边界元法计算近边界点参量的一个通用算法

A GERNERAL ALGORITHM FOR CALCULATING THE QUANTITIES AT INTERIOR POINTS CLOSE TO THE BOUNDARY BY THE BEM

针对边界元法存在近边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，提出了一整套计算方案．算例证明了本法 的有效性．

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.