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Article type: Research Article
Authors: Gao, Yanga; b; * | Xu, Bai-Xiangc
Affiliations: [a] College of Science, China Agricultural University, P.O. Box 74, Beijing 100083, P.R. China | [b] Institute of Mechanics, Department of Mechanical Engineering, University of Kassel, Moenchebergstrasse 7, D-34125 Kassel, Germany | [c] State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Aerospace Engineering, Peking University, Beijing 100871, P.R. China
Correspondence: [*] Corresponding author. E-mail: gaoyangg@gmail.com
Abstract: Without employing ad hoc stress or deformation assumptions, various two-dimensional equations and solutions for plane problems have been deduced systematically and directly from thick plate theory by using the general solution of magnetoelastic theory for the soft ferromagnetic elastic solids and the Lur'e method. These equations and solutions are used to construct the refined theory for the plane problems. In the case of homogeneous boundary conditions, the exact governing differential equations and solutions for the plate are derived, which consist of four governing differential equations. It can be noted that the refined theory is consistent with the decomposition theorem by Gregory. In the case of nonhomogeneous boundary conditions, the approximate governing differential equations and solutions for the plate are accurate up to the second-order terms. The correctness of the stress assumptions in the classic plane stress problems is revised. In two illustrative examples of plates, it is shown that the exact or accurate solutions can be obtained in use of the refined theory deduced herein.
Keywords: Plane problems, plates, the refined theory, magnetoelastic, governing equations
DOI: 10.3233/JAE-2010-1064
Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 32, no. 1, pp. 31-46, 2010
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