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

本课题从理论上研究了均匀磁场作用下结构构件的热弹性行为，讨论了热弹性场和磁场对结构构件变形和应力的耦合效应。在解析模型中，我们考虑磁场作用下的平板，磁场作用方向与平板纵向方向平行，磁场作用方向与圆柱体轴线平行或垂直，磁场作用方向均匀分布。我们假设这些模型突然被周围的介质加热。现在，我们假定平板和圆柱体的材料性质由铁磁性材料和顺磁性材料组成。在分析发展中，考虑了温度场与弹性场之间的耦合项，但由于对弹性场的影响不显著，忽略了惯性项。在考虑均匀分布磁场变化的情况下，对几种情况进行了数值计算，所得结果总结如下：对于非铁磁性（顺磁性）材料，由于热变形引起的磁场扰动对应力分布的影响，以及磁场作用下的麦克斯韦应力分布可以明显看到。此外，对于铁磁性材料而言，与上述应力一致的感应磁化对顺磁性材料的磁感应应力更为明显。从圆柱体的数值结果可以看出，当磁场与圆柱体轴线平行作用时，其弹性行为保持轴对称，而当磁场与圆柱体轴线垂直作用时，其弹性变形变为非轴对称变形。对于磁场对应力分布的影响，发现当均匀分布的磁场为1特斯拉时，磁致应力分布与热弹性应力相比不显著。然而，当磁场作用更强时，如100或1000特斯拉，与热弹性应力相比，磁诱导应力明显出现。少

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