轴对称应力问题边界元公式的计算机推导

提出用数学软件Maple进行边界元法公式推导。它首先对有关边界积分进行分解,并通过引入变量代换与限定参数范围,使各项定积分表示成Maple能够处理的形式。再用Maple完成积分计算,进而化简成人们便于阅读的形式。通过对轴对称应力分析问题边界元法的公式推导实践,表明这一方法能较大地减轻工作量,值得推广应用。

Computer Formula Derivation for Boundary Element Methods in Stress Analysis Problems of Symmetrical Structures

A method based on the application of the mathematic software Maple was proposed.First the related boundary integrations were reduced to several simple terms together with the transformation of the variables and the assigning of the ranges of the parameters.In this way the definite integrations were expressed in the form of which is convenient for the processing of Maple.Then the integrations were calculated with Maple commands.Afterwards,the results were simplified to be the form that was easy for reading with Maple commands.The proposed method was applied to the boundary element method in stress analysis problems of symmetrical structures.It shows that the amount of the work is reduced greatly.The method is worth popularizing.