基于热-磁-弹性耦合的二维导电薄柱壳数值分析

Numerical Analysis of a Two-Dimensional Thin Conductive Cylindrical Shell Based on Thermo-Magneto-Elastic Coupling

基于几何方程、物理方程、运动方程和电动力学方程,建立了二维导电薄柱壳热磁弹性基本方程.考虑到Joule热效应,引入热平衡方程及广义Ohm定律,得出导电薄柱壳的温度场.利用变量代换方法,整理成具有10个基本未知量的标准型方程组.采用差分法和准线性化方法,给出准线性微分方程组.对于二维导电薄柱壳,导出了Lorentz力表达式、温度场积分特征值.通过实例计算,得到了二维导电薄柱壳应力、位移、温度随外加电磁参量的变化规律.研究结果可为二维导电薄壳热磁弹性问题研究提供理论参考.

Based on the geometric equations, the physical equations, the kinetic equations, and the electrodynamics equations, the thermo-magneto-elastic fundamental equations for the two-dimensional thin conductive cylindrical shell were established. The temperature field in a thin conductive cylindrical shell was given after considering the Joule’s heat effect in an electromagnetic field and introducing the thermal equilibrium equation and the generalized Ohm’s law. The standard equations in terms of ten basic unknown variables were obtained by the variable replacement method. Using the difference method and the quasi-linearization methods, the quasi-linear differential equations were given. For the two-dimensional thin conductive cylindrical shell, the expressions for the Lorentz force and the integral eigenvalues of the temperature field were derived. The variation rules of stresses, displacements, and temperatures in the thin conductive cylindrical shell with the electromagnetic parameters were obtained through the example calculation. The results presented here are expected to provide a theoretical reference for the two-dimensional thermo-magneto-elastic analysis of a thin conductive shell.