Statics of FGM circular plate with magneto-electro-elastic coupling: axisymmetric solutions and their relations with those for corresponding rectangular beam

doi:10.1007/s10483-015-1934-7

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (5): 581-598.doi: https://doi.org/10.1007/s10483-015-1934-7

Statics of FGM circular plate with magneto-electro-elastic coupling: axisymmetric solutions and their relations with those for corresponding rectangular beam

收稿日期:2014-06-20 修回日期:2014-10-07 出版日期:2015-05-01 发布日期:2015-05-01
通讯作者: Xiangyu LI E-mail:zjuparis6@hotmail.com
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11321202 and 11272281), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20130101110120), the Program for New Century Excellent Talents in University of Ministry of Education of China (No.NCET-13-0973), the Program for Sichuan Provincial Youth Science and Technology Innovation Team (No. 2013-TD-0004), and the Scientific Research Foundation for Returned Scholars (Ministry of Education of China)

Statics of FGM circular plate with magneto-electro-elastic coupling: axisymmetric solutions and their relations with those for corresponding rectangular beam

1. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China;
2. State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou 310058, China;
3. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China

Received:2014-06-20 Revised:2014-10-07 Online:2015-05-01 Published:2015-05-01
Contact: Xiangyu LI E-mail:zjuparis6@hotmail.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11321202 and 11272281), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20130101110120), the Program for New Century Excellent Talents in University of Ministry of Education of China (No.NCET-13-0973), the Program for Sichuan Provincial Youth Science and Technology Innovation Team (No. 2013-TD-0004), and the Scientific Research Foundation for Returned Scholars (Ministry of Education of China)

摘要/Abstract

摘要：

This paper investigates the static behavior of a functionally graded circular plate made of magneto-electro-elastic (MEE) materials under tension and bending. The analysis is directly based on the three-dimensional governing equations for magnetoelectro- elasticity, with the boundary conditions on the upper and lower surfaces satisfied exactly and those on the cylindrical surface satisfied approximately (in the Saint Venant sense). The analytical solutions, derived with a direct displacement method, are valid for any functionally graded material (FGM) with its properties varying independently in a continuous manner along the thickness direction. For homogeneous materials, these solutions are degenerated to the ones available in the literature. Interesting relations are also found between the solutions for a functionally graded magneto-electro-elastic (FGMEE) circular plate and those for an FGMEE rectangular beam, and even those for a functionally graded elastic beam when only the elastic displacements are considered. The beam solutions are also derived using a direct displacement method. Numerical examples are presented to verify the present analytical solutions, show the effects of material heterogeneity and multi-field coupling, and indicate the correspondence between the plate solutions and beam solutions.

关键词: direct displacement method, solution correspondence, circular plate, magneto-electro-elastic (MEE) behavior, functionally graded material (FGM)

Key words: magneto-electro-elastic (MEE) behavior, solution correspondence, functionally graded material (FGM), circular plate, direct displacement method

中图分类号:

Yanzheng WANG, Weiqiu CHEN, Xiangyu LI. Statics of FGM circular plate with magneto-electro-elastic coupling: axisymmetric solutions and their relations with those for corresponding rectangular beam[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(5): 581-598.

