导电圆柱薄壳的热磁弹性效应分析

研究了磁场环境中受机械载荷作用的导电圆柱薄壳的热磁弹性问题．首先，根据电动力学方程和广义Ohm定律，得到了导电薄壳电流密度的分布，考虑到Joule热效应及热平衡方程，得到了导电薄壳的温度分布．其次，通过几何方程、物理方程、运动方程和电动力学方程导出了导电薄壳在机械场、电磁场以及温度场作用下的基本方程．最后，采用差分法及准线性化方法，得到了可以应用离散正交法求解的准线性微分方程组．对于导电圆柱薄壳，得到了Lorentz力表达式，并且推导了温度场积分特征值．讨论了导电圆柱薄壳应力、温度及变形随外加电磁参量的变化规律，并通过实例证实了可以通过改变电、磁、力场的参数来实现对薄壳的应力、应变、温度的控制．

Thermal-Magnetic-Elastic Effect Analysis of a Thin Conductive Cylindrical Shell

The thermal-magnetic-elastic problem of a thin conductive cylindrical shell subjected to mechanical loadings in a magnetic field was studied. First, based on the electrodynamic equations and the generalized Ohm’s law, the distribution of electric current density in a thin conductive shell was obtained. The temperature distribution in a thin conductive shell was obtained after considering Joule’s heat effect and the thermal equilibrium equation. Secondly, based on the geometric equations, physical equations, kinetic equations, and electrodynamic equations, the fundamental equations were derived for a thin conductive shell under the interactions of a mechanical field, an electromagnetic field, and a temperature field. Finally, using the difference and the quasi-linearization methods, the quasi-linear differential equations were obtained; which can be solved by the discrete orthogonalization method. The expressions of Lorentz force were obtained and the eigenvalues of the temperature field integral were derived. The law of the change of the stresses, temperatures, and deformations in the thin conductive cylindrical shell with variation of the electromagnetic parameters are discussed. It was proved by considering a specific example that the stresses, strains, and temperatures in thin shells can be controlled by changing the electromagnetic and mechanical parameters.