MAPLE用于轴对称热传导问题边界奇异积分计算

轴对称热传导问题是能源动力工程中基本问题之一。对这类问题应用边界元法必然会遇到奇异积分，其有效而准确的计算是关键。传统的处理方法是通过近似方法或积分变换方法将被积函数表示为简单形式的初等函数，处理手段既不统一，又不那么简洁。为此提出使用MAPLE软件处理轴对称热传导问题边界元奇异积分，它将被积函数表示为多项式和椭圆函数乘积形式，能使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，便于推广应用。

Using MAPLE on the Calculation of Singular Boundary Integrations in Thermal Conduction Problems of Symmetrical Structures

Thermal conduction of a symmetrical structure is a basic problem in power engineering. When a boundary element method is adopted for this kind of problem, singular integrations would be encountered. How to calculate them validly and accurately is a key point. Traditionally, the function to be integrated was expressed in a simpler form through math transformation or accumulation methods to ensure that it could be integrated out. These traditional methods are not unified, and are not brief, either. To this end, it presented a MAPLE based method for the calculation of the singular integrations. It expresses the function to be integrated as the product of a polynomial and an elliptic function. In this way the singular integration could be calculated out by MAPLE. The new method is brief and unified in form, and it is easy to be programmed. It is worth being popularized.