摘要为提高板结构-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-声场耦合问题的分析中，提出了板结构-声场耦合问题分析的FE-LSPIM/FE-LSPIM方法，推导了FE-LSPIM/FE-LSPIM分析板结构-声场耦合问题的计算公式。FE-LSPIM/FE-LSPIM方法应用有限元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，提高了计算精度。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/FE-LSPIM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 of plate structural- acoustic coupling systems, the finite element-least square point interpolation method (FE-LSPIM) was extended to solve the plate structural- -acoustic coupling problems and a coupled FE-LSPIM/FE-LSPIM method for the analysis of plate structural- acoustic coupling systems was proposed. In the proposed method, the shape functions of the finite element method and the least square point interpolation method were used for local approximation; the compatibility properties of finite element method and the quadratic polynomial completeness properties of LSPIM were inherited. Thus the accuracy of simulation analysis can be improved. Numerical example of a box structural- acoustic coupled model was presented, which shows that the FE-LSPIM/FE-LSPIM method achieves higher accuracy as compared with FEM/ FEM and SFEM/ FEM for the analysis of plate structural - acoustic coupling problems.
2014, Vol. 33 
