【摘 要】
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This study presents an improved sinh transformation for numerical evaluation of nearly singular 2D integrals over the eight-node second-order quadrilateral
【出 处】
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第五届亚太国际工程中计算方法学术会议暨第11届全国工程计算方法学术会议
论文部分内容阅读
This study presents an improved sinh transformation for numerical evaluation of nearly singular 2D integrals over the eight-node second-order quadrilateral geometry elements arising in 3D BEM.Other than the previous sinh transformation techniques,in which the projection point is defined in a rigorous way,namely,the line consisting of the evaluation point and the projection point must be perpendicular to the tangential plane through the projection point,named the conventional projection point(CPP),for curved surface elements,the new scheme introduces the notion of the generalized projection point(GPP)by defining it as being the nearest to the evaluation point for all the points on the integration element.Based on this,for the computational modelling,an exact formula of distance is proposed,in which the exact means that this formula is equal to the actual distance,r,between the source and the field point instead of an approximation of r.And then an extended form of the sinh transformation is developed to smooth out the rapid variation of the distance function on the integration interval.
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