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.
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References
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.
J. N. Reddy, Mechanics of laminated composite plates and shells, New York: CRC Press (2004).
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.
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.
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).
P. Heyliger and S. Brooks, Exact solutions for laminated piezoelectric plates in cylindrical bending, ASME Jornal of Applied Mechanics, 63 (1996) 903–910.
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.
P. R. Heyliger and E. Pan, Static fields in magnetoelectroelastic laminates, AIAA Journal, 42 (2004) 1435–1443.
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.
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.
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.
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.
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.
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.
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).
J. N. Reddy, Energy and variational methods in applied mechanics, New York: John Wiley & Sons, Ltd. (1984).
B. Yimin, Static and dynamic analysis of piezothermoelastic laminated shell composites with distributed sensors and actuators, Mechanical Engineering, University of Kentucky: Lexington, Kentucky (1996).
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.
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.
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.
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.
A. W. Leissa and J. Chang, Elastic deformation of thick, laminated composite shallow shells, Compos. Struct., 35 (1996) 53–170.
M. S. Qatu, Vibration of laminated shells and plates, London: Elsevier (2004).
J. Yang, An introduction to the theory of piezoelectricity, Advances in Mechanics and Mathematics, Lincoln, Nebraska: Springer (2005).
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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.
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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
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DOI: https://doi.org/10.1007/s12206-015-1209-4