载流条形悬臂薄板的非线性磁弹性分析

该文在给出载流薄板在耦合场作用下的磁弹性非线性运动方程、电动力学方程和洛仑兹力表达式的基础上,通过变量代换将描述载流薄板的磁弹性状态方程整理成含有10个基本未知函数的标准柯西(Cauchy)型.并通过差分法及准线性化方法,将标准柯西型的非线性偏微分方程组,变换成为能够用正交离散法编程求解的准线性微分方程组,给出了这些方程的数值解系统.应用该法计算了条形悬臂薄板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.

Nonlinear Magnetoelastic Analysis of Thin Current-carrying Cantilever Strip-plates

The nonlinear magnetoelastic kinetic equations, the electrodynamics equations and the expressions of Lorentz force of thin current-carrying plate under the action of the coupled field are given. The normal Cauchy form nonlinear differential equations, which include ten basic unknown functions in all, are obtained by means of variable replacement. Using the difference method and quasi-linearization method, the nonlinear magnetoelastic equations are reduced to a sequence of quasi-linear differential equations, which can be solved by the method of orthogonalization discrete, and the numerical solutions of these equations are obtained. The stresses and deformations of thin cantilever strip-plate under the coupled action of the electromagnetic field and mechanical load are calculated; the relations between the stresses, the deformations and the applied electromagnetic parameters are discussed.