The refined theory of magnetoelastic beams for tension and compression deformation

Abstract

Without employing ad hoc assumptions, various equations and solutions for magnetoelastic beams are deduced systematically and directly from the two-dimensional magnetoelasticity. These equations and solutions can be used to construct the refined theory of magnetoelastic beams for tension and compression deformation. By using the general solution for the soft ferromagnetic elastic solids and the Lur'e method, the refined theory can now be explicitly established. In the case of homogeneous boundary conditions, the exact governing differential equations and solutions for beams are derived, which consist of three governing differential equations. In the case of non-homogeneous boundary conditions, a traction free boundary condition is considered. In two illustrative examples of beams, it is shown that the exact or accurate solutions can be obtained in use of the refined theory deduced herein.