Affiliations: [a] College of Science, China Agricultural University,
P.O. Box 74, Beijing 100083, P.R. China | [b] School of Mechanical Engineering, University of
Science and Technology Liaoning, Anshan, 114044, P.R. China
Abstract: The problem of deducing two-dimensional theory from
three-dimensional theory for a soft ferromagnetic elastic isotropic body is
investigated. By using the general solution for the soft ferromagnetic elastic
solids and Lur'e method, it is shown that the general deformation can be
decomposed into two independent parts: the asymmetric deformations (plate
problems) and the symmetric part (plane problems). A refined plate theory which
takes into account the transverse shear deformation can now be explicitly
established without employing assumptions. The exact equations and solutions
for the plate with homogeneous boundary conditions are derived, and the
equations can be decomposed into four governing differential equations.
Moreover, the approximate equations and solutions for the plate under
transverse loadings and magnetic field perturbations are derived directly from
the refined plate theory. By omitting higher order terms and coupling effect,
the refined plate theory can be degenerated into other well-known elastic and
magnetoelastic theoretical models.
Keywords: Rectangular plates, the refined theory, magnetoelastic body, governing equation
