Advertisement

Acta Mechanica Sinica

, Volume 34, Issue 4, pp 689–705 | Cite as

A refined finite element method for bending analysis of laminated plates integrated with piezoelectric fiber-reinforced composite actuators

Research Paper
  • 38 Downloads

Abstract

This research presents a finite element formulation based on four-variable refined plate theory for bending analysis of cross-ply and angle-ply laminated composite plates integrated with a piezoelectric fiber-reinforced composite actuator under electromechanical loading. The four-variable refined plate theory is a simple and efficient higher-order shear deformation theory, which predicts parabolic variation of transverse shear stresses across the plate thickness and satisfies zero traction conditions on the plate free surfaces. The weak form of governing equations is derived using the principle of minimum potential energy, and a 4-node non-conforming rectangular plate element with 8 degrees of freedom per node is introduced for discretizing the domain. Several benchmark problems are solved by the developed MATLAB code and the obtained results are compared with those from exact and other numerical solutions, showing good agreement.

Keywords

Finite element method Laminated plate Piezoelectric fiber-reinforced composite (PFRC) actuator Piezoelectric Refined plate theory Smart structures 

References

  1. 1.
    Kumar, A., Chakraborty, D.: Effective properties of thermo-electro-mechanically coupled piezoelectric fiber reinforced composites. Mater. Des. 30, 1216–1222 (2009)CrossRefGoogle Scholar
  2. 2.
    Mallik, N., Ray, M.: Effective coefficients of piezoelectric fiber-reinforced composites. AIAA J. 41, 704–710 (2003)CrossRefGoogle Scholar
  3. 3.
    Mitchell, J., Reddy, J.: A refined hybrid plate theory for composite laminates with piezoelectric laminae. Int. J. Solids Struct. 32, 2345–2367 (1995)CrossRefMATHGoogle Scholar
  4. 4.
    Saravanos, D.A., Heyliger, P.R., Hopkins, D.A.: Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates. Int. J. Solids Struct. 34, 359–378 (1997)CrossRefMATHGoogle Scholar
  5. 5.
    Lam, K., Peng, X., Liu, G., et al.: A finite-element model for piezoelectric composite laminates. Smart Mater. Struct. 6, 583 (1997)CrossRefGoogle Scholar
  6. 6.
    Correia, V.M.F., Gomes, M.A.A., Suleman, A., et al.: Modelling and design of adaptive composite structures. Comput. Method Appl. Mech. 185, 325–346 (2000)CrossRefMATHGoogle Scholar
  7. 7.
    Ray, M.C., Mallik, N.: Finite element analysis of smart structures containing piezoelectric fiber-reinforced composite actuator. AIAA J. 42, 1398–1405 (2004)CrossRefGoogle Scholar
  8. 8.
    Mallik, N., Ray, M.: Exact solutions for the analysis of piezoelectric fiber reinforced composites as distributed actuators for smart composite plates. Int. J. Mech. Mater. Des. 2, 81–97 (2005)CrossRefGoogle Scholar
  9. 9.
    Moita, J.M.S., Soares, C.M.M., Soares, C.A.M.: Active control of forced vibrations in adaptive structures using a higher order model. Compos. struct. 71, 349–355 (2005)CrossRefGoogle Scholar
  10. 10.
    Cotoni, V., Masson, P., Cĉté, F.: A finite element for piezoelectric multilayered plates: combined higher-order and piecewise linear C0 formulation. J. Intell. Mater. Syst. Struct. 17, 155–166 (2006)CrossRefGoogle Scholar
  11. 11.
    Panda, S., Ray, M.: Nonlinear finite element analysis of functionally graded plates integrated with patches of piezoelectric fiber reinforced composite. Finite Elem. Anal. Des. 44, 493–504 (2008)CrossRefGoogle Scholar
  12. 12.
    Torres, D.A.F., Mendonça, P.T.R., Barcellos, C.S.: Evaluation and verification of an HSDT-layerwise generalized finite element formulation for adaptive piezoelectric laminated plates. Comput. Methods Appl. Mech. 200, 675–691 (2011)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Shiyekar, S., Kant, T.: Higher order shear deformation effects on analysis of laminates with piezoelectric fibre reinforced composite actuators. Compos. Struct. 93, 3252–3261 (2011)CrossRefGoogle Scholar
  14. 14.
