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边界元法计算近边界点参量的一个通用算法
引用本文:牛忠荣,王秀喜,周焕林.边界元法计算近边界点参量的一个通用算法[J].力学学报,2001,33(2):275-283.
作者姓名:牛忠荣  王秀喜  周焕林
作者单位:1. 中国科技大学力学系,
2. 合肥工业大学力学所,
基金项目:国家自然科学基金!(19572060),机械工业部科学基金资助项目
摘    要:针对边界元法存在近力界点参量计算的困难,给出了一个通用性方法,将近边界点到边界单元的距离参数通过分部积分变换到积分式之外,从而计算出二维问题近边界点参量的几乎强奇异和超奇异积分,由此,对任何近边界点参量,提出了整套计算方案,算例证明了本法的有效性。

关 键 词:边界元法  奇异积分  近力界点  弹性力学
修稿时间:1998年12月20

A GERNERAL ALGORITHM FOR CALCULATING THE QUANTITIES AT INTERIOR POINTS CLOSE TO THE BOUNDARY BY THE BEM
Niu Zhongrong,Wang Xiuxi,Zhou Huanlin.A GERNERAL ALGORITHM FOR CALCULATING THE QUANTITIES AT INTERIOR POINTS CLOSE TO THE BOUNDARY BY THE BEM[J].chinese journal of theoretical and applied mechanics,2001,33(2):275-283.
Authors:Niu Zhongrong  Wang Xiuxi  Zhou Huanlin
Abstract:This paper gives a general algorithm to deal with the difficult problem of calculating the quantities at interior points very close to the boundary by the boundary element method. In the algorithm, which is applied to solving two dimensional problems, the least distance from the source point to near boundary element is transformed out of the integral representations of the element with an integration by parts. The nearly singular integrals at any interior point close to the boundary are converted the sum of analytical parts and non-singular integrals, so that the nearly strongly singular and nearly hypersingular integrals are successfully computed, occurring in the boundary integral equations. Based on the present method we develop a series of implement steps. for calculating the nearly singular integrals at any interior point. It is used to analyze the twodimensional elasticity problems. Some examples demonstrate the effectiveness of the algorithm. The technique can be applied to evaluation of the nearly singular integral occurring in the BIEs of plate and shell bending problems.
Keywords:BEM  nearly singular integrals  interior points close to the boundary  mechanics of elasticity
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