载流悬臂柱壳的非线性数值分析

针对在电磁场和机械场耦合作用下的载流柱壳的非线性变形问题的数值解法进行了研究。给出了载流柱壳在耦合场作用下的几何方程、物理方程、二维电动力学方程、磁弹性非线性运动方程和洛仑兹力表达式,建立了差分格式和线性化迭代方程,给出了这些方程的数值解系统,并以悬臂柱壳为例,计算了该壳在电磁场和机械载荷耦合作用下的应力及变形;讨论了其应力及变形与外加电磁参量之间的关系;证明了变化电磁参量可以对壳的工作状态实施控制。

NONLINEAR NUMERICAL ANALYSIS OF CURRENT-CARRYING CANTILEVER COLUMNAR SHELLS

The numerical method for nonlinear deformation problems of current-carrying columnar shell under the coupled action of electromagnetic field and mechanical field are studied. The geometric equations, the physical equations, the two-dimensional electrodynamics equations, the nonlinear magneto-elastic kinetic equations and the expressions of Lorentz force of current-carrying columnar shell under the coupled action of the two fields are given. The corresponding finite difference form and linearized iteration equations are developed, the numerical solutions of which are obtained. A cantilever columnar shell is used as an example to analyze the stresses and deformations under the coupled action of the electromagnetic field and mechanical load. The relations between the stresses, the deformations and the applied electromagnetic parameters are discussed. The results show that the working conditions of the shells can be controlled by changing the electromagnetic parameters.