ON THE ANALOGY BETWEEN THE CURRENT DENSITY DISTRIBUTION IN A THIN CONDUCTIVE PLATE AND THE ANTI-PLANE SHEAR PROBLEM
导电薄板内电流密度分布与反平面剪切的比拟

Qualitative analysis of current density distribution in a thin conductive plate containing cracks is the first problem to be solved for the crack-preventing technology based on the electromagnetic heating effect. To investigate the singular distribution of the current density at the crack tips, most of the existing solutions are complicated or are only valid for a specific arrangement of the cracks. In this paper it is found that there exists a close analogy between the current density distribution and the anti-plane shear problem. Hence the solution to the current density distribution in a cracked conductive plate can be deduced by considering a corresponding mode III crack problem. The current density factor is defined in a similar way as the stress intensity factor, as its counterpart in the mode III crack problem. The consequent crack problem can be solved efficiently by the distributed dislocation technique, which is a widely applied tool in fracture mechanics. A numerical example is provided to demonstrate that the proposed numerical method is convenient and accurate and also helps to the understanding of the singularity of the current density distribution at the crack tip.