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
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
