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Nonlinear analysis of functionally graded laminates considering piezoelectric effect

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Abstract

In this paper, static bending analysis of functionally graded plates with piezoelectric layers has been carried out considering geometrical nonlinearity in different sets of mechanical and electrical loadings. Only the geometrical nonlinearity has been taken into account. The governing equations are obtained using potential energy and Hamilton’s principle. The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect by using higher order elements. The present finite element used displacement and electric potential as nodal degrees of freedom. Results are presented for two constituent FGM plate under different mechanical boundary conditions. Numerical results for FGM plate are given in dimensionless graphical forms. Effects of material composition and boundary conditions on nonlinear response of the plate are also studied.

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References

  1. G. N. Praveen and J. N. Reddy, Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, Int. J. Solids Struct., 35 (1998) 4457–4476.

    Article  MATH  Google Scholar 

  2. J. Yang and H. -S. Shen, Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermomechanical loads under various boundary conditions, Composites: Part B, 34 (2003) 103–115.

    Article  Google Scholar 

  3. N. Sundararajan, T. Prakash and M. Ganapathi, Nonlinear free flexural vibrations of functionally graded rectangular and skew plates under thermal environments, Finite Elements in Analysis and Design, 42 (2005) 152–168.

    Article  Google Scholar 

  4. J. Yang and X. -L. Huang, Nonlinear transient response of functionally graded plates with general imperfections in thermal environments, Comput. Methods Appl. Mech. Engrg., 196 (2007) 2619–2630.

    Article  MATH  Google Scholar 

  5. A. Nosier and F. Fallah, Non-linear analysis of functionally graded circular plates under asymmetric transverse loading, Int. J. Non-Linear Mechanics, 44 (2009) 928–942.

    Article  MATH  Google Scholar 

  6. X. Zhao and K. M. Liew, Geometrically nonlinear analysis of functionally graded shells, Int. J. Mechanical Sciences, 51 (2009) 131–144.

    Article  Google Scholar 

  7. X. Zhao and K. M. Liew, Geometrically nonlinear analysis of functionally graded plates using the element-free kp-Ritz method, Comput. Methods Appl. Mech. Engrg., 198 (2009) 2796–2811.

    Article  MATH  Google Scholar 

  8. S. J. Mehrabadi, M. H. Kargarnovin and M. M. Najafizadeh, Free vibration analysis of functionally graded coupled circular plate with piezoelectric layers, Journal of Mechanical Science and Technology, 23 (2009) 2008–2021.

    Article  Google Scholar 

  9. E. Orakdögen, S. Küçükarslan, A. Sofiyev and M. H. Omurtag, Finite element analysis of functionally graded plates for coupling effect of extension and bending, Meccanica, 45 (2010) 63–72.

    Article  MATH  Google Scholar 

  10. H. -S. Shen and Z. -X. Wang, Nonlinear bending of functionally garded plates subjected to combined loading and resting on elastic foundations, Composite Structures, 92 (2010) 2517–2524.

    Article  Google Scholar 

  11. G. Nie and Z. Zhong, Dynamic analysis of multidirectional functionally graded annular plates, Applied Mathematical Modeling, 34 (2010) 608–616.

    Article  MathSciNet  MATH  Google Scholar 

  12. S. V. Levyakov and V. V. Kuznetsov, Application of triangular element invariants for geometrically nonlinear analysis of functionally graded shells, Comput. Mech., DOI: 10.1007/ s00466-011-0603-8.

  13. K. M. Liew, X. Q. He, T. Y. Ng and S. Sivashanker, Active control of FGM plates subjected to a temperature gradient: Modeling via finite element method based on FSDT, Int. J. Numer. Meth. Engng., 52 (2001) 1253–1271.

    Article  MATH  Google Scholar 

  14. J. Yang, S. Kitipornchai and K. M. Liew, Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates, Comput. Methods Appl. Mech. Engrg., 192 (2003) 3861–3885.

