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力学与实践 ›› 2006, Vol. 28 ›› Issue (6): 0-0.doi: 10.6052/1000-0992-2006-142

• 应用研究 •    

导电薄板内电流密度分布与反平面剪切的比拟

金晓清 李辉   

  1. 美国西北大学土木工程系 中科院力学所工程科学部
  • 收稿日期:2006-04-05 修回日期:2006-07-28 出版日期:2006-12-10 发布日期:2006-12-10

ON THE ANALOGY BETWEEN THE CURRENT DENSITY DISTRIBUTION IN A THIN CONDUCTIVE PLATE AND THE ANTI-PLANE SHEAR PROBLEM

  • Received:2006-04-05 Revised:2006-07-28 Online:2006-12-10 Published:2006-12-10

摘要: 定量分析电流密度在含裂纹载流薄板内的分布是当前利用电流热效应止裂技术中一个 首先要解决的问题. 由于裂纹的存在,电流密度在裂尖形成带奇异性分布的高度密集. 现有 的分析方法往往比较复杂或局限于特殊布置形式的裂纹. 通过电流密度分布与弹性力学 里反平面剪切问题的比拟,把分析含裂纹载流薄板内电流密度的分布等效于考虑相应的III 型裂纹问题,并比照III型裂纹的应力强度因子来定义电流密度因子. 而对于裂纹问题的处 理可采用分布位错法这一断裂力学里便利有效的分析手段. 由给出的算例可见,所提出 的比拟解法可以方便精确地求解电流密度在裂尖附近的奇异分布,并有助于对这一奇异性在概 念上的直观理解.

关键词: 电流密度因子,III型裂纹, 反平面剪切, 分布位错法

Abstract: 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.

Key words: current density factor, mode III crack, anti-plane