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Optimal Design of Piezoelectric Microactuators: Linear vs Non-linear Modeling

  • David RuizEmail author
  • José Carlos Bellido
  • Alberto Donoso
Chapter
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 18)

Abstract

The main point of this work is the comparison between linear and geometrically non-linear elasticity modeling in the field of piezoelectric actuators fabricated at the micro-scale. Manufacturing limitations such as non-symmetrical lamination of the structure or minimum length scale are taken into account during the optimization process. The robust approach implemented in the problem also reduces the sensitivity of the designs to small manufacturing errors.

Keywords

Piezoelectric actuators Topology optimization Electrode profile Heterogeneous bimorph Large displacements 

Notes

Acknowledgements

This research has been founded through grant MTM2013-47053-P from the Spanish Ministerio de Economía y Competitividad. Special thanks to José Luis Sánchez-Rojas from Microsystems Actuators and Sensors Group (UCLM) and Ole Sigmund from the Department of Mechanical Engineering, Section of Solid Mechanics (DTU).

References

  1. 1.
    Bruns, T.E., Tortorelli, D.A.: Topology optimization of non-linear elastic structures and compliant mechanisms. Comput. Methods Appl. Mech. Eng. 190, 3443–3459 (2001)CrossRefGoogle Scholar
  2. 2.
    Buhl, T., Pedersen, C., Sigmund, O.: Stiffness design of geometrically nonlinear structures using topology optimization. Struct. Multidiscip. Optim. 19, 93–104 (2000)CrossRefGoogle Scholar
  3. 3.
    Carbonari, R.C., Silva, E.C.N., Nishiwaki, S.: Optimum placement of piezoelectric material in piezoactuator design. Smart Mater. Struct. 16, 207–220 (2007)CrossRefGoogle Scholar
  4. 4.
    Díaz A.R., Kikuchi, N.: Solution to shape and topology eigenvalue optimization problems using a homogenization method. Int. J. Numer. Methods Eng. 35, 1487–1502 (1992)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Frecker, M.I., Ananthasuresh, G.K., Nishiwaki, S., Kota, S.: Topological synthesis of compliant mechanisms using multi-criteria optimization. Trans. ASME 199, 238–245 (1997)CrossRefGoogle Scholar
  6. 6.
    Gibbs, G., Fuller, C.: Excitation of thin beams using asymmetric piezoelectric actuators. J. Acoust. Soc. Am. 92, 3221–3227 (1992)CrossRefGoogle Scholar
  7. 7.
    Jensen, J., Sigmund, O.: Topology optimization for nano-photonics. Laser Photonics Rev. 5, 308–321 (2011)CrossRefGoogle Scholar
  8. 8.
    Kang, Z., Tong, L.: Integrated optimization of material layout and control voltage for piezoelectric laminated plates. J. Intell. Mater. Syst. Struct. 19, 889–904 (2008)CrossRefGoogle Scholar
  9. 9.
    Kang, Z., Tong, L.: Topology optimization-based distribution design of actuation voltage in static shape control of plates. Comput. Struct. 86, 1885–1893 (2008)CrossRefGoogle Scholar
  10. 10.
    Kang, Z., Wang, R., Tong, L.: Combined optimization of bi-material structural layout and voltage distribution for in-plane piezoelectric actuation. Comput. Methods Appl. Mech. Eng. 200, 1467–1478 (2011)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Kang, Z., Wang, X., Luo, Z.:. Topology optimization for static shape control of piezoelectric plates with penalization on intermediate actuation voltage. J. Mech. Des. 134, 051006 (2012)CrossRefGoogle Scholar
  12. 12.
    Kögl, M., Silva, E.C.N.: Topology optimization of smart structures: design of piezoelectric plate and shell actuators. Smart Mater. Struct. 14, 387–399 (2005).CrossRefGoogle Scholar
  13. 13.
    Kucera, M., Wistrela, E., Pfusterschmied, G., Ruiz-Díez, V., Manzaneque, T., Hernando-García, J., Sánchez-Rojas, J.L., Jachimowicz, A., Schalko, J., Bittner, A., Schmid, U.: Design-dependent performance of self-actuated and self-sensing piezoelectric-AlN cantilevers in liquid media oscillating in the fundamental in-plane bending mode. Sensors Actuators B Chem. 200, 235–244 (2014)CrossRefGoogle Scholar
  14. 14.
    Lazarov, B.S., Schevenels, M., Sigmund, O.: Robust design of large-displacement compliant mechanisms. Mech. Sci. 2, 175–182 (2011)CrossRefGoogle Scholar
  15. 15.
    Luo, Z., Gao, W., Song, C.: Design of multi-phase piezoelectric actuators. J. Intell. Mater. Syst. Struct. 21, 1851–1865 (2010)CrossRefGoogle Scholar
  16. 16.
