Skip to main content
SpringerLink
Log in

Shape Control of Composite Plates with Distributed Piezoelectric Actuators in a Three-Dimensional Formulation

  • Published:
Mechanics of Composite Materials Aims and scope

Based on the method of sampling surfaces, a hybrid finite-element model is developed for a three-dimensional analysis of laminated composite plates with piezoelectric patches. According to this method, the sampling surfaces inside the layers and piezoelectric patches parallel to the middle surface are selected, and displacements and electric potentials of these surfaces are introduced as unknown functions. The sampling surfaces are located inside the layers and patches at the nodes of Chebyshev polynomials that allows one to obtain numerical solutions asymptotically approaching the solutions of electroelasticity as the number of sampling surfaces tends to infinity. A method to determine the optimal voltages applied to the electrodes of piezoelectric patches that makes it possible to bring the plate to the desired shape by using the inverse piezoelectric effect is proposed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.

Similar content being viewed by others

References

  1. E. F. Crawley and K. B.Lazarus, “Induced strain actuation of isotropic and anisotropic plates,” AIAA J, 29, No. 6, 944-951 (1991).

    Article  Google Scholar 

  2. D. A. Saravanos, “Mixed laminate theory and finite element for smart piezoelectric composite shell structures,” AIAA J., 35, No. 8, 1327-1333 (1997).

    Article  Google Scholar 

  3. R. Lammering and S. Mesecke-Rischmann, “Multi-field variational formulations and related finite elements for piezoelectric shells,” Smart Mater. Struct., 12, No. 6, 904-913 (2003).

    Article  Google Scholar 

  4. K. Y. Sze and L. Q. Yao, “Modelling smart structures with segmented piezoelectric sensors and actuators,” J. Sound Vib., 235, No. 3, 495-520 (2000).

    Article  Google Scholar 

  5. K. Y. Sze, L. Q. Yao, and S. Yi, “A hybrid stress ANS solid-shell element and its generalization for smart structure modelling. Part II: Smart structure modelling,” Int. J. Numer. Meth. Eng., 48, No. 4, 565-582 (2000).

    Article  Google Scholar 

  6. S. Zheng, X. Wang, and W. Chen, “The formulation of a refined hybrid enhanced assumed strain solid shell element and its application to model smart structures containing distributed piezoelectric sensors/actuators,” Smart Mater. Struct., 13, No. 4, N43-N50 (2004).

    Article  Google Scholar 

  7. X. G. Tan and L. Vu-Quoc, “Optimal solid shell element for large deformable composite structures with piezoelectric layers and active vibration control,” Int. J. Numer. Meth. Eng., 64, No. 15, 1981-2013 (2005).

    Article  Google Scholar 

  8. S. Klinkel and W. Wagner, “A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation,” Int. J. Numer. Meth. Eng., 65, No. 3, 349-382 (2006).

    Article  Google Scholar 

  9. S. Klinkel and W. Wagner, “A piezoelectric solid shell element based on a mixed variational formulation for geometrically linear and nonlinear applications,” Computers Struct., 86, No. 1-2, 38-46 (2008).

    Article  Google Scholar 

  10. S. Lentzen, “Nonlinearly coupled thermopiezoelectric modelling and FE-simulation of smart structures,” Fortschritt-Berichte VDI, Reihe 20, Nr. 419. - Düsseldorf: VDI Verlag, (2009).

    Google Scholar 

  11. G. M. Kulikov and S. V. Plotnikova, “Solution of a coupled thermoelasticity problem based on a geometrically exact shell element,” Mech. Compos. Mater., 46, No. 4, 349-364 (2010).

    Article  Google Scholar 

  12. G. M. Kulikov and S. V. Plotnikova, “Exact geometry piezoelectric solid-shell element based on the 7-parameter model,” Mech. Adv. Mater. Struct., 18, No. 2, 133-146 (2011).

    Article  Google Scholar 

  13. G. M. Kulikov and S. V. Plotnikova, “Finite rotation piezoelectric exact geometry solid-shell element with nine degrees of freedom per node,” Comput. Mater. Continua., 23, No. 3, 233-264 (2011).

    Google Scholar 

  14. G. M. Kulikov and S. V. Plotnikova, “The use of 9-parameter shell theory for development of exact geometry 12-node quadrilateral piezoelectric laminated solid-shell elements,” Mech. Adv. Mater. Struct., 22, No. 6, 490-502 (2015).

    Article  Google Scholar 

  15. E. Carrera, S. Brischetto, and P. Nali, Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis, Chichester: John Wiley and Sons Ltd, (2011).

