边界元耦合径向基点插值无网格法在求解声散射问题中的应用

Application of boundary element coupling radial basis point interpolation meshless method in acoustic scattering

边界元耦合有限元方法(BEM-FEM)在求解无限域弹性结构声散射问题中得到广泛应用。传统有限元方法的计算精度依赖网格的类型和质量,而无网格方法离散问题域时不需要传统意义上的网格划分,其形函数构造不依赖网格且相对灵活。因此无网格方法相比传统有限元方法可以减少网格划分成本并减缓数值污染效应。将边界元方法(BEM)和径向基点插值无网格法(RPIM)结合,形成边界元耦合径向基点插值无网格法(BEMRPIM),用于求解无限域弹性结构声散射问题。本文分别从计算精度、收敛性和对不规则节点分布的适应性对BEM-RPIM和BEM-FEM进行比较,结果表明提出的BEM-RPIM在求解声散射问题中优于BEM-FEM。

The coupled BEM-FEM approach is a popular numerical tool for the acoustic scattering problems by elastic structures in infinite domain.However,the solution accuracy of traditional FEM relies on the type and quality of the mesh.In contrast,the formulation of the shape functions in the meshfree methods is flexible and doesn’t count on the mesh.Compared with FEM,using meshfree methods can save the cost of meshing and reduce the effect of numerical pollution.In this work,we propose a coupled BEM-RPIM approach for the acoustic scattering problems of elastic structures in infinite domain by combining BEM and meshfree method based on conventional radial point interpolation shape function(RPIM).The BEM-RPIM and the BEM-FEM are compared in terms of accuracy,convergence and adaptability to irregular node distribution.Numerical solutions show that the BEM-RPIM perform better than the BEM-FEM.