    Maute, K., Frangopol, D.M.: Reliability-based design of MEMS mechanisms by topology optimization. Comput. Struct. 81, 813–824 (2003)CrossRefGoogle Scholar
  17. 17.
    Molter, A., Fonseca, J.S.O., dos Santos Fernandez, L.: Simultaneous topology optimization of structure and piezoelectric actuators distribution. Appl. Math. Model. 40, 5576–5588 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Oñate, E.: Cálculo de Estructuras por el Método de Elementos Finitos, Análisis estático lineal, 2nd edn. CIMNE, Barcelona (1995)Google Scholar
  19. 19.
    Pedersen, N.L.: Maximization of eigenvalues using topology optimization. Struct. Multidiscip. Optim. 20, 2–11 (2000)CrossRefGoogle Scholar
  20. 20.
    Pedersen, C.B.W., Buhl, T., Sigmund, O.: Topology synthesis of large-displacement compliant mechanism. Int. J. Numer. Methods Eng. 50, 2683–2705 (2001)CrossRefGoogle Scholar
  21. 21.
    Ruiz, D., Sigmund, O.: Optimal design of robust piezoelectric microgrippers undergoing large displacements. Struct. Multidiscip. Optim. 57, 71–82 (2018)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Ruiz, D., Bellido, J.C., Donoso, A.: Design of piezoelectric modal filters by simultaneously optimizing the structure layout and the electrode profile. Struct. Multidiscip. Optim. 53, 715–730 (2016)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Ruiz, D., Donoso, A., Bellido, J.C., Kucera, M., Schmid, U., Sánchez-Rojas, J.L.: Design of piezoelectric microtransducers based on the topology optimization method. Microsyst. Technol. 22, 1733–1740 (2016)CrossRefGoogle Scholar
  24. 24.
    Ruiz, D., Díaz-Molina, A., Sigmund, O., Donoso, A., Bellido, J.C., Sánchez-Rojas, J.L.: Optimal design of robust piezoelectric unimorph microgrippers. Appl. Mech. Eng. 55, 1–12 (2017)MathSciNetGoogle Scholar
  25. 25.
    Sigmund, O.: On the design of compliant mechanisms using topology optimization. Mech. Struct. Mach. 25, 493–524 (1997)CrossRefGoogle Scholar
  26. 26.
    Sigmund, O.: Design of multiphysics actuators using topology optimization. Part I: one-material structures. Comput. Methods Appl. Mech. Eng. 190, 6577–6604 (2001)zbMATHGoogle Scholar
  27. 27.
    Sigmund, O.: Design of multiphysics actuators using topology optimization. Part II: two-material structures. Comput. Methods Appl. Mech. Eng. 190, 6605–6627 (2001)Google Scholar
  28. 28.
    Sigmund, O.: Manufacturing tolerant topology optimization. Acta Mech. Sin. 25, 227–239 (2009)CrossRefGoogle Scholar
  29. 29.
    Sigmund, O., Jensen, J.S.: Systematic design of phononic band gap materials and structures by topology optimization. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 361, 1001–1019 (2003)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Sigmund, O., Torquato, S.: Design of materials with extreme thermal expansion using a three-phase topology optimization method. J. Mech. Phys. Solids 45, 1037–1067 (1997)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Sigmund, O., Torquato, S., Aksay, I.A.: On the design of 1–3 piezo-composites using topology optimization. J. Mater. Res. 13, 1038–1048 (1998)CrossRefGoogle Scholar
  32. 32.
    Silva, E.C.N., Kikuchi, N.: Design of piezoelectric transducers using topology optimization. Smart Mater. Struct. 8, 350–364 (1999)CrossRefGoogle Scholar
  33. 33.
    Silva, E.C.N., Fonseca, J.S.O., Kikuchi, N.: Optimal design of piezoelectric microstructures. Comput. Mech. 19, 397–410 (1997)CrossRefGoogle Scholar
  34. 34.
    Svanberg, K.: The method of moving asymptotes-a new method for structural optimization. Int. J. Numer. Meth. Eng. 24, 359–373 (1987)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Struct. Multidiscip. Optim. 43, 767–784 (2011)CrossRefGoogle Scholar
  36. 36.
    Wang, F., Lazarov, B., Sigmund, O., Jensen, J.S.: Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems. Comput. Methods Appl. Mech. Eng. 276, 453–472 (2014)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Zienkiewicz, O.C., Taylor, R.L., Fox, D.: The Finite Element Method for Solid and Structural Mechanics, 7th edn. Butterworth-Heinemann, Oxford (2014)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • David Ruiz
    • 1
    Email author
  • José Carlos Bellido
    • 1
  • Alberto Donoso
    • 1
  1. 1.Departamento de Matemáticas, ETSIIUniversidad de Castilla-La ManchaCiudad RealSpain

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