  • Fabian Wein
Chapter
Part of the International Series of Numerical Mathematics book series (ISNM, volume 160)

Abstract

We present topology optimization of piezoelectric loudspeakers using the SIMP method and topology gradient based methods along with analytical and numerical results.

Keywords

Topology optimization piezoelectricity loudspeakers 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Allaire, F. Jouve, and A.-M. Toader. Structural optimization using sensitivity analysis and a level-set method. J. Comp. Physics, 194:363–393, 2004.CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Martin P. Bendsøe and N. Kikuchi. Generating optimal topologies in optimal design using a homogenization method. Comp. Meth. Appl. Mech. Engn., 71:197–224, 1988.CrossRefGoogle Scholar
  3. 3.
    Martin P. Bendsøe and Ole Sigmund. Topology Optimization: Theory, Methods and Applications. Springer-Verlag, 2002.Google Scholar
  4. 4.
    J.P. Berenger. A Perfectly Matched Layer for the Absorption of Electromagnetic Waves. Journal of Computational Physics, 1994.Google Scholar
  5. 5.
    Matthias Bollhöfer and Yousef Saad. Multilevel preconditioners constructed from inverse-based ilus. SIAM Journal on Scientific Computing, 27(5):1627–1650, 2006.CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    D. Braess and Manfred Kaltenbacher. Efficient 3D-Finite-Element-Formulation for Thin Mechanical and Piezoelectric Structures. Int. J. Numer. Meth. Engng., 73:147–161, 2008.CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    R.C. Carbonari, E.C.N. Silva, and S. Nishiwaki. Design of piezoelectric multiactuated microtools using topology optimization. Smart Materials and Structures, 14(6):1431, 2005.CrossRefGoogle Scholar
  8. 8.
    R.C. Carbonari, E.C.N. Silva, and G.H. Paulino. Topology optimization design of functionally graded bimorph-type piezoelectric actuators. Smart Materials and Structures, 16(6):2605, 2007.CrossRefGoogle Scholar
  9. 9.
    G. Cardone, S.A. Nazarov, and Jan Sokołowski. Topological derivatives in piezoelectricity. Preprint, 2008.Google Scholar
  10. 10.
    Jean Céa, Stéphane Garreau, Philippe Guillaume, and Mohamed Masmoudi. The shape and topological optimizations’ connection. Comput. Methods Appl. Mech. Eng., 188(4):713–726, 2000.CrossRefzbMATHGoogle Scholar
  11. 11.
    P.W. Christensen and A. Klarbring. An Introduction to Structural Optimization. Springer Verlag, 2008.Google Scholar
  12. 12.
    J. Diaz and J. Joly. A time domain analysis of pml models in acoustics. Comput. Meth. Appl. Mech. Engrg., 2005.Google Scholar
  13. 13.
    Maria B. Döhring, Jakob S. Jensen, and Ole Sigmund. Acoustic design by topology optimization. submitted, 2008.Google Scholar
  14. 14.
    A. Donoso and J.C. Bellido. Distributed piezoelectric modal sensors for circular plates. Journal of Sound and Vibration, 2008.Google Scholar
  15. 15.
    A. Donoso and J.C. Bellido. Systematic design of distributed piezoelectric modal sensors/actuators for rectangular plates by optimizing the polarization profile. Structural and Multidisciplinary Optimization, 2008.Google Scholar
  16. 16.
    A. Donoso and Ole Sigmund. Optimization of piezoelectric bimorph actuators with active damping for static and dynamic loads. Structural and Multidisciplinary Optimization, 2008.Google Scholar
  17. 17.
    H. Du, G.K. Lau, M.K. Lim, and J. Qiu. Topological optimization of mechanical amplifiers for piezoelectric actuators under dynamic motion. Smart Materials and Structures, 9(6):788–800, 2000.CrossRefGoogle Scholar
  18. 18.
    J. Du and N. Olhoff. Minimization of sound radiation from vibrating bi-material structures using topology optimization. Structural and Multidisciplinary Optimization, 33(4):305–321, 2007.CrossRefMathSciNetGoogle Scholar
  19. 19.
    B. Flemisch, M. Kaltenbacher, and B.I. Wohlmuth. Elasto-Acoustic and Acoustic-Acoustic Coupling on Nonmatching Grids. Int. J. Numer. Meth. Engng., 67(13): 1791–1810, 2006.CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Piotr Fulmanski, Antoine Laurain, Jean-François Scheid, and Jan Sokołowski. A level set method in shape and topology optimization for variational inequalities. Int. J. Appl. Math. Comput. Sci., 17(3):413–430, 2007.CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    M. Hintermüller. A combined shape-Newton topology optimization technique in realtime image segmentation. Technical report, University of Graz, 2004. Preprint.Google Scholar
  22. 22.
    Jakob S. Jensen. A note on sensitivity analysis of linear dynamic systems with harmonic excitation. Handout at DCAMM advanced school June 20–26, 2007 at DTU in Lyngby, Denmark, June 2007.Google Scholar
  23. 23.
    Jakob S. Jensen. Topology optimization of dynamics problems with pade approximants. Int. J. Numer. Meth. Engng., 72:1605–1630, 2007.CrossRefzbMATHGoogle Scholar
