一个特殊插值函数在边界元法中的应用

来源期刊：中南大学学报(自然科学版)1998年第1期

论文作者：陈枫

文章页码：97 - 99

关键词：边界元法;应力;强度因子;插值函数;应力集中系数

Key words：boundary element method; stress; intensity factor; interplation function; stress concentration factor

摘    要：边界元法被广泛应用于边值问题的数值分析中.由于它将问题的维数减少1,所以使问题大为简化.对于断裂问题的边界元法,其精度取决于裂尖附近边界的离散性.作者提出的一个裂纹尖端应力插值函数,能反映裂纹尖端的应力奇异性,使应力强度因子的计算更为简捷.对两类问题(应力集中系数和应力强度因子)的计算表明,在边界元划分较少的情况下也能获得很高的精度,这对减少输入工作量和降低计算成本具有重要的实际意义.最后给出了采用本文方法与采用其它数值方法所得出的结果比较.

Abstract: Boundary element method is widely used in a numerical analysis of boundary value problems.Since the dimensions of the problems can be reduced by one,the problem will be greatly simplified.The precision of fracture problems using BEM is governed by discretion of boundary near crack tip.A special stress interplation function which can reflect the stress singularity near crack tip is presented in this paper.It can simplify the calculation of SIF.Two kinds of numerical implementations show that higher precision can be achieved even with less boundary elements.The comparsion between results obtained using the present method and those by other numerical method is also given in this paper.