二维声学数值计算的径向插值有限元法

Radial Interpolation Finite Element Method for Two Dimension Acoustic Numerical Computation

针对声学有限元分析中四节点等参单元计算精度低,对网格质量敏感的问题,将无网格径向插值技术引入到标准有限元中,构造径向插值形函数,推导径向插值有限元法(Radial interpolation finite element method,RIFEM)的二维声学数值计算公式。二维声学RIFEM采用标准有限元法形函数构造系统离散方程的声学刚度矩阵和边界积分矢量,保证了声压梯度和边界条件在区域边界的积分精度;采用径向插值形函数构造系统离散方程的质量矩阵,提高了声压数值近似函数的插值精度。对管道二维声腔模型和某轿车二维声腔模型的数值分析结果表明,与标准有限元法和SFEM相比,RIFEM的计算精度更高,对波数、单元尺寸和网格扭曲程度的灵敏度更低。因此RIFEM可以很好地应用于二维声学数值分析,具有广阔的工程应用前景。

Aiming at the problems of low accuracy and sensitivity to the mesh＇s quality of four-node isoparametric element in the acoustic finite element method（FEM）,the radial interpolation finite element method（RIFEM）,whose shape function is based on the meshless radial interpolation method,is proposed for two dimension acoustic problem.In acoustic RIFEM,the acoustic stiffness matrix and the vectors of the boundary integrals are constructed by the bilinear shape function,to maintain the integral accuracy of the sound pressure derivatives and the accurate boundary conditions applied on region boundary.The acoustic mass matrix is constructed by the shape function of the RIFEM by using the four-node isoparametric element,to improve the interpolation accuracy of the approximated sound pressure function.Numerical examples of a two-dimensional tube and a two-dimensional acoustic cavity of automobile are presented to show that RIFEM achieves higher accuracy,and is less sensitive to the wave number,the size of mesh,the level of mesh distortion as compared with FEM and SFEM.Hence the RIFEM can be well applied in solving two dimensional acoustic problems,and has a wide application foreground.