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Numerical characterizations of a piezoelectric micromotor using topology optimization design

  • Olyaie, M. Sadeghbeigi (Mechanical Engineering Department, Amirkabir University of Technology) ;
  • Razfar, M.R. (Mechanical Engineering Department, Amirkabir University of Technology)
  • 투고 : 2012.03.06
  • 심사 : 2012.08.17
  • 발행 : 2013.03.25

초록

This paper presents the optimum load-speed diagram evaluation for a linear micromotor, including multitude cantilever piezoelectric bimorphs, briefly. Each microbeam in the mechanism can be actuated in both axial and flexural modes simultaneously. For this design, we consider quasi-static and linear conditions, and a relatively new numerical method called the smoothed finite element method (S-FEM) is introduced here. For this purpose, after finding an optimum volume fraction for piezoelectric layers through a standard numerical method such as quadratic finite element method, the relevant load-speed curves of the optimized micromotor are examined and compared by deterministic topology optimization (DTO) design. In this regard, to avoid the overly stiff behavior in FEM modeling, a numerical method known as the cell-based smoothed finite element method (CS-FEM, as a branch of S-FEM) is applied for our DTO problem. The topology optimization procedure to find the optimal design is implemented using a solid isotropic material with a penalization (SIMP) approximation and a method of moving asymptotes (MMA) optimizer. Because of the higher efficiency and accuracy of S-FEMs with respect to standard FEMs, the main micromotor characteristics of our final DTO design using a softer CS-FEM are substantially improved.

