【作者】 张晓宏；

【导师】 邢誉峰；

【作者基本信息】 北京航空航天大学 ， 固体力学， 2011， 硕士

【摘要】 电磁-热-弹性理论专门研究电磁场、热场与弹性场之间的耦合,即研究电磁场、热场和弹性场的相互作用。电磁场对变形场的作用是由运动方程中的洛仑兹力引起。弹性场会影响磁场的强度、磁弹性波和电磁波的传播速度与相位,具体表现在欧姆定律中多了电流密度增长项,而且该项取决于变形物体在磁场中的速度。变化的电磁场在导体中产生涡流,激发热场作用于介质,产生热应力。热作用于介质又影响变形,弹性场对热场的影响主要表现在热传导方程中多出了应变率项。本文致力于研究任意时变电磁场作用下的环状柱体的电磁-热-力耦合问题,其力学模型为圆板,分别研究了强耦合和弱耦合两种情况,但不考虑弹性场对温度场的影响。给出了电磁场、热场和弹性场的基本方程,采用高精度和高效的微分求积方法求解了在任意时变磁场作用下的环状圆柱的热磁弹性应力。计算时采用微分求积方法在时间和空间域离散基本微分方程和时变边界条件,在整个时间、空间域求解同时满足微分方程组、边界条件及初始条件的未知量。微分求积方法的效率很高,在时间和空间域只需很少数目的结点就可得到很高精度的结果。以图示的形式给出了磁场、温度变化和应力与位移,还给出了两种耦合情况结果的比较。更多还原

【Abstract】 Magneto-thermo-elasticity is a special subject, in which we investigate the interaction among the strain, electromagnetic fields and temperature fields. The influence of the electromagnetic field on the strain occurs by means of Lorentz forces appearing in the equations of motion. The Ohm law contains a term describing the increment of density of the electric field developing on the velocity of the material particles moving in the magnetic field. The arbitrary variation of magnetic field can generate eddy current in the media. The eddy current heats the body, which generates thermo stress. The influence of the strain on the temperature field occurs by means of a term containing strain rate appearing in the heat conduction function.The article aims at the analysis of the coupling problem in a conducting hollow circular cylinder subjected to an arbitrary variation of magnetic field. The model is assumed as a circular plate, and the coupling problem will be discussed in two ways, with and without the coupling term which shows the interact between strain and electromagnetic field, but the influence strain rate to thermal field is not considered. The fundamental equation of electromagnetic field, temperature field and elastic field are formulated. An accurate and efficient differential quadrature method is employed for numerical simulation of magneto-thermo-elastic stresses in a conducting hollow circular cylinder subjected to an arbitrary variation of magnetic field. The fundamental equations and both boundary conditions and initial conditions are discretized in spatial and temporal domain by differential quadrature rules. The unknown variables satisfy the governing equations, the boundary conditions and the initial conditions simultaneously, and they are computed in entire domain by means of DQM. Accurate solutions can be obtained by using less grid points in both spatial and time domain. Solutions of magnetic field, temperature field and stresses and deformation are illustrated graphically. The comparison between two kinds of calculated results is also illustrated graphically and analyzed theoretically.更多还原