An element free Galerkin method for static behavior of a magneto-electro-elastic beam in thermal environments

Abstract

In this article, an element free Galerkin method (EFGM) has been used for the static analysis of a magneto-electro-elastic (MEE) beam in thermal environments. The influence of pyro effects (pyroelectric and pyromagnetic) on the physical characteristics (displacements and the potentials) of the MEE beam under plane strain conditions in various thermal conditions are studied. The system governing equations of MEE structures are derived from the Hamilton principle and constitutive equations of linear coupling between elastic, electric, magnetic and thermal properties of MEE materials. In EFGM, the moving least squares (MLS) method is utilized to generate shape functions. Since it does not satisfy the principle of Kronecker delta, the penalty method is implemented to impose approximate boundary conditions. The result is verified and applied to reveal the effects of thermo-magnetic and thermo-electric coupling by MEE column. Further, a comparative study is made to evaluate the variations of physical characteristics along the longitudinal direction of the MEE beam in different thermal environments. Numerical results demonstrate the efficiency and accuracy of the EFG formulation to multi-physics simulation of MEE structures in thermal environments.