Min(max)imization of horizontal and vertical displacements of a fibre‐reinforced magneto‐elastic cantilever rod

Abstract

In this brief note we suggest a procedure for extremization of horizontal and vertical displacements of a nonlinear fibre‐reinforced magneto‐elastic rod subjected to an oblique magnetic field and a concentrated load applied at the rod end‐point. The control parameter is the angle formed by the magnetic field and the rod axis. The governing equation is nonlinear in both the unknown function and in the control parameter. The exact (implicit) solution of the governing equation is obtained. Moreover, we apply the Bubnov‐Galerkin procedure and the Newton‐Raphson iterative method to obtain an approximate solution to the problem. Numerical analysis of the approximate solution allows to study the influence of the magnetic field and concentrated force on the rod displacement field.