求解二维磁弹性问题的一种数值方法——差分正交离散(DOD)法

Difference orthogonal discrete method:a new numerical method solving two-dimensional magneto-elastic problem

通过运动方程、物理方程、几何方程及电动力学方程给出了载流薄板在机械场、电磁场作用下的基本方程,以二维平板磁弹性问题为例,建立差分格式,得到了一系列的非线性常微分方程组。利用准线性叠代式对非线性微分方程组进行线性化处理,最后利用正交离散法得到了该问题的解。本文建立的载流板壳二维磁弹性问题的数值计算方法——差分正交离散法(DOD法)不仅对二维问题有效,同样也为三维磁弹性的边值问题的解决奠定了理论基础。

In this paper, based on the equation ofmotion, physicalequation, geometric equation and electrical dynamics, thefundamental equations of current-carrying thin plate located in the mechanical and electromagnetic fields are given. As example, the difference scheme is built in the two-dimensional plate, and a series of nonlinear ordinary differential equations are obtained. The nonlinear equations are dealt by the quasi linear iteration equation, at last, by the orthogonal discrete method, the solutions of the initial problem are obtained. The two-dimension magneto-elastic problem is solved by this method, it is presented that the difference orthogonal discrete method, which is a numerical method for solving the two-dimensional magneto-elastic problem in the current carrying plate. The method can not only be effect on the two-dimensional problem, but also build the basis of solving the three-dimensional boundary problem.