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

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Abstract

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 magneto-electro-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.

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Authors and Affiliations

  1. Department of Engineering Mechanics, Zhejiang University, Hangzhou, 310027, China

    Yanzheng Wang & Weiqiu Chen

  2. State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou, 310058, China

    Weiqiu Chen

  3. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Xiangyu Li

Authors
  1. Yanzheng Wang
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  2. Weiqiu Chen
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  3. Xiangyu Li
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Corresponding author

Correspondence to Xiangyu Li.

Additional information

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)

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Wang, Y., Chen, W. & Li, X. Statics of FGM circular plate with magneto-electro-elastic coupling: axisymmetric solutions and their relations with those for corresponding rectangular beam. Appl. Math. Mech.-Engl. Ed. 36, 581–598 (2015). https://doi.org/10.1007/s10483-015-1934-7

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  • DOI: https://doi.org/10.1007/s10483-015-1934-7

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2010 Mathematics Subject Classification

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