DOI QR코드

DOI QR Code

On FEM modeling of piezoelectric actuators and sensors for thin-walled structures

  • Received : 2011.09.16
  • Accepted : 2012.04.02
  • Published : 2012.05.25

Abstract

Thin-walled adaptive structures render a large and important group of adaptive structures. Typical material system used for them is a composite laminate that includes piezoelectric material based sensors and actuators. The piezoelectric active elements are in the form of thin patches bonded onto or embedded into the structure. Among different types of patches, the paper considers those polarized in the thickness direction. The finite element method (FEM) imposed itself as an essential technical support for the needs of structural design. This paper gives a brief description of a developed shell type finite element for active/adaptive thin-walled structures and the element is, furthermore, used as a tool to consider the aspect of mesh distortion over the surface of actuators and sensors. The aspect is of significance for simulation of behavior of adaptive structures and implementation of control algorithms.

Keywords

Acknowledgement

Supported by : Ministry of Science and Technological Development of Republic of Serbia

References

  1. Ahmad, S., Irons, B.M. and Zienkiewicz, O.C. (1970), "Analysis of thick and thin shell structures by curved finite elements", Int. J. Numer. Meth. Eng., 2(3), 419-451. https://doi.org/10.1002/nme.1620020310
  2. 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
  3. Benjeddou, A., Deü, J.F. and Letombe, S. (2002) "Free vibrations of simply-supported piezoelectric adaptive plates: an exact sandwich formulation", Thin. Wall. Struct., 40(7), 573-593. https://doi.org/10.1016/S0263-8231(02)00013-7
  4. Gandhi, M.V. and Thompson, B.S. (1992), Smart materials and structures, Chapman and Hall, London. Hwang, W.S. and Park, H.C. (1993), "Finite element modeling of piezoelectric sensors and actuators", AIAA J., 31(5), 930-937. https://doi.org/10.2514/3.11707
  5. Klinkel, S. and Wagner, W. (2006), "A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation", Int. J. Num. Meth. Eng., 65(3), 349-382. https://doi.org/10.1002/nme.1447
  6. Lammering, R. (1991), "The application of a finite shell element for composites containing piezo-electric polymers in vibration control", Comput. Struct., 41(5), 1101-1109. https://doi.org/10.1016/0045-7949(91)90305-6
  7. Liu, G.R., Dai, K.Y., Lim, K.M. and Gu, Y.T. (2002) "A point interpolation mesh free method for static and frequency analysis of two-dimensional piezoelectric structures", Comput. Mech., 29(6), 510-519. https://doi.org/10.1007/s00466-002-0360-9
  8. Liu, G.R., Dai, K.Y., Lim, K.M. and Gu, Y.T. (2003), "A radial point interpolation method for simulation of twodimensional piezoelectric structures", Smart Mater. Struct., 12(2), 171-180. https://doi.org/10.1088/0964-1726/12/2/303
  9. Liu, G.R., Dai, K.Y. and Nguyen, T.T. (2007), "Theoretical aspects of the smoothed finite element method (SFEM)", Int. J. Num. Meth. Eng., 71(8), 902-930. https://doi.org/10.1002/nme.1968
  10. Long, C.S., Loveday, P.W. and Groenwold, A.A. (2006), "Planar four node piezoelectric elements with drilling degrees of freedom", Int. J. Num. Meth. Eng., 65(11), 1802-1830. https://doi.org/10.1002/nme.1524
  11. Marinkovic, D. (2007), A new finite composite shell element for piezoelectric active structures, Ph.D. Thesis, Otto-von-Guericke Universitaet Magdeburg, Germany, Fortschritt-Berichte VDI, Reihe 20: Rechnerunterstuetzte Verfahren, Nr. 406, Duesseldorf.
  12. Marinkovic, D., Koeppe, H. and Gabbert, U. (2006), "Numerically efficient finite element formulation for modeling active composite laminates", Mech. Adv. Mater. Struct., 13, 379-392. https://doi.org/10.1080/15376490600777624
  13. Marinkovi, D., Koppe, H. and Gabbert, U. (2007), "Accurate modeling of the electric field within piezoelectric layers for active composite structures", Int. J. Intell. Mater. Syst., 18(5), 503-513. https://doi.org/10.1177/1045389X06067139
  14. Marinkovi, D., Koppe, H. and Gabbert U. (2009), "Aspects of modeling piezoelectric active thin-walled structures", Int. J. Intell. Mater. Syst., 20(15), 1835-1844. https://doi.org/10.1177/1045389X09102261
  15. Nguyen-Van, H., Mai-Duy, N. and Tran-Cong, T. (2008), "Analysis of piezoelectric solids with an efficient nodebased smoothing element", Proceedings of the WCCM8 and ECCOMAS 2008, Venice, Italy.
  16. 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
  17. Rudolf, C., Martin, T. and Wauer, J. (2010), "Control of PKM machine tools using Piezoelectric self-sensing Actuators on basis of the functional principle of a scale with a vibrating string", Smart Struct. Syst., 6(2), 167- 182. https://doi.org/10.12989/sss.2010.6.2.167
  18. Sze, K.Y. and Pan, Y.S. (1999), "Hybrid finite element models for piezoelectric materials", J. Sound Vib., 226(3), 519-547. https://doi.org/10.1006/jsvi.1999.2308
  19. Tzou, H.S. and Tseng, C.I. (1990), "Distributed piezoelectric sensor/actuator design for dynamic measurement/ control of distributed parameter systems: a finite element approach", J. Sound Vib., 138, 17-34. https://doi.org/10.1016/0022-460X(90)90701-Z
  20. Ye, L., Lin, Y., Dong, W., Limin, Z. and L, C. (2010), "Piezo-activated guided wave propagation and interaction with damage in tubular structures", Smart Struct.Syst., 6(7), 835-849. https://doi.org/10.12989/sss.2010.6.7.835
  21. Zemcik, R., Rolfes, R., Rose, M. and Tessmer, J. (2006), "High-performance 4-node shell element with piezoelectric coupling", Mech. Adv. Mater. Struct., 13, 393-401. https://doi.org/10.1080/15376490600777657