  24. 24.
    M. Kaltenbacher. Numerical Simulation of Mechatronic Sensors and Actuators. Springer Berlin-Heidelberg-New York, 2nd edition, 2007. ISBN: 978-3-540-71359-3.Google Scholar
  25. 25.
    Manfred Kaltenbacher. Advanced Simulation Tool for the Design of Sensors and Actuators. In Proc. Eurosensors XXIV, Linz, Austria, September 2010.Google Scholar
  26. 26.
    B. Kapitonov, B. Miara, and G. Perla-Menzala. Boundary observation and exact control of a quasi-electrostatic piezoelectric system in multilayered media. SIAM J. CONTROL OPTIM., 46(3):1080–1097, 2007.CrossRefzbMATHMathSciNetGoogle Scholar
  27. 27.
    M. Kögl and E.C.N. Silva. Toplogy optimization of smart structures: design of piezoelectric plate and shell actuators. Smart Mater. Struct., 14:387–399, 2005.CrossRefGoogle Scholar
  28. 28.
    Günter Leugering and Jan Sokołowski. Topological derivatives for elliptic problems on graphs. Variational Formulations in Mechanics: Theory and Application, 2006.Google Scholar
  29. 29.
    J. Lieneman, A. Greiner, J.G. Korvink, and Ole Sigmund. Optimization of integrated magnetic field sensors. ORBIT, 2007:2006, 2008.Google Scholar
  30. 30.
    P.H. Nakasone and C.N.S. Silva. Design of dynamic laminate piezoelectric sensors and actuators using topology optimization. In Proceedings of the 6th International Conference on Computation of Shell and Spatial Structures. IASS-IACM 2008, May 2008.Google Scholar
  31. 31.
    P.H. Nakasone, C.Y. Kiyono, and E.C.N. Silva. Design of piezoelectric sensors, actuators, and energy harvesting devices using topology optimization. In Proceedings of SPIE, volume 6932, page 69322W. SPIE, 2008.Google Scholar
  32. 32.
    Julian A. Norato, Martin P. Bendsoe, Robert B. Haber, and Daniel A. Tortorelli. A topological derivative method for topology optimization. Struct. Multidisc. Optim., 33:375–386, 2007.CrossRefMathSciNetGoogle Scholar
  33. 33.
    G. Perla-Menzala, A. Feij’oo Novotny, Günter Leugering, and Jan Sokołowski. Wellposedness of a dynamic wave-propagation problem in a coupled piezoelectric-elasticacoustic structure. Preprint, 2008.Google Scholar
  34. 34.
    O. Schenk and K. Görtner. Solving unsymmetric sparse systems of linear equations with PARDISO. Journal of Future Generation Computer Systems, 20(3):475–487, 2004.CrossRefGoogle Scholar
  35. 35.
    Ole Sigmund. A 99 Line topology optimization code written in MATLAB. J. Struct. Multidiscip. Optim., 21:120–127, 2001.CrossRefGoogle Scholar
  36. 36.
    E.C.N. Silva and N. Kikuchi. Design of piezoelectric transducers using topology optimization. Smart Mater. Struct., 8:350–364, 1999.CrossRefGoogle Scholar
  37. 37.
    E.C. N. Silva, N. Kikuchi, and S. Nishiwaki. Topology optimization design of flextensional actuators. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 47(3):657–671, 2000.CrossRefGoogle Scholar
  38. 38.
    F. Wein, M. Kaltenbacher, F. Schury, G. Leugering, and E. Bönsch. Topology Optimization of Piezoelectric Actuators using the SIMP Method. In Proceedings of the 10th Workshop on Optimization and Inverse Problems in Electromagnetism – OIPE 2008, pages 46–47, September 2008. TU Ilmenau, 14.–17.09.2008.Google Scholar
  39. 39.
    Fabian Wein. C++SCPIP, a C++ wrapper for SCPIP. Online, August 2007. http://cppmath.sourceforge.net.
  40. 40.
    Fabian Wein, Manfred Kaltenbacher, Barbara Kaltenbacher, Günter Leugering, Eberhard Bänsch, and Fabian Schury. Topology optimization of piezoelectric layers using the simp method. Submitted for review, July 2008.Google Scholar
  41. 41.
    Fabian Wein, Manfred Kaltenbacher, Günter Leugering, Eberhard Bänsch, and Fabian Schury. Topology optimization of a piezoelectric-mechanical actuator with single- and multiple-frequency excitation. Submitted for review, October 2008.Google Scholar
  42. 42.
    Gil Ho Yoon, Jakob S. Jensen, and Ole Sigmund. Topology optimization of acousticstructure interaction problems using a mixed finite element formulation. International Journal for Numerical Methods in Engineering, 70:1049–1075, 2006.CrossRefMathSciNetGoogle Scholar
  43. 43.
    Bin Zheng, Ching-Jui Chang, and Hae Chang Gea. Topology optimization of energy harvesting devices using piezoelectric materials. Structural and Multidisciplinary Optimization, 2008.Google Scholar
  44. 44.
    Ch. Zillober. SCPIP – an efficient software tool for the solution of structural optimization problems. Structural and Multidisciplinary Optimization, 24(5):362–371, 2002.CrossRefGoogle Scholar

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Eberhard Bänsch
    • 1
    Email author
  • Manfred Kaltenbacher
    • 2
  • Günter Leugering
    • 3
  • Fabian Schury
    • 4
  • Fabian Wein
    • 4
  1. 1.ErlangenGermany
  2. 2.KlagenfurtAustria
  3. 3.ErlangenGermany
  4. 4.ErlangenGermany

Personalised recommendations