zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Symplectic analytical solutions for the magnetoelectroelastic solids plane problem in rectangular domain. (English) Zbl 1213.74135
Summary: The transversely isotropic magnetoelectroelastic solids plane problem in rectangular domain is derived to Hamiltonian system. In symplectic geometry space with the origin variables-displacements, electric potential, and magnetic potential, as well as their duality variables-lengthways stress, electric displacement, and magnetic induction, on the basis of the obtained eigensolutions of zero-eigenvalue, the eigensolutions of nonzero-eigenvalues are also obtained. The former are the basic solutions of Saint-Venant problem, and the latter are the solutions which have the local effect, decay drastically with respect to distance, and are covered in the Saint-Venant principle. So the complete solution of the problem is given out by the symplectic eigensolutions expansion. Finally, a few examples are selected and their analytical solutions are presented.

MSC:
74F15Electromagnetic effects in solid mechanics
WorldCat.org
Full Text: DOI EuDML
References:
[1] J. H. Huang and W. S. Kuo, “The analysis of piezoelectric/piezomagnetic composite materials containing ellipsoidal inclusions,” Journal of Applied Physics, vol. 81, no. 3, pp. 1378-1386, 1997.
[2] B. M. Singh, J. Rokne, and R. S. Dhaliwal, “Closed-form solutions for two anti-plane collinear cracks in a magnetoelectroelastic layer,” European Journal of Mechanics, A/Solids, vol. 28, no. 3, pp. 599-609, 2009. · Zbl 1158.74456 · doi:10.1016/j.euromechsol.2008.10.004
[3] S. M. Xiong and G. Z. Ni, “2D Green’s functions for semi-infinite transversely isotropic electro-magneto-thermo-elastic composite,” Journal of Magnetism and Magnetic Materials, vol. 321, no. 12, pp. 1867-1874, 2009. · doi:10.1016/j.jmmm.2008.12.010
[4] C. C. Ma and J. M. Lee, “Theoretical analysis of generalized loadings and image forces in a planar magnetoelectroelastic layered half-plane,” Journal of the Mechanics and Physics of Solids, vol. 57, no. 3, pp. 598-620, 2009. · Zbl 05600193 · doi:10.1016/j.jmps.2008.11.001
[5] H. J. Ding and A. M. Jiang, “A boundary integral formulation and solution for 2D problems in magneto-electro-elastic media,” Computers and Structures, vol. 82, no. 20-21, pp. 1599-1607, 2004. · doi:10.1016/j.compstruc.2004.05.006
[6] W. Q. Chen, K. Y. Lee, and H. J. Ding, “On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates,” Journal of Sound and Vibration, vol. 279, no. 1-2, pp. 237-251, 2005. · doi:10.1016/j.jsv.2003.10.033
[7] W. X. Zhong, Duality System in Applied Mechanics and Optimal Control, Kluwer Academic Publishers, Boston, Mass, USA, 2004. · Zbl 1078.70001
[8] W. A. Yao, W. X. Zhong, and C. W. Lim, Symplectic Elasticity, World Scientific, Singapore, 2009.
[9] W. A. Yao and H. T. Yang, “Hamiltonian system based Saint Venant Solutions for multi-layered compostie plane anisotropic plates,” International Journal of Solids and Structures, vol. 38, no. 32-33, pp. 5807-5817, 2001. · Zbl 0987.74046 · doi:10.1016/S0020-7683(00)00371-1
[10] A. Y. T. Leung and J. J. Zheng, “Closed form stress distribution in 2D elasticity for all boundary conditions,” Applied Mathematics and Mechanics, vol. 28, no. 12, pp. 1629-1642, 2007. · Zbl 1231.74266 · doi:10.1007/s10483-007-1210-z
[11] C. W. Lim, C. F. Lü, Y. Xiang, and W. A. Yao, “On new symplectic elasticity approach for exact free vibration solutions of rectangular Kirchhoff plates,” International Journal of Engineering Science, vol. 47, no. 1, pp. 131-140, 2009. · Zbl 1213.74203 · doi:10.1016/j.ijengsci.2008.08.003
[12] X. S. Xu, Q. Gu, A. Y. T. Leung, and J. J. Zheng, “Symplectic eigensolution method in transversely isotropic piezoelectric cylindrical media,” Journal of Zhejiang University Science, vol. 6, no. 9, pp. 922-927, 2005. · Zbl 1099.74515 · doi:10.1631/jzus.2005.A0922
[13] W. A. Yao and X. C. Li, “Symplectic duality system on plane magnetoelectroelastic solids,” Applied Mathematics and Mechanics, vol. 27, no. 2, pp. 195-205, 2006. · Zbl 1145.74011 · doi:10.1007/s10483-006-0207-z
[14] E. Pan, “Exact solution for simply supported and multilayered magneto-electro-elastic plates,” Journal of Applied Mechanics, Transactions ASME, vol. 68, no. 4, pp. 608-618, 2001. · Zbl 1110.74612 · doi:10.1115/1.1380385
[15] X. Wang and Y. P. Shen, “Inclusions of arbitrary shape in magnetoelectroelastic composite materials,” International Journal of Engineering Science, vol. 41, no. 1, pp. 85-102, 2003. · Zbl 1211.74104 · doi:10.1016/S0020-7225(02)00110-6