Increasing attention is being devoted to the interaction between magnetic fields, strain and temperature in a thermoelastic solid due to its many applications in the fields of magnetic storage elements, magnetic structural elements, geophysical physics, plasma physics, space shuttles, supersonic airplanes, rockets and missiles, the corresponding measurement techniques of magnetoelasticity, geophysics and related topics. The theory of magnetothermoelasticity is concerned with the interacting effects of the applied magnetic field on the elastic and thermoelastic deformations of a solid body. Also functionally graded materials (FGMs) are advanced composites, microscopically engineered to have a smooth spatial variation of material properties in order to improve overall performance. This is achieved by fabricating the composite material to have a gradual spatial variation in the constituent materials relative volume fractions and microstructure.These materials usually are used in the fields that need to good mechanical and thermal properties.Therefore these materials usually are used in the structures that are subjected to the magnetothermoelastic loads. In this thesis, the magneto–thermo–elastic analysis of a functionally graded hollow sphere is done. The sphere's material is assumed to be described with an power function of the radial.The governing magneto–thermo–elastic equation decomposed into a quasi-static homogeneous equation with inhomogeneous boundary conditions and an inhomogeneous dynamic equation with homogeneous boundary conditions. Firstly, the quasi-static equation is solved by the direct integral. Secondly, the solution to the inhomogeneous dynamic equation which satisfies homogeneous boundary conditions is obtained by utilizing the corresponding Hankel and Laplace transforms and their inverse transforms. Thus, the exact expressions for the transient responses of stresses and perturbation of magnetic field vector in the functionally graded hollow sphere are obtained. Finally, numerical examples are calculated and discussed.
