CAJ | 학술논문

正则区域法可将不规则区域嵌入规则矩形区域中，能有效解决复杂区域上的偏微分方程的边值问题。文章利用重心插值正则区域法研究不规则板的弯曲问题，分析了在不规则板嵌入的矩形区域上的离散不规则板弯曲问题的控制方程和边界条件，建立了矩形区域内的离散代数方程组；采用最小二乘法对离散代数方程组进行求解，并对不规则板上任意节点的挠度值与其对应的解析解进行了比较与分析。结果表明：重心插值正则区域法的计算公式简单，程序实施方便；利用重心有理插值法可插值得到不规则区域内任意节点函数值，求出不规则板上任意点的挠度值；利用重心插值正则区域法解决任意不规则板的弯曲问题上的计算精度可高达10-8以上。
정칙구역법가장불규칙구역감입규칙구형구역중，능유효해결복잡구역상적편미분방정적변치문제。문장이용중심삽치정칙구역법연구불규칙판적만곡문제，분석료재불규칙판감입적구형구역상적리산불규칙판만곡문제적공제방정화변계조건，건립료구형구역내적리산대수방정조；채용최소이승법대리산대수방정조진행구해，병대불규칙판상임의절점적뇨도치여기대응적해석해진행료비교여분석。결과표명：중심삽치정칙구역법적계산공식간단，정서실시방편；이용중심유리삽치법가삽치득도불규칙구역내임의절점함수치，구출불규칙판상임의점적뇨도치；이용중심삽치정칙구역법해결임의불규칙판적만곡문제상적계산정도가고체10-8이상。
The bending problems of irregular thin plate can be modeled by boundary problem of partial differential equation in complex domain. This paper describes a regular domain collocation method based on the barycentric rational interpolation for solving the bending problems of irregular thin plate. Embedded the irregular domain into a rectangular domain,the governing equation and boundary condition equation of bending plate in a rectangular domain is discretized by the differentiation matrix derived from barycentric rational interpolation to form a system of algebraic equations. The paper uses the least square method to solve the equations and get the node displacement values in rectangular domain. The deflection values of arbitrary point on irregular plate are solved by using interpolation of the barycentric interpolation to get function values of any node in the irregular plate. The calculation formula of the method is simple and program of it is convenient. By comparing and analyzing the numerical error of the deflection values of arbitrary point on irregular plate by a regular domain collocation method based on the barycentric rational interpolation with the analytical solutions of the deflection values of irregular plate according to the numerical examples in this paper,we can conclude that the method is a new method with high efficiency and calculation precision of over 10 - 8 for solving bending problems of any irregular thin plate.