    Book  Google Scholar 

  16. E. Carrera, S. Valvano, and G. M. Kulikov, “Multilayered plate elements with node-dependent kinematics for electromechanical problems,” Int. J. Smart Nano Mater., 9, No. 4, 279-317 (2018).

    Article  Google Scholar 

  17. G. M. Kulikov and S. V. Plotnikova, “Three-dimensional exact analysis of piezoelectric laminated plates via a sampling surfaces method,” Int. J. Solids Struct., 50, No. 11-12, 1916-1929 (2013).

    Article  Google Scholar 

  18. G. M. Kulikov, S. V. Plotnikova, and E. Carrera, “Hybrid-mixed solid-shell element for stress analysis of laminated piezoelectric shells through higher-order theories,” Adv. Struct. Mater., 81, 45-68 (2018).

    Article  Google Scholar 

  19. G. M. Kulikov and S. V. Plotnikova, “Exact geometry SaS solid-shell element for 3D stress analysis of FGM piezoelectric structures,” Curved Layered Struct., 5, No. 1, 116-135 (2018).

    Article  Google Scholar 

  20. H. Irschik, “A review on static and dynamic shape control of structures by piezoelectric actuation,” Eng. Struct., 24, No. 1, 5-11 (2002).

    Article  Google Scholar 

  21. D. B. Koconis, L. P. Kollar, and G. S. Springer, “Shape control of composite plates and shells with embedded actuators. II. Desired shape specified,” J. Compos. Mater., 28, No. 5, 459-482 (1994).

    Article  CAS  Google Scholar 

  22. A. O. Vatul’yan, A. V. Nasedkin, A. S. Skaliukh, A. N. Solovyev, and N. B. Lapitskaya, “Controlling the surface of a segmented bimorph plates,” Prikl. Mekh. Tekhn. Fiz., 36, No. 4, 131-136 (1995).

    Google Scholar 

  23. C. Y. Hsu, C. C. Lin, and L. Gaul, “Shape control of composite plates by bonded actuators with high performance configuration,” J. Reinf. Plast. Compos., 8, No. 2, 112-124 (1997).

    Google Scholar 

  24. K. Chandrashekhara and S. Varadarajan, “Adaptive shape control of composite beams with piezoelectric actuators,” J. Intell. Mater. Syst. Struct., 8, No. 2, 112-124 (1997).

    Article  Google Scholar 

  25. C. Y. K. Chee, L. Tong, and G. P. Steven, “A buildup voltage distribution (BVD) algorithm for shape control of smart plate structures,” Comput. Mech., 26, No. 2, 115-128 (2000).

    Article  Google Scholar 

  26. C. Y. K. Chee, L. Tong, and G. P. Steven, “Static shape control of composite plates using a slope-displacement-based algorithm,” AIAA J. 40, No. 8, 1611-1618 (2002).

    Article  Google Scholar 

  27. S. D. Mota Silva, R. Ribeiro, J. D. Rodrigues, M. A. P. Vaz, and J. M. Monteiro, “The application of genetic algorithms for shape control with piezoelectric patches - an experimental comparison,” Smart Mater. Struct., 13, No. 1, 220-226 (2004).

    Article  Google Scholar 

  28. K. M. Liew, X. Q. He, and S. A. Meguid, “Optimal shape control of functionally graded smart plates using genetic algorithm,” Comput. Mech., 33, No. 4, 245-253 (2004).

    Article  Google Scholar 

  29. M. S. I. Shaik Dawood, L. Iannucci, and E. S. Greenhalgh, “Three-dimensional static shape control analysis of composite plates using distributed piezoelectric actuators,” Smart Mater. Struct., 17, No. 2, 1-10 (2008).

    Article  Google Scholar 

  30. S. S. Vel and R. S. Batra, “Cylindrical bending of laminated plates with distributed and segmented piezoelectric actuators/sensors,” AIAA J., 38, No. 5, 857-867 (2000).

    Article  Google Scholar 

Download references

This work was supported by the Russian Scientific Fund (project No. 18-19-00092).

Author information

Authors and Affiliations

  1. The Tambov State Technical University, Tambov, Russia

    S. V. Plotnikova & G. M. Kulikov

Authors
  1. S. V. Plotnikova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. M. Kulikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. M. Kulikov.

Additional information

Translated from Mekhanika Kompozitnykh Materialov, Vol. 56, No. 5, pp. 821-840, September-October, 2020.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Plotnikova, S.V., Kulikov, G.M. Shape Control of Composite Plates with Distributed Piezoelectric Actuators in a Three-Dimensional Formulation. Mech Compos Mater 56, 557–572 (2020). https://doi.org/10.1007/s11029-020-09904-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11029-020-09904-3

Keywords

Search

Navigation