基于MAPLE的泵轴对称应力分析边界奇异积分方法

用边界元法进行泵轴对称应力分析问题时,会遇到奇异积分, 典型的处理方法是将被积函数中的椭圆函数用对数函数近似,以及基于积分变换的方法.但这类方法的精确性依赖于边界单元的划分方法,给程序的统一处理带来了不便.为此,提出使用MAPLE软件处理奇异积分的方法,将被积函数中出现奇异性的部分表示成若干项,每项是一个初等函数和椭圆函数的乘积,将此初等函数用分段样条多项式近似,使MAPLE直接算得对应积分的具体数值结果. 这一方法程序处理统一,简单明了,便于应用.

Calculation of singular boundary integrations by using MAPLE in the stress analysis of symmetrical structures

Stress analysis problems of symmetrical structures are widely encountered in industries. When the boundary element method is used on this kind of problem, singular integrations would exist. How to calculate them validly and accurately is a key point. Typically, the elliptical functions in the integrated functions are accumulated with corresponding log functions. Also, integration transformation methods have been used for the case. But the accuracies of these methods depend on the delimiting of the boundary elements, which makes the program difficult to be coded uniformly. To this end, a new method based on using of software MAPLE is presented. It expresses an integrated function as the sum of several terms, each term may be a polynomial or the product of a polynomial and an elliptic function by segmental interpolating methods. In this way MAPLE could calculate the concrete integration results. The codes for the new method could be programmed in an unified and brief form.