The refined theory for a magnetoelastic body – II. Plane problems

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.

The refined theory for a magnetoelastic body–I. plate problems

“…The plane problems will be discussed in a companion paper [27]. In the case of the bending of a plate, the plate is subjected only to anti-symmetrical loadings, the perturbation of magnetic intensity and edge conditions, thus only odd functions of z are required for u x and u y , and even functions of z for u z .…”

The Refined Equations of Special Orthotropic Piezoelectric Plate-II: Symmetrical Transverse Surface Loadings

“…Base on the refined theory of generalized plane problem with transversely isotropic, the refined theory of deep rectangular beams for symmetrical deformation [4], the refined theory for a magnetoelastic plane problem [5], and the refined theory of plane problems for one-dimensional quasicrystalline bodies [6] was studied.…”