    Moleiro, F., Soares, C.M., Soares, C.M., et al.: Assessment of a layerwise mixed least-squares model for analysis of multilayered piezoelectric composite plates. Comput. Struct. 108, 14–30 (2012)CrossRefGoogle Scholar
  15. 15.
    Phung-Van, P., De Lorenzis, L., Thai, C.H., et al.: Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements. Comput. Mater. Sci. 96, 495–505 (2015)CrossRefGoogle Scholar
  16. 16.
    Plagianakos, T.S., Papadopoulos, E.G.: Higher-order 2-D/3-D layerwise mechanics and finite elements for composite and sandwich composite plates with piezoelectric layers. Aerosp. Sci. Technol. 40, 150–163 (2015)CrossRefGoogle Scholar
  17. 17.
    Rouzegar, J., Abad, F.: Analysis of cross-ply laminates with piezoelectric fiber-reinforced composite actuators using four-variable refined plate theory. J. Theor. Appl. Mech. 53, 439–452 (2015)CrossRefGoogle Scholar
  18. 18.
    Rouzegar, J., Abad, F.: Free vibration analysis of FG plate with piezoelectric layers using four- variable refined plate theory. Thin Walled Struct. 89, 76–83 (2015)CrossRefGoogle Scholar
  19. 19.
    Cinefra, M., Valvano, S., Carrera, E.: A layer-wise MITC9 finite element for the free-vibration analysis of plates with piezo-patches. Int. J. Smart Nano Mater. 6, 85–104 (2015)Google Scholar
  20. 20.
    Lu, S.F., Zhang, W., Song, X.J.: Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force. Acta Mech. Sin. (2017).  https://doi.org/10.1007/s10409-017-0705-4. (in press)
  21. 21.
    Shimpi, R.P.: Refined plate theory and its variants. AIAA J. 40, 137–146 (2002)CrossRefGoogle Scholar
  22. 22.
    Shimpi, R., Patel, H.: A two variable refined plate theory for orthotropic plate analysis. Int. J. Solids Struct. 43, 6783–6799 (2006)CrossRefMATHGoogle Scholar
  23. 23.
    Thai, H.T., Kim, S.E.: Analytical solution of a two variable refined plate theory for bending analysis of orthotropic Levy-type plates. Int. J. Mech. Sci. 54, 269–276 (2012)CrossRefGoogle Scholar
  24. 24.
    Kim, S.E., Thai, H.T., Lee, J.: A two variable refined plate theory for laminated composite plates. Compos. Struct. 89, 197–205 (2009)CrossRefGoogle Scholar
  25. 25.
    Shimpi, R., Patel, H.: Free vibrations of plate using two variable refined plate theory. J. Sound Vib. 296, 979–999 (2006)CrossRefGoogle Scholar
  26. 26.
    Kim, S.E., Thai, H.T., Lee, J.: Buckling analysis of plates using the two variable refined plate theory. Thin Walled Struct. 47, 455–462 (2009)CrossRefGoogle Scholar
  27. 27.
    Rouzegar, J., Abdoli Sharifpoor, R.: A finite element formulation for bending analysis of isotropic and orthotropic plates based on two-variable refined plate theory. Sci. Iran. Trans. B Mech. Eng. 22, 196–207 (2015)Google Scholar
  28. 28.
    Rouzegar, J., Abdoli Sharifpoor, R.: Finite element formulations for free vibration analysis of isotropic and orthotropic plates using two-variable refined plate theory. Sci. Iran. Trans B Mech. Eng. 23, 1787–1799 (2016)Google Scholar
  29. 29.
    Rouzegar, J., Abdoli Sharifpoor, R.: Finite element formulations for buckling analysis of isotropic and orthotropic plates using two-variable refined plate theory. Iran. J. Sci. Technol. Trans. Mech. Eng. 41, 77–187 (2017)CrossRefGoogle Scholar
  30. 30.
    Tiersten, H.F.: Linear Piezoelectric Plate Vibrations: Elements of the Linear Theory of Piezoelectricity and the Vibrations Piezoelectric Plates. Springer, Berlin (1969)CrossRefGoogle Scholar
  31. 31.
    Melosh, R.: Structural analysis of solids. ASCE Struct J. 89, 205–223 (1963)Google Scholar
  32. 32.
    Pagano, N.: Exact solutions for rectangular bidirectional composites and sandwich plates. J. Compos. Mater. 34, 86–101 (1970)Google Scholar
  33. 33.
    Tzou, H., Tseng, C.: Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: a piezoelectric finite element approach. J. Sound Vib. 138, 17–34 (1990)CrossRefGoogle Scholar
  34. 34.
    Ray, M., Bhattacharyya, R., Samanta, B.: Static analysis of an intelligent structure by the finite element method. Comput. Struct. 52, 617–631 (1994)CrossRefMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringShiraz University of TechnologyShirazIran

Personalised recommendations