Static studies of stepped functionally graded magneto-electro-elastic beam subjected to different thermal loads

In this article, a three dimensional finite element (FE) formulation for a multilayered magneto-electro-elastic (MEE) beam in thermal environment is presented. The equilibrium equations of the system are attained using the principle of total potential energy and linear coupled constitutive equations of MEE material. The corresponding FE equations are derived and the numerical evaluation of stepped functionally graded (SFG) MEE beam is carried out. The influence of various in-plane and through thickness temperature distributions on the direct quantities (displacements and potentials) and derived quantities (stresses, electric displacement and magnetic flux density), across the thickness of SFG-MEE cantilever beam is analyzed. In addition, an attempt has been made to investigate the effect of stacking sequence, thermo-magnetic and thermo-electric coupling on the direct quantities of the SFG-MEE beam. Further, a comparative study is made to evaluate the variations of displacements, potentials, electric displacements, magnetic flux density and stresses at different regions of the beam. It is expected that the results presented in this article may be useful in the design and analysis of MEE smart structures and sensor applications.