키워드

참고문헌

  1. Allik, H. and Hughes, T.J.R. (1970), "Finite element method for piezo-electric vibration", Int. J. Numer. Meth. Eng., 2(2), 151-157. https://doi.org/10.1002/nme.1620020202
  2. Arora, J.S. (2004), Introduction to optimum design. 2nd edition, Elsevier academic press.
  3. Begg, D.W. and Liu. X. (2000), "On simultaneous optimization of smart structures-Part II: algorithms and examples", Comput. Method. Appl. M., 184(1), 25-37. https://doi.org/10.1016/S0045-7825(99)00317-5
  4. Bendsoe, M.P. (1989), "Optimal shape design as a material distribution problem", Struct. Optimization, 1(4), 193-202. https://doi.org/10.1007/BF01650949
  5. Bendsoe, M.P. and Kikuchi, N. (1988), "Generating optimal topologies in structural design using a homogenization method", Comput. Method. Appl. M., 71(2), 197-224. https://doi.org/10.1016/0045-7825(88)90086-2
  6. Bendsoe, M.P. and Sigmund, O. (1999), "Material interpolations in topology optimization", Arch. Appl. Mech., 69(9-10), 635-654. https://doi.org/10.1007/s004190050248
  7. Bendsoe, M.P. and Sigmund, O. (2003), Topology optimization: theory, methods and applications, Springer, Berlin.
  8. Benjeddou, A. (2000), "Advances in piezoelectric finite element modeling of adaptive structural elements: a survey", Comput. Struct., 76(1-3), 347-363. https://doi.org/10.1016/S0045-7949(99)00151-0
  9. Bordas, S.P.A., Rabczuk. T., Hung, N.X., Nguyen, V.P, Natarajan, S., Bog, T., Quan, D.M. and Hiep, N.V. (2010), "Strain smoothing in FEM and XFEM", Comput. Struct., 88(23-24), 1419-1443. https://doi.org/10.1016/j.compstruc.2008.07.006
  10. Carbonari, R.C., Nader, G. and Silva, E.C.N. (2006), "Experimental and numerical characterization of piezoelectric mechanisms designed using topology optimization", Int. ABCM symposium series in Mechatronics , 2, 425-432.
  11. Carbonari, R.C., Silva, E.C.N. and Nishiwaki, S. (2005), "Design of piezoelectric multi-actuated microtools using topology optimization", Smart Mater. Struct., 14(6) , 1431-1447. https://doi.org/10.1088/0964-1726/14/6/036
  12. Chang, S.J., Rogacheva, N.N. and Chou, C.C. (1995), "Analysis of methods for determining electromechanical coupling coefficients of piezoelectric elements", IEEE T. Ultrason. Ferr., 42(4), 630-640. https://doi.org/10.1109/58.393106
  13. Chen, J.S., Wu, C.T. and Yoon, S. Y. (2001), "A stabilized conforming nodal integration for Galerkin meshfree methods", Int. J. Numer. Meth. Eng., 50, 435-466. https://doi.org/10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A
  14. Choi, K.K. and Kim, N.H. (2005), Structural sensitivity analysis and optimization, Springer Science and Business Media, Inc., New York.
  15. Dai, K.Y., Liu, G.R. and Nguyen, T.T. (2007), "An n-sided polygonal smoothed finite element method (nSFEM), for solid mechanics", Finite Elem. Anal. Des., 43(11-12), 847-860. https://doi.org/10.1016/j.finel.2007.05.009
  16. Donoso, A.; Sigmund, O. (2009), "Optimization of piezoelectric bimorph actuators with active damping for static and dynamic loads", Struct. Multidiscip. O., 38(2), 171-183. https://doi.org/10.1007/s00158-008-0273-0
  17. Friend, J., Umeshima, A., Ishii, T., Nakamura, K. and Ueha, S. (2004), "A piezoelectric linear actuator formed from a multitude of bimorphs", Sensor. Actuat. A-Phys., 109(3), 242-251. https://doi.org/10.1016/j.sna.2003.10.040
  18. Huang, X. and Xie, Y.M. (2010), Evolutionary Topology Optimization of Continuum Structures Methods and Applications, John Wiley and Sons Ltd.
  19. Jensen, J.S. (2009), A Note on Sensitivity Analysis of Linear Dynamic Systems with Harmonic Excitation, Report. Department of Mechanical Engineering, Technical University of Denmark.
  20. Kang, Zh. and Wang, X. (2010), "Topology optimization of bending actuators with multilayer piezoelectric Material", Smart Mater. Struct., 19, 075018(11p). https://doi.org/10.1088/0964-1726/19/7/075018
  21. Kim, J.E., Kim, D.S., Ma, P.S. and Kim, Y.Y. (2010), "Multi-physics interpolation for the topology optimization of piezoelectric systems", Comput. Method. Appl. M., 199(49-52), 3153-3168. https://doi.org/10.1016/j.cma.2010.06.021
  22. Kogl, M. and Silva, E.C.N. (2005), "Topology optimization of smart structures: design of piezoelectric plate and shell actuators", Smart Mater. Struct., 14(2) , 387-399. https://doi.org/10.1088/0964-1726/14/2/013
  23. Liu, G.R., Dai, K.Y., Lim, K.M. and Gu, Y.T. (2003), "A radial point interpolation method for simulation of two-dimensional piezoelectric structures", Smart Mater. Struct., 12(2), 171-180. https://doi.org/10.1088/0964-1726/12/2/303
  24. Liu, G.R., Dai, K.Y. and Nguyen, T.T. (2007), "A smoothed finite element method for mechanics problems", Comput. Mech., 39(6), 859-877. https://doi.org/10.1007/s00466-006-0075-4
  25. Liu, G.R. and Nguyen, T.T. (2010), Smoothed finite element methods, CRC press, Taylor and Francis group.
  26. Liu, G.R., Nguyen, T.T., Dai, K.Y. and Lam, K.Y. (2007), "Theoretical aspects of the smoothed finite element method (SFEM)", Int. J. Numer. Meth. Eng., 71(8), 902-930. https://doi.org/10.1002/nme.1968
  27. Liu, G.R., Nguyen, T.T. and Lam, K.Y. (2009), "An edge-based smoothed finite element method (ES-FEM) for static, free and force vibration analyses of solids", J. Sound Vib., 320(4-5), 1100-1130. https://doi.org/10.1016/j.jsv.2008.08.027
  28. Liu, G.R., Nguyen, X.H. and Nguyen, T.T. (2010), "A theoretical study on the smoothed FEM (S-FEM) models: Properties, accuracy and convergence rates", Int. J. Numer. Meth. Eng., 84(10), 1222-1256. https://doi.org/10.1002/nme.2941
  29. Long, C.S., Loveday, P.W. and Groenwold, A.A. (2006), "Planar four node piezoelectric with drilling degrees of freedom", Int. J. Numer. Meth. Eng., 65(11), 1802-1830. https://doi.org/10.1002/nme.1524
  30. Nguyen, X.H., Liu, G.R., Nguyen, T.T. and Nguyen, C.T. (2009), "An edge-based smoothed finite element method for analysis of two-dimensional piezoelectric structures", Smart Mater. Struct., 18(6), 065015(12pp). https://doi.org/10.1088/0964-1726/18/6/065015
  31. Ohs, R.R. and Aluru, N.R. (2001), "Meshless analysis of piezoelectric devices", Comput. Mech., 27(1), 23-36. https://doi.org/10.1007/s004660000211
  32. Rozvany, G., Zhou, M. and Birker, T. (1992), "Generalized shape optimization without homogenization", Struct. Optimization, 4(3-4), 250-254. https://doi.org/10.1007/BF01742754
  33. Sadeghbeigi Olyaie, M., Razfar, M.R. and Kansa, E.J. (2011), "Reliability based topology optimization of a linear piezoelectric micromotor using the cell-based smoothed finite element method", CMES, 75(1), 43-88.
  34. Sigmund, O. (1994), Design of Material Structures Using Topology Optimization, Ph.D. Thesis, Department of Solid mechanics, Technical University of Denmark.
  35. Sigmund, O. (1997), "On the design of compliant mechanisms using topology optimization", Mech. Struct. Mach., 25(4), 495-526.
  36. Silva, E.C.N. (2003), "Topology optimization applied to the design of linear piezoelectric motors", Smart Mater. Struct., 14(4), 309-322.
  37. Silva, R.C.N. and Kikuchi, N. (1999), "Design of piezocomposite materials and piezoelectric transducers using topology optimization-part III", Arch. Comput. Method E., 6(4), 305-329. https://doi.org/10.1007/BF02818918
  38. Svanberg, K. (1987), "Method of moving asymptotes-a new method for structural optimization", Int. J. Numer. Meth. Eng., 24(2), 359-373. https://doi.org/10.1002/nme.1620240207
  39. Sze, K.Y., Yang, X.M. and Yao, L.Q. (2004), "Stabilized plane and axisymmetric piezoelectric finite element models", Finite Elem. Anal. Des. 40(9-10), 1105-1122. https://doi.org/10.1016/j.finel.2003.06.002
  40. Ueha, S. and Tomikawa, Y. (1993), Ultrasonic Motors-Theory and Applications. Monographs in Electrical and Electronic Engineering, 29, Clarendon Press, Oxford.

피인용 문헌

  1. Design and evaluation of an experimental system for monitoring the mechanical response of piezoelectric energy harvesters vol.22, pp.2, 2018, https://doi.org/10.12989/sss.2018.22.2.133
  2. Topology optimization of multiphase elastic plates with Reissner-Mindlin plate theory vol.22, pp.3, 2013, https://doi.org/10.12989/sss.2018.22.3.249