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SOLUTION OF BOUNDARY INTEGRAL EQUATIONS FOR EDDY CURRENT NONDESTRUCTIVE EVALUATION IN THREE DIMENSIONS

机译:三维涡流非破坏性评价的边界积分方程解

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摘要

Eddy current nondestructive evaluation (NDE) of airframe structures involves the detection of electromagnetic field irregularities due to non‐conducting inhomogeneities in an electrically conducting material, which often treats with complicated geometrical features such as cracks, fasteners, sharp corners∕edges, multi‐layered structures, etc. The eddy‐current problem can be formulated by the boundary integral equations (BIE) and discretized into matrix equations by the method of moments (MoM) or the boundary element method (BEM). This paper introduces the implementation of Stratton‐Chu formulation for the conductive medium, in which the induced electric and magnetic surface currents are expanded in terms of Rao‐Wilton‐Glisson (RWG) vector basis function and the normal component of magnetic field is expanded in terms of pulse basis function. Also, a low frequency approximation is applied in the external medium, that is, free space in our case. Computational tests are presented to demonstrate the accuracy and capability of the BIE method with a complex wave number for three‐dimensional objects described by a number of triangular patches. This work prepares the BIE solution procedure that will be embedded with the Fast Multipole Method (FMM), which is a well‐established and effective method for accelerating numerical solutions of the matrix equations. When accelerated by the FMM, the BIE method will have the capability of solving large‐scale electromagnetic wave propagation and eddy‐current problems.
机译:飞机结构的涡流无损评估(NDE)涉及检测由于导电材料中的非导电不均匀性而引起的电磁场不规则性,这种不规则性通常具有复杂的几何特征,例如裂缝,紧固件,尖角∕边,多层涡流问题可以由边界积分方程(BIE)表示,并可以通过矩量法(MoM)或边界元方法(BEM)离散为矩阵方程。本文介绍了用于导电介质的Stratton-Chu公式的实现,其中感应电流和磁表面电流根据Rao-Wilton-Glisson(RWG)矢量基函数进行扩展,而磁场的法向分量在脉冲基函数另外,低频近似应用于外部介质,即本例中的自由空间。提出了计算测试来证明BIE方法的精度和能力,该方法对于由多个三角形斑块描述的三维物体具有复杂的波数。这项工作准备了将被嵌入到快速多极子方法(FMM)中的BIE解算程序,该方法是一种公认​​的有效方法,可用于加速矩阵方程的数值解。当通过FMM加速时,BIE方法将具有解决大规模电磁波传播和涡流问题的能力。

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