板结构-声场耦合分析的FE-LSPIM/FE法

Analysis of plate structural-acoustic coupling systems based on finite element-least square point interpolation and finite element method

为提高板结构-声场耦合分析的计算精度,将有限元-最小二乘点插值法(Finite Element-Least Square Point Interpolation Method,FE-LSPIM)推广到板结构-声场耦合问题的结构域分析中,提出了板结构-声场耦合问题分析的FE-LSPIM/FEM(Finite Element-Least Square Point Interpolation Method/Finite Element Method),推导了FELSPIM/FEM分析板结构-声场耦合问题的计算公式。此方法在结构域中应用四边形单元形函数和最小二乘点插值法进行局部逼近,继承了有限元法的单元兼容性和最小二乘插值法的二次多项式完备性,提高了结构域的计算精度;在流体域中应用标准有限元模型进行分析。以一六面体声场-结构耦合模型为研究对象进行分析,结果表明,与板结构-声场耦合问题分析的FEM/FEM和光滑有限元/有限元(Smoothed Finite Element Method/Finite Element Method,SFEM/FEM)相比,FE-LSPIM/FEM在分析板结构-声场耦合问题时具有更高的精度。

In order to improve the accuracy of simulation analysis on plate structural acoustic coupled systems, a finite elementleast square point interpolation method （FE LSPIM） was extended to solve the plate structural acoustic coupled problems, a coupled FE-LSPIM/FEM method for the plate structural acoustic coupled systems was proposed and the formulation of FE- LSPIM/FEM was presented. The quadrilateral elements were used to discretize the structure domain and the shape functions of the quadrilateral element and the least square point interpolation method were used for local approximation. The present meth- od inherited the compatibility properties of finite element method and the quadratic polynomial completeness properties of LSPIM, which improved the accuracy of simulation analysis on structure domain. The standard FEM model was used for acoustic domain. Numerical example of a box structural acoustic coupled model was presented, which shows that FE-LSPIM/ FEM achieves higher accuracy as compared with FEM/FEM and SFEM/FEM for plate structural-acoustic problems.