吴国荣, 钟伟芳, 吴永东, 梁以德. 应用分形有限元方法于外域声场计算[J]. 力学与实践, 2004, 26(5). DOI: 10.6052/1000-0992-2003-184
引用本文: 吴国荣, 钟伟芳, 吴永东, 梁以德. 应用分形有限元方法于外域声场计算[J]. 力学与实践, 2004, 26(5). DOI: 10.6052/1000-0992-2003-184

应用分形有限元方法于外域声场计算

  • 摘要: 应用二级分形有限元方法计算了外域声场. 用一人工边界把外域声场分为两部分,人工边界以内使用常规有限元方法,人工边界以外的无限大区域使用分形有限元方法.使用分形有限元方法的优点是:一方面形成几何自相似网格使得相邻层之间的单元刚度矩阵和质量矩阵具有非常简单的关系;另一方面引用自动满足无限远辐射条件的全域插值函数把节点自由度变换为一组广义坐标,因而计算量可以大大减少. 数值算例表明:该方法对于计算无限大外域声场是有效的.

     

    Abstract: The fractal finite element method is extended to solveexterior acoustic problems. An artificial boundary is introduced to dividethe exterior domain into two parts. The conventional finite element methodis adopted within the artificial boundary, and the fractal finite elementmethod is employed in the outer region beyond the artificial boundary.Because of the facts that the relationships of element matrices between theadjacent fractal layers are very simple and the node degrees of freedom aretransformed into a set of general coordinates by using the globalinterpolation functions, which satisfy automatically Sommerfeld's radiationconditions, the computer time can be reduced greatly by the fractal finiteelement method. The numerical results show that this method is effective insolving exterior acoustic problems.

     

/

返回文章
返回