弹性理论几类导数边界积分方程之间的变换关系

导数场边界积分方程通常难以应用，因为存在着超奇异主值积分的计算障碍。弹性理论中有几类不同的位移导数边界积分方程，本文采用算子δij和∈ij(排列张量)作用于这些导数边界积分方程，做一系列变换，原有的超奇异积分被正则化为强奇异积分获解。从而建立了这些位移导数边界积分方程之间的转换关系，它们均可以归结为自然边界积分方程。自然边界积分方程仅存在容易计算的Cauchy主值积分。自然边界积分方程分析可直接获得边界应力和位移导数。

Transformation Relations of the Several Derivative Boundary Integral Equations in Elasticity Problem

The several different displacement derivative boundary integral equations (BIE) have been proposed in elasticity problem. Generally, there exists difficulty on the application of derivative BIE because of the puzzle of the evaluation of hypersingular integrals. In this paper, two operators and(permutation symbols) are used to act on the displacement derivative boundary integral equations, respectively. By the use of a series of derivation, the hypersingular integrals are reduced to the strongly singular integrals, which are easily calculated. As a result, it is interesting that all of the different displacement derivative BIE can be transformed to the natural BIE. In addition, the natural BIE only contains Cauchy principal value integrals. The natural BIE can be employed directly to obtain boundary stresses and displacement derivatives.