轴对称双倒易边界元法的f函数及其奇性处理

Function f in Axisymmetric Dual Reciprocity Boundary Element Method and its Singularity Processing

基于右端项为径基函数的三维泊松方程,推导了轴对称情况下双倒易边界元方程求和形式的 f函数通式.通过对f函数取积分平均和根据计算区域特点选取不同类型的 f函数组合,消除了f函数在对称轴上呈现奇性的不足.通过计算轴对称实心圆柱体和球体的非稳态导热问题,很好地验证了对f函数的选择和处理的可行性.

A universal function f with summed form in dual reciprocity boundary element formulation for axisymmetric problems has been derived from three dimensional Poisson's equation whose right hand is radial basis function. The singularity on symmetric axis of the function f was eliminated by integral average of function f and selecting different function f on the basis of the different characteristic of calculated zones. The feasibility of present selection and the singularity processing of function f was well proved by the calculation of the transient heat conduction problems in solid cylinder and sphere.