等参管单元及其在热传导问题边界元法中的应用

Isoparametric tube elements and their application in heat conduction BEM analysis

采用边界元法(BEM)求解实际工程问题时,很大一部分误差来自于离散误差。为此,本文基于Lagrange插值原理,提出了一种三维等参管单元边界元算法,该单元能很好地模拟管状结构的几何外形并对物理量进行高阶插值,大大地消除了离散误差。另外,当在边界元法中使用等参管单元时,提出了一种在等参平面内消除积分奇异性的方法。算例表明,本文算法具有划分网格少,求解精度高的优点。

When using boundary element method （BEM） to solve practical engineering problems, consid- erable error comes from the discretization error. To overcome this problem, an algorithm for using isoparametric tube elements in BEM is proposed based on the Lagrange interpolation formulation. This type of elements can well model the geometry with tube shapes and interpolate physical quantities defined on the tube surface. As a result,the discretization error can be reduced considerably. In addition, a new technique for eliminating singularities involved in the boundary integrals is also presented in the intrinsic plane when using the proposed isoparametric tube elements in BEM. Numerical examples show that the proposed elements have the advantages of less element discretization and high computational accuracy.