三维弹塑性边界元1/r^3积分奇异性的处理

Treatments of the Integrals with Singularity 1/r3 in 3-D Elastoplastic Boundary Element Methods

本文将文[2]的基本思想与方法,推广应用于处理三维弹塑性边界元法塑性单元中的1/r^3积分奇异性问题,推导了有关的具体公式,并从理论上证明了该方法处理1/r^3奇异性的有效性。针对奇异性单元。本文提出旋转与坐标转换的分割技术,可大大减少工作量。并使计算机编程更简洁。数值算例研究表明,文中采用的方法是十分有效的。

The basic idea and approach in Ref. [2] is extended and applied to treat the problems on the integrals with singularity 1/r3in 3-D elastoplastic boundary element methods in this paper. The corresponding concrete formula are derived, and its effectiveness of the treat-ments on singularity 1/r3 is proved in the theory. For the elements with singular points, the dividing techniques of rotating and coordinate transformation are proposed in this pa-per as well. It enables the amounts of work on dividing the blocks to decrease greatly and makes the programming of computers much simpler. The numerical results show that the approach in this paper is very effective.