极坐标下薄板弯曲问题的重心有理插值法

doi:10.3976/j.issn.1002-4026.2016.02.015

山东科学 ›› 2016, Vol. 29 ›› Issue (2): 82-87.doi: 10.3976/j.issn.1002-4026.2016.02.015

极坐标下薄板弯曲问题的重心有理插值法

庄美玲，王兆清*，张磊，纪思源

山东建筑大学力学研究所，山东济南 250101

收稿日期:2015-04-05 出版日期:2016-04-20 发布日期:2016-04-20
通信作者: 王兆清（1965-）, 男,副教授,博士,研究方向为工程数值方法。Email:sdjzuwang@gmail.com E-mail:sdjzuwang@gmail.com
作者简介:庄美玲（1989-），女，硕士研究生，研究方向为工程数值方法。Email:18036558037@163.com
基金资助:
国家自然科学基金（51379113）

Barycentric rational interpolation collocation method for bending problem of a thin plate in polar coordinates

ZHUANG Meiling, WANG Zhaoqing*,ZHANG Lei, JI Siyuan

Institute of Mechanics, Shandong Jianzhu University, Jinan 250101, China

Received:2015-04-05 Online:2016-04-20 Published:2016-04-20

摘要/Abstract

摘要：

利用重心有理插值配点法(BRICM)研究了极坐标下薄板的弯曲问题，该方法是以重心有理插值近似未知函数强迫微分方程在离散节点处成立，得到微分方程的离散代数方程组，进而采用重心有理插值的微分矩阵将离散代数方程组表达为矩阵的形式。利用置换法施加边界条件，求解微分方程组。数值算例结果表明，该方法在解决极坐标下薄板弯曲问题上公式简单，程序实施方便且计算精度高。

关键词: 极坐标, 重心有理插值, 双调和方程, 边界值, 弯曲问题

Abstract:

We apply barycentric rational interpolation collocation method (BRICM) to the bending problem of a thin plate in polar coordinates. It approximates an unknown function with barycentric rational interpolation by compelling a biharmonic equation to equal to the unknown function at discrete nodes, and acquires the discrete algebraic equations of the biharmonic equation. It further denotes the discrete algebraic equations as a matrix by the differential matrix of barycentric rational interpolation. It eventually solves the differential equations with a boundary conditions mixed replacement method. Numerical instances demonstrate that the method has simple calculation formulae for bending problem of a thin plate in polar coordinates, convenient program and high calculation precision.

Key words: polar coordinate, bending problem, barycentric rational interpolation method, biharmonic equation, boundary value problem

中图分类号:

O241

庄美玲，王兆清，张磊，纪思源. 极坐标下薄板弯曲问题的重心有理插值法[J]. 山东科学, 2016, 29(2): 82-87.

ZHUANG Meiling, WANG Zhaoqing,ZHANG Lei, JI Siyuan. Barycentric rational interpolation collocation method for bending problem of a thin plate in polar coordinates[J]. SHANDONG SCIENCE, 2016, 29(2): 82-87.

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[3]	李淑萍. 基于重心型插值的数值计算方法[J]. J4, 2010, 23(4): 13-16.

极坐标下薄板弯曲问题的重心有理插值法

Barycentric rational interpolation collocation method for bending problem of a thin plate in polar coordinates

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