Mixed State Hamiltonian Element for Plane Transversely Isotropic Magnetoelectroelastic Solids

Abstract:

Hamiltonian dual equation of plane transversely isotropic magnetoelectroelastic solids is derived from variational principle and mixed state Hamiltonian elementary equations are established. Similar to the Hamiltonian formulation in classic dynamics, the z coordinate is treated analogous to the time coordinate. Then the x-direction is discreted with the linear elements to obtain the state-vector governing equations, which are a set of first order differential equations in z and are solved by the analytical approach. Because present approach is analytic in z direction, there is no restriction on the thickness of plate through the use of the present element. Using the propagation matrix method, the approach can be extended to analyze the problems of magnetoelectroelastic laminated plates. Present semi-analytical method of mixed Hamiltonian element has wide application area.

• Periodical: Applied Mechanics and Materials (Volumes 275-277)
• Pages: 1978-1983
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.275-277.1978
• Online since: January 2013
• Authors: Xiao Chuan Li, Jin Shuang Zhang
• Keywords: Hamiltonian Element, Magnetoelectroelastic Solid, Semi-Analytical Method, Variational Principle

References

[1] J. H. Huang, W. S. Kuo: Journal of Applied Physics, Vol. 81(1997), p.1378.

[2] S. M. Xiong, G. Z. Ni: Journal of Magnetism and Magnetic Materials, Vol. 321(2009), p.1867.

[3] G. R. Buchanan: Composites: Part B, Vol. 35(2004), p.413.

[4] R. Garcia Lage, C. M. Mota Soares, C. A. Mota Soares, et al.: Computers and Structures, Vol. 82(2004), p.1293.

DOI: 10.1016/j.compstruc.2004.03.026

[5] H. J. Ding, A. M. Jiang: Science in China (series E), Vol. 33(2003), p.845 (in Chinese).

[6] H. J. Ding, A. M. Jiang: Computers and Structures, Vol. 82(2004), p.1599.

[7] X. C. Li, W. A. Yao: Engineering Analysis with Boundary Elements, Vol. 30 (2006), p.709.

[8] L. M. Tang, Z. Z. Chu, G. P. Zou, et al.: Computational Structural Mechanics and Application, Vol. 9(1992), p.347(in Chinese).

[9] H. J. Ouyang, W. X. Zhong, Q. Yang, et al.: Computational Structural Mechanics and Application, Vol. 10(1993), p.129(in Chinese).

[10] G. H. Qing, J. J. Qiu and Y. H. Liu: Applied Mathematics and Mechanics, Vol. 28(2007), p.51.

[11] G. H. Qing, J. J. Qiu and Y. H. Liu: Applied Mathematics and Mechanics, Vol. 26(2005), p.722.

[12] E. Pan: Journal of Applied Mechanics, Vol. 68(2001), p.608.

[13] X. Wang, Y. P. Shen: International Journal of Engineering Science, Vol. 41(2003), p.85.

[14] W. A. Yao: Chinese Journal of Computational Mechanics, Vol. 20(2003), p.487 (in Chinese).

[15] W. A. Yao, X. C. Li: Applied Mathematics and Mechanics, Vol. 27(2006), p.195.