对能够求解一系列线性常微分方程组边值问题的数值计算方法——离散正交法(DOM)进行了离散点的正交分析，给出了计算机实现数值计算的程序设计原理与计算流程图，指出了该方法能够克服传统计算方法由于所求函数的快速增长所引起的边界效应和局部效应的缺点，给出了得到稳定计算过程的可能性。为了推广应用，文中介绍了离散正交法的基本原理、实现方法和求解过程，讨论了采用离散正交法来求解非线性问题的处理方法。并且以承受均布载荷的环形板为例，将采用离散正交法的计算结果与经典解作了对比。

Heating by an electromagnetic field is an effective method for stopping internal crack propagation in metal components, thus extending their service life by improving safety and reliability. Theoretical calculations, numerical simulation and experimental surveys show that a small spherical crater can be formed near the crack tip using a concentrated current which melts metal at the desired point. Experiments also show that the sharp point around the crack tip is rounded, which decreases the stress concentration and forms a compressive stress area, and also prevents the main crack from propagating further. At the same time, a white-bright layer is formed around the crack tip under the influence of a precipitous temperature gradient. The white-bright layer is so hard and tough that it prevents crack propagation. The present study of this physical phenomenon, its further development and the prospect of its application in the near future are described in this paper.

The electromagnetic field and temperature field around the tip of a finite crack in an infinite thin current-carrying plate under the repeated action of a pulse current is presented. The formula for calculating the temperature of the crack tip is also suggested and some examples for numerical calculation are enumerated. These examples show that if the intensity and times of the pulse current are properly adjusted, the crack tip could be melted and the welded joints be formed, and therefore the propagation of the crack would be prevented.

Heating by an electromagnetic field is an effective method for stopping internal crack propagation in metal components, thus extending their service life by improving safety and reliability. Experimental surveys show that a small spherical crater can be formed near the crack tip using a concentrated current which melts metal at the desired point. Experiments also show that the sharp point around the crack tip is rounded, which decreases the stress concentration and forms a compressive stress area. The structure around the crack tip is refined obviously. At the same time, a white-bright layer is formed around the crack tip under the influence of a precipitous temperature gradient. Thermal compressive stresses and phase transformation stresses, together with the influence of a super-fine microstructure, promote the ability of metals to withstand intense wear. From the experiments we also find many factors have an effect on the efficiency of crack arresting.

研究了在带有有限长裂纹的无限大导电薄板中，垂直裂纹通入阶跃递增电流的情况下，裂纹尖端处的电磁场和温度场，给出了裂纹尖端温度的计算方法和算例。指出适当调整阶跃电流的变化值和阶跃次数，可使裂纹尖端处熔化形成焊点，从而遏制了裂纹的扩展。