参考文献

[1] Harshe, G., Dougherty, J. P., and Newnham, R. E. Theoretical modeling of multilayer magnetoelectric composites. International Journal of Applied Electromagnetics in Materials, 4(2), 145-159 (1993)
[2] Nan, C. W. Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Physical Review B, 50(9), 6082 (1994)
[3] Pan, E. Exact solution for simply supported and multilayered magneto-electro-elastic plates. Journal of Applied Mechanics, 68(4), 608-618 (2001)
[4] Zhou, Z. and Wang, B. Scattering of harmonic anti-plane shear waves by an interface crack in magneto-electro-elastic composites. Applied Mathematics and Mechanics (English Edition), 26(1), 17-26 (2005) DOI 10.1007/BF02438360
[5] Jiang, Z. Q. and Liu, J. X. Coupled fields of two-dimensional anisotropic magneto-electro-elastic solids with an elliptical inclusion. Applied Mathematics and Mechanics (English Edition), 21(10), 1213-1220 (2000) DOI 10.1007/BF02459001
[6] Chen. J., Pan, E., and Chen, H. Wave propagation in magneto-electro-elastic multilayered plates. International Journal of Solids and Structures, 44(3), 1073-1085 (2007)
[7] Koizumi, M. FGM activities in Japan. Composites Part B: Engineering, 28(1), 1-4 (1997)
[8] Chen, W. Q., Lee, K. Y., and Ding, H. J. On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates. Journal of Sound and Vibration, 279(1), 237-251 (2005)
[9] Chen, W. Q. and Lee, K. Y. Alternative state space formulations for magnetoelectric thermoelasticity with transverse isotropy and the application to bending analysis of nonhomogeneous plates. International Journal of Solids and Structures, 40(21), 5689-5705 (2003)
[10] Pan, E. and Han, F. Exact solution for functionally graded and layered magneto-electro-elastic plates. International Journal of Engineering Science, 43(3), 321-339 (2005)
[11] Bhangale, R. K. and Ganesan, N. Static analysis of simply supported functionally graded and layered magneto-electro-elastic plates. International Journal of Solids and Structures, 43(3), 3230-3253 (2006)
[12] Huang, D. J., Ding, H. J., and Chen, W. Q. Analytical solution for functionally graded magnetoelectro-elastic plane beams. International Journal of Engineering Science, 45(2), 467-485 (2007)
[13] Timoshenko, S. P. and Goodier, J. N. Theory of Elasticity, 3rd ed., McGraw-Hill, New York, 380-432 (1970)
[14] Wang, Y., Xu, R. Q., and Ding, H. J. Axisymmetric bending of functionally graded circular magneto-electro-elastic plates. European Journal of Mechanics-A/Solids, 30(6), 999-1011 (2011)
[15] Wang, Y., Xu, R. Q., and Ding, H. J. Three-dimensional solution of axisymmetric bending of functionally graded circular plates. Composite Structures, 92(7), 1683-1693 (2010)
[16] Wang, Y., Xu, R. Q., and Ding, H. J. Analytical solutions of functionally graded piezoelectric circular plates subjected to axisymmetric loads. Acta Mechanica, 215(1-4), 287-305 (2010)
[17] Yang, B., Ding, H. J., and Chen, W. Q. Elasticity solutions for a uniformly loaded rectangular plate of functionally graded materials with two opposite edges simply supported. Acta Mechanica, 207(3-4), 245-258 (2009)
[18] Yang, B., Ding, H. J., and Chen, W. Q. Elasticity solutions for a uniformly loaded annular plate of functionally graded materials. Structural Engineering and Mechanics, 30(4), 501-512 (2008)
[19] Mian, M. A. and Spencer, A. J. M. Exact solutions for functionally graded and laminated elastic materials. Journal of the Mechanics and Physics of Solids, 46(12), 2283-2295 (1998)
[20] Li, X. Y., Ding, H. J., and Chen, W. Q. Three-dimensional analytical solution for functionally graded magneto-electro-elastic circular plates subjected to uniform load. Composite Structures, 83(4), 381-390 (2008)
[21] Li, X. Y., Ding, H. J., and Chen, W. Q. Pure bending of simply supported circular plate of transversely isotropic functionally graded material. Journal of Zhejiang University Science A, 7(8), 1324-1328 (2006)
[22] Li, X. Y., Ding, H. J., and Chen, W. Q. Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qr^k. International Journal of Solids and Structures, 45(1), 191-210 (2008)
[23] Li, X. Y., Ding, H. J., Chen, W. Q., and Li, P. D. Three-dimensional piezoelectricity solutions for uniformly loaded circular plates of functionally graded piezoelectric materials with transverse isotropy. Journal of Applied Mechanics, 80(4), 041007 (2013)
[24] Li, X. Y., Ding, H. J., and Chen, W. Q. 3D analytical solution for a functionally graded transversely isotropic piezoelectric circular plate under tension and bending. International Journal of Engineering Science, 49(7), 664-676 (2011)

Statics of FGM circular plate with magneto-electro-elastic coupling: axisymmetric solutions and their relations with those for corresponding rectangular beam

Statics of FGM circular plate with magneto-electro-elastic coupling: axisymmetric solutions and their relations with those for corresponding rectangular beam

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	Jian ZANG, Ronghuan XIAO, Yewei ZHANG, Liqun CHEN. A novel way for vibration control of FGM fluid-conveying pipes via NiTiNOL-steel wire rope[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(6): 877-896.
[2]	Ying MENG, Xiaoye MAO, Hu DING, Liqun CHEN. Nonlinear vibrations of a composite circular plate with a rigid body[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(6): 857-876.
[3]	Sha XIAO, Zhongqi YUE. Complete solutions for elastic fields induced by point load vector in functionally graded material model with transverse isotropy[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(3): 411-430.
[4]	Zhaonian LI, Juan LIU, Biao HU, Yuxing WANG, Huoming SHEN. Wave propagation analysis of porous functionally graded piezoelectric nanoplates with a visco-Pasternak foundation[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(1): 35-52.
[5]	Xin LYU, Liaoliang KE, Jiayong TIAN, Jie SU. Contact vibration analysis of the functionally graded material coated half-space under a rigid spherical punch[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(8): 1187-1202.
[6]	Ye TANG, Jiye XU, Tianzhi YANG. Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(4): 479-496.
[7]	H. V. TUNG, L. T. N. TRANG. Nonlinear stability of advanced sandwich cylindrical shells comprising porous functionally graded material and carbon nanotube reinforced composite layers under elevated temperature[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(9): 1327-1348.
[8]	Wei PENG, Like CHEN, Tianhu HE. Nonlocal thermoelastic analysis of a functionally graded material microbeam[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(6): 855-870.
[9]	Xin FENG, Liangliang ZHANG, Yuxuan WANG, Jinming ZHANG, Han ZHANG, Yang GAO. Static response of functionally graded multilayered two-dimensional quasicrystal plates with mixed boundary conditions[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(11): 1599-1618.
[10]	S. ZGHAL, A. FRIKHA, F. DAMMAK. Large deflection response-based geometrical nonlinearity of nanocomposite structures reinforced with carbon nanotubes[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(8): 1227-1250.
[11]	Yuan YUAN, Ke ZHAO, S. SAHMANI, B. SAFAEI. Size-dependent shear buckling response of FGM skew nanoplates modeled via different homogenization schemes[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(4): 587-604.
[12]	M. ESMAEILZADEH, M. KADKHODAYAN, S. MOHAMMADI, G. J. TURVEY. Nonlinear dynamic analysis of moving bilayer plates resting on elastic foundations[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(3): 439-458.
[13]	N. V. VIET, W. ZAKI, Quan WANG. Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(12): 1787-1804.
[14]	S. MONDAL, S. A. SAHU, K. K. PANKAJ. Transference of Love-type waves in a bedded structure containing a functionally graded material and a porous piezoelectric medium[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(8): 1083-1096.
[15]	Yuda HU, Bingbing MA. Magnetoelastic combined resonance and stability analysis of a ferromagnetic circular plate in alternating magnetic field[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(7): 925-942.