混合支撑载流条形薄板的非线性力学分析

在给出耦合场作用下载流条形薄板的磁弹性非线性运动方程、几何方程、物理方程和电动力学方程的基础上，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；并通过差分法和准线性化方法，将标准柯西型的非线性偏微分方程组，变换成为能够用离散正交法编程求解的准线性微分方程组。通过具体算例，得到了固定简支混合支撑载流条形薄板的磁弹性麻力与变形的数值解。变换电磁参量讨论了固定简支混合支撑载流条形薄板的麻力及变形的变化规律，通过实例说明了通过变化电磁参量可实现对条形板的变形控制。

Nonlinear mechanics analysis of thin current-carrying strip-plates with mixed supports

In this paper, the nonlinear magneto-elastic kinetic equations, the geometric equations, the physical equations and the electrodynamics equations of thin current-carrying strip-plate under the action of the coupled field are given, and the normal Cauchy form nonlinear differential equations, which includes ten basic unknown functions in all, were obtained by means of variable replacement method. Using the difference method and quasi-linearization method, the nonlinear magneto-elastic equations were reduced to a sequence of quasi-linear differential equations, which can be solved by the method of discrete orthogonalization. Through specific example, the numerical solutions of the stresses and deformations in the thin current-carrying strip-plate mixed with fixed and simply supported edges were obtained. The results that the stresses and deformations of the thin current-carrying strip-plate mixed with fixed and simply supported edges are altered with the variation of the electromagnetic parameters were discussed. Through a special case, it is shown that the deformations of the strip-plate can be controlled by changing the electromagnetic parameters.