Cited by

  1. A numerically accurate and efficient coupled polynomial field interpolation for Euler–Bernoulli piezoelectric beam finite element with induced potential effect vol.26, pp.12, 2015, https://doi.org/10.1177/1045389X14544149
  2. Health monitoring sensor placement optimization for Canton Tower using virus monkey algorithm vol.15, pp.5, 2015, https://doi.org/10.12989/sss.2015.15.5.1373
  3. An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite element vol.12, pp.1, 2015, https://doi.org/10.1590/1679-78251401
  4. SH-wave in a piezomagnetic layer overlying an initially stressed orthotropic half-space vol.17, pp.2, 2016, https://doi.org/10.12989/sss.2016.17.2.327
  5. Co-rotational shell element for numerical analysis of laminated piezoelectric composite structures vol.125, 2017, https://doi.org/10.1016/j.compositesb.2017.05.061
  6. A Timoshenko Piezoelectric Beam Finite Element with Consistent Performance Irrespective of Geometric and Material Configurations vol.13, pp.5, 2016, https://doi.org/10.1590/1679-78251750
  7. Efficient three-node finite shell element for linear and geometrically nonlinear analyses of piezoelectric laminated structures vol.29, pp.3, 2018, https://doi.org/10.1177/1045389X17705538
  8. A consistently efficient and accurate higher order shear deformation theory based finite element to model extension mode piezoelectric smart beams vol.27, pp.9, 2016, https://doi.org/10.1177/1045389X15588626
  9. Modeling of piezoelectric sensors adhesively bonded on trusses using a mathematical programming approach vol.58, pp.3, 2018, https://doi.org/10.1007/s00158-018-1933-3
  10. Linear shell elements for active piezoelectric laminates vol.20, pp.6, 2017, https://doi.org/10.12989/sss.2017.20.6.729
  11. Control-structure interaction in piezoelectric deformable mirrors for adaptive optics vol.21, pp.6, 2012, https://doi.org/10.12989/sss.2018.21.6.777