    Article  MATH  Google Scholar 

  15. S. -C. Woo and N. S. Goob, Prediction of Actuating Displacement in a Piezoelectric Composite Actuator with a Thin Sandwiched PZT Plate by a Finite Element Simulation, Journal of Mechanical Science and Technology, 21 (2007) 455–464.

    Article  Google Scholar 

  16. S. Panda and M. C. Ray, Nonlinear finite element analysis of functionally graded plates integrated with patches of piezoelectric fiber reinforced composite, Finite Elements in Analysis and Design, 44 (2008) 493–504.

    Article  Google Scholar 

  17. X. -K. Xia and H. -S. Shen, Nonlinear vibration and dynamic response of FGM plates with piezoelectric fiber reinforced composite actuators, Composite Structures, 90 (2009) 254–262.

    Article  Google Scholar 

  18. F. Ebrahimi, M. H. Naei and A. Rastgoo, Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation, Journal of Mechanical Science and Technology, 23 (2009) 2107–2124.

    Article  Google Scholar 

  19. B. Behjat, M. Salehi, M. Sadighi, A. Armin and M. Abbasi, Static, Dynamic and free vibration analysis of functionally graded piezoelectric panels using finite element method, J. of Intelligent Material Systems and Structures, 20 (2009) 1635–1646.

    Article  Google Scholar 

  20. B. Behjat, M. Salehi, A. Armin, M. Sadighi and M. Abbasi, Static and dynamic analysis of functionally graded piezoelectric plates under mechanical and electrical loading, Scientia Iranica Transactions B: Mechanical Engineering, 18 (2011) 986–994.

    Article  Google Scholar 

  21. M. Yiqi and F. Yaiming, Nonlinear dynamic response and active vibration control for piezoelectric functionally graded plate, J. of Sound and Vibration, 329 (2010) 2015–2028.

    Article  Google Scholar 

  22. K. J. Bathe and S. Bolourchi, A geometric and material nonlinear plate and shell element, Computers and Structures, 11 (1980) 23–48.

    Article  MATH  Google Scholar 

  23. K. J. Bathe, Finite Element procedures, New Jersey: Prentic-Hall, 1996.

    Google Scholar 

  24. Y. Jiashi, An Introduction to the Theory of Piezoelectricity, USA: Springer science, 2005.

    MATH  Google Scholar 

  25. X. Q. He, T. Y. Ng, S. Sivashanker and K. M. Liew, Active control of FGM plates with integrated piezoelectric sensors and actuators, Int. J. of Solids and structures, 38 (2001) 1641–1655.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Mechanical Engineering Faculty Sahand University of Technology Sahand New Tawn, Tabriz, Iran

    Bashir Behjat

  2. Mechanical Engineering Department, Tabriz University, Tabriz, Iran

    Mohamad Reza Khoshravan

Authors
  1. Bashir Behjat
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  2. Mohamad Reza Khoshravan
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Correspondence to Bashir Behjat.

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Recommended by Associate Editor Heung Soo Kim

Bashir Behjat entered the Mechanical Engineering program at the Amirkabir University of Technology. He received his bachelor’s degree, along with a major degree in Solid Mechanics in 2006. After getting as an honored student among the students of the faculty, Bashir Behjat was accepted into the master’s program in the Mechanical Engineering department at Amirkabir University of Technology in 2006. After accepting as a PhD student in Tabriz University in Iran in September 2009, he continued his Ph.D in this university as a researcher in the field of Nonlinear Finite element method and FGPM Materials and now he is associate professor in the Sahnad University of Technology in Sahand, Iran.

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Behjat, B., Khoshravan, M.R. Nonlinear analysis of functionally graded laminates considering piezoelectric effect. J Mech Sci Technol 26, 2581–2588 (2012). https://doi.org/10.1007/s12206-012-0638-6

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  • DOI: https://doi.org/10.1007/s12206-012-0638-6

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