Three-dimensional analysis of a magnetoelectroelastic half-space under axisymmetric temperature loading

Considering the coupling effects between mechanical, electrical, magnetic and thermal fields, we have presented an analytical solution for the thermo-magneto-electro-elastic problem of a magnetoelectroelastic half-space under axisymmetric thermal loading based on the linear theory. Integral transform method and integral equation technique are applied to analytically solve the heat conduction equation, the governing equations of the magnetoelectroelastic material, and the mixed boundary value problem on the boundary of the magnetoelectroelastic half-space. A general closed-form solution is presented for the complementary and particular parts of the components of the displacement, electric potential and magnetic potential. Traction-free and open circuit electro-magnetic conditions are applied on the boundary surface and an integral form solution for the displacement, electric and magnetic potentials in the magnetoelectroelastic half-space has been successfully obtained. Temperature field in the half-space has been obtained analytically and the expression of the stresses, electric displacements and magnetic induction due to the temperature change applied on the surface are derived and given in an explicit closed form. Numerical results show that the temperature loading has much effect on the field distribution of the mechanical, electric and magnetic fields in the magnetoelectroelastic half-space. As the radius of the constant temperature loading increases, the distance from the region of the maximum normal stress to the free boundary will become larger, and the normal stress becomes much smaller in the regions outside of the circular region. The maximum shear stress appears just below the boundary surface at the edge of the circular region. The electric field is found to be intensified near to the boundary surface within the circular region, and similarly, intensities of the positive and negative magnetic fields are observed at different locations in the half-space under the temperature loading applied on the boundary. The results of this study are helpful for the design and manufacturing of smart materials/structures under thermal loading. © 2020, Chinese Journal of Theoretical and Applied Mechanics Press. All right reserved.