导数场边界积分方程分析近边界应力分布

研究二维弹性力学问题边界积分方程,通过分部积分变换消除了常规导数边界积分方程中的超奇异积分,获得仅含强奇异积分的应力自然边界积分方程.对于近边界应力的计算,进一步运用正则化算法解析计算其中的几乎强奇异积分.较常规边界元法相比,应力自然边界积分方程可以求解离边界更加接近的内点应力值.算例证明了文中方法的可应用性和有效性.

THE EVALUATION OF THE STRESS DISTRIBUTIONS IN THE DOMAIN CLOSE TO THE BOUNDARY BY THE DERIVATIVE BIE

This paper studies the boundary integral equations (BIE) in the elasticity problems.A series of transformations are performed to the displacement derivative BIE in order to eliminate the hyper-singular principal value integrals.Hence,a new stress natural BIE is developed,in which there only exist the strongly singular integrals instead of the hypersingular integrals in the conventional stress BIE.Furthermore,when a source point tends to the boundary,the small dominant factor leading to the nearly strongly singular integrals in the natural BIE is removed from the integral representations by the integration by parts,so that the values of the singular integrals are accurately calculated.Numerical examples demonstrate that the natural BIE can successfully determine the stress distributions in the domain much closer to the boundary in comparison with the conventional BIE.