CAJ | 학술논문

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。
위제고판결구-성장우합분석적계산정도，장유한원-최소이승점삽치법（Finite Element-Least Square Point Interpolation Method，FE-LSPIM）추엄도판결구-성장우합문제적분석중，제출료판결구-성장우합문제분석적 FE-LSPIM/FE-LSPIM방법，추도료 FE-LSPIM/FE-LSPIM분석판결구-성장우합문제적계산공식。FE-LSPIM/FE-LSPIM방법응용유한원단원형함수화최소이승점삽치법진행국부핍근，계승료유한원법적단원겸용성화최소이승삽치법적이차다항식완비성，제고료계산정도。이일륙면체성장-결구우합모형위연구대상진행분석，결과표명，여판결구-성장우합문제분석적 FEM/FEM화광활유한원/유한원（Smoothed Finite Element Method /Finite Element Method，SFEM/FEM）상비，FE-LSPIM/FE-LSPIM재분석판결구-성장우합문제시구유경고적정도。
In order to improve the accuracy of simulation analysis of plate structural-acoustic coupled systems,the finite element-least square point interpolation method (FE-LSPIM)was extended to solve plate structural -acoustic coupled problems and a coupled FE-LSPIM for plate structural-acoustic coupled systems was proposed.With the proposed method,the shape functions of the finite element method and the least square point interpolation were used for local approximation,the element-compatibility of the finite element method and the quadratic polynomial completeness of LSPIM were inherited.Thus,the accuracy of simulation analysis could be improved.Numerical example of a box structural-acoustic coupled model was presented.Its results showed that using FE-LSPIMachieves a higher accuracy,compared with using FEMand smoothed FEMfor simulation of plate structural -acoustic coupled problems.