Theoretical Analysis of Transient Thermoelastic Problem of Solid Structure due to the Coupling Effects of Magnetic Field and Unsteady Temperature Change

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In this research project, the thermoelastic behaviors for structural elements subject to the uniformly distributed magnetic field are treated theoretically, and the coupling effects of thermoelastic field and magnetic field on the deformation and stresses are discussed. As for the analytical models, we considered a plate subject to the action of the magnetic field, which is uniformly distributed in the parallel direction with the longitudinal one of the plate, furthermore, a solid cylinder subject to the actions of the magnetic field uniformly distributed in the parallel or the perpendicular direction of the axis of the cylinder. And we assumed that these models are suddenly heated from the surrounding medium. We now supposed that the material property of the plate and the cylinder are composed of ferromagnetic material and paramagnetic one. For the analytical developments, the coupling term between the temperature field and the elastic field is considered, however, the inertia term of … More the elastic field is neglected because the effect is insignificant. We have carried out the numerical calculations for several cases taking into account the variations of uniformly distributed magnetic field, and the results obtained from the numerical data are summarized as follows.1. For the non-ferromagnetic (paramagnetic) materials, the influences of the disturbance of the magnetic field due to the thermal deformation affected on the stress distribution, and the Maxwell stress distribution due to the action of the magnetic field can be seen significantly. Moreover, for the ferromagnetic materials, the magnetically induced stresses due to the induced magnetization in accordance with the above-mentioned stresses for the paramagnetic materials can be seen more significantly.2. It can be seen, from the numerical results of the cylinder, that the elastic behavior maintain axisymmetrically when the magnetic field is acted in the parallel direction with the axis of the cylinder, however, the deformation is changed into the non-axisymmetrical one when the magnetic field is acted perpendicularly with the axis of the cylinder.3. As for the effect of the magnetic field on the stress distribution, it is found that the magnetically induced stress distribution is insignificant compared with the thermoelastic stresses when the uniformly distributed magnetic field is 1 tesla. However, when the magnetic field acts more strongly such as 100 or 1000 tesla, the magnetically induced stresses are significantly appeared in comparison with the thermoelastic stresses. Less