The transverse shear deformation behaviour of magneto-electro-elastic shell

Abstract

Compared to the large number of possible magneto-electro-elastic shell theories, very few exact solutions determining the in-plane stresses, electric displacements and magnetic inductions are possible. While, solving the magneto-electro-elastic shell equations in terms of thermo-magneto-electro-elastic generalized field functions on arbitrary domains and for general conditions exactly are not always possible. In the present work, a linear version of magneto-electro-elastic shell with simply supported boundary conditions, solved exactly, provided that the lamination scheme is cross-ply or anti-symmetric angle-ply laminates. The exact solution that introduced herein can measure the in-plane stresses, electric displacements and magnetic inductions. It also allow for an accurate and usually elegant and conclusive investigation of the various sensations in a shell structure. However, it is important for micro-electro-mechanical shell applications to have an approach available that gives the transverse shear deformation Behaviourfor cases that cannot examine experimentally. An investigated examples were accompanied and noteworthy conclusions were drawn which highlight the issues of the implementation of the exact solution, implication of the effects of the material properties, lay-ups of the constituent layers, and shell parameters on the static Behaviour.

This is a preview of subscription content, access via your institution.

References

  1. [1]

    J. M. S. Moita, C. M. M. Soares and C. A. M. Soares, Analyses of magneto-electro-elastic plates using a higher order finite element model, Composite Structures, 91 (2009) 421–426.

    Article  Google Scholar 

  2. [2]

    J. N. Reddy, Mechanics of laminated composite plates and shells, New York: CRC Press (2004).

    MATH  Google Scholar 

  3. [3]

    R. G. Lage, C. M. M. Soares, C. A. M. Soares and J. N. Reddy, Layerwise partial mixed finite element analysis of magneto-electro-elastic plates, Comput Structure, 82 (2004) 1293–301.

    Article  Google Scholar 

  4. [4]

    R. K. Bhangale and N. Ganesan, Free vibration of simply supported functionally graded and layered magneto-electroelastic plates by finite element method, Journal of Sound and Vibration, 294 (2006) 1016–1038.

    Article  Google Scholar 

  5. [5]

    T. M. Badri and H. H. Al-Kayiem, Dynamic analysis of laminated composite thermo-magneto-electro-elastic shells, Journal of Mechanical Science and Technology, 9 (28) (2014).

  6. [6]

    P. Heyliger and S. Brooks, Exact solutions for laminated piezoelectric plates in cylindrical bending, ASME Jornal of Applied Mechanics, 63 (1996) 903–910.

    Article  MATH  Google Scholar 

  7. [7]

    D. A. Savravanos, P. R. Heyliger and D. Hopkins, A layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates, International Journal of Solid Structures, 34 (3) (1997) 359–378.

    Article  MATH  Google Scholar 

  8. [8]

    P. R. Heyliger and E. Pan, Static fields in magnetoelectroelastic laminates, AIAA Journal, 42 (2004) 1435–1443.

    Article  Google Scholar 

  9. [9]

    P. R. Heyliger, F. Ramirez and E. Pan, Two dimensional static fields in magnetoelectroelastic laminates, Journal of Intelligent Material Systems and Structures, 15 (2004) 689–709.

    Article  Google Scholar 

  10. [10]

    E. Pan and F. Han, Exact solution for functionally graded and layered magneto-electro-elastic plates, International Journal of Engineering Science, 43 (2005) 321–339.

    Article  Google Scholar 

  11. [11]

    J. Wang, L. Chen and S. Fang, State vector approach to analysis of multilayered magneto-electro-elastic plates, International Journal of Solids and Structures, 40 (2003) 1669–1680.

    Article  MATH  Google Scholar 

  12. [12]

    W. Chih-Ping and Y.-H. Tsai, Static behaviour of functionally graded magneto-electro-elastic shells under electric displacement and magnetic flux, International Journal of Engineering Science, 45 (2007) 744–769.

    Article  Google Scholar 

  13. [13]

    Y.-H. Tsai, W. Chih-Ping and S. Yun-Siang, Threedimensional analysis of doubly curved functionally graded magneto-electro-elastic shells, European Journal of Mechanics A/Solids, 27 (2008) 79–105.

    MathSciNet  Article  MATH  Google Scholar 

  14. [14]

    A. Gülay and C. M. Dokmeci, On the fundamental equations of electromagnetoelasticity media in variational form with an application to shell/lamina equations, International Journal of Solids and Structures, 47 (2010) 466–492.

    Article  MATH  Google Scholar 

  15. [15]

    T. M. Badri, H. H. Al-Kayiem and M. B. Taufiq, The theory of functional and adaptive shell structures, ISBN: 978-3-8465-2175-5, LAP LAMBERT Academic Pub. (2013).

    Google Scholar 

  16. [16]

    J. N. Reddy, Energy and variational methods in applied mechanics, New York: John Wiley & Sons, Ltd. (1984).

    MATH  Google Scholar 

  17. [17]

    B. Yimin, Static and dynamic analysis of piezothermoelastic laminated shell composites with distributed sensors and actuators, Mechanical Engineering, University of Kentucky: Lexington, Kentucky (1996).

    Google Scholar 

  18. [18]

    H. S. Tzou, H.-J. Lee and S. M. Arnold, Smart materials, precision sensors/ actuators, smart structures, and structronic systems, Mechanics of Advanced Materials and Structures, 11 (2004) 367–393.

    Google Scholar 

  19. [19]

    T. M. B. Albarody and H. H. Al-Kayiem, Laminated smart shell structures; theory and analysis, in Shell Structures: Theory and Application, W. Pietraszkiewicz, Editor, CRC Press, Taylor & Francis: London (2013) 49.

    Google Scholar 

  20. [20]

    L. D. Perez-Fernandez et al., On the constitutive relations and energy potentials of linear thermo-magneto-electroelasticity, Mechanics Research Communications, 36 (2009) 343–350.

    MathSciNet  Article  MATH  Google Scholar 

  21. [21]

    F. Yang et al., The effective properties of smart composites with linear coupling Behaviours, International Journal of Mechanics and Materials in Design, 4 (3) (2008) 255–263.

    Article  Google Scholar 

  22. [22]

    A. W. Leissa and J. Chang, Elastic deformation of thick, laminated composite shallow shells, Compos. Struct., 35 (1996) 53–170.

    Google Scholar 

  23. [23]

    M. S. Qatu, Vibration of laminated shells and plates, London: Elsevier (2004).

    MATH  Google Scholar 

  24. [24]

    J. Yang, An introduction to the theory of piezoelectricity, Advances in Mechanics and Mathematics, Lincoln, Nebraska: Springer (2005).

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Thar M. Badri Albarody.

Additional information

Thar M. BadriAlbarody received PDRF., Ph.D., MSc. and BSc. in Applied Mechanic. He is senior lecturer in Mechanical Eng. Dept. of UniversitiTeknologi PETRONAS. His areas of interest are summarized as; computational continuum mechanic, vibration of shell and plate, functional composite materials, and condensed matter in physics and mechanic.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Albarody, T.M.B., Al-Kayiem, H.H. & Faris, W. The transverse shear deformation behaviour of magneto-electro-elastic shell. J Mech Sci Technol 30, 77–87 (2016). https://doi.org/10.1007/s12206-015-1209-4

Download citation

Keywords

  • Structronic shell
  • Thermo-magneto-electro-elastic
  • Laminated shell
  • Smart composite
  • Linear analysis
  • Exact solution