边界积分方程中近边界点几乎奇异积分的计算

The calculation of nearly singular integrals about points close to boundary in boundary integral equation

:该文针对边界元法存在近边界点力学量计算的困难 ,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。该法同样适用于板壳问题的边界元法 ,尤其是对于将超奇异边界积分方程正则化为强奇异边界积分方程的边界元法 ,求解近边界点参量更加有效。

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(BEM). 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, so that the nearly strongly singular and nearly hypersingular integrals are successfully computed.The algorithin can also be used to analyze the plates and shells problems with the BEM.Especially,it is more efficient for solving the nearly singular integrals when the supersingular boundary integral equation(BIE) are regularized to the strongly singular BIE.