重心插值配点法分析矩形薄板弯曲问题  

Barycentric interpolation collocation method for thin rectangular plates bending problems

作　　者：赵晓伟[1] 李西斌[2] 王兆清[1] 范书敏 

机构地区：[1]山东建筑大学工程结构现代分析与设计研究所,山东济南250101 [2]福州大学土木工程学院,福建福州350108 [3]滨州建工集团有限公司,山东滨州256600

出　　处：《福州大学学报（自然科学版）》2009年第4期555-559,共5页Journal of Fuzhou University(Natural Science Edition)

基　　金：福建省自然科学基金资助项目(2007J0153);福州大学科技发展基金资助项目(2007XQ23)

摘　　要：采用重心Lagrange插值近似未知函数建立未知函数各阶导数的微分矩阵.采用微分矩阵近似未知函数的导数,利用配点法将矩形薄板的控制方程和边界条件离散为代数方程组,通过求解代数方程组,求得矩形薄板的各个离散点的挠度,进而利用微分矩阵求得矩形薄板的内力.给出详细的控制方程和边界条件的离散公式.数值算例表明,重心插值配点法具有原理简单,易于程序实现和数值计算精度高的优点.Barycentric Lagrange interpolation has excellent numerical stability and highly accuracy. With barcentric Lagrange interpolation to approximate the unknown function, the differentiation matriees of unknown function were constructed. Approximate partial derivatives of unknown function by differentiation matrices, the governing equation and boundary conditions of thin plate bending problems were converted into algebraic equations using collocation method. By solving these algebraic equations, the deflections of thin plates at discrete points were obtained. Then the bending moments of thin plate can be given by using differentiation matrices. The computational formulas of differentiation matrices and collocation method were given in detail. The numerical examples demonstrate the effectiveness and accuracy of proposed method.

关 键 词：LAGRANGE插值 微分矩阵 配点法 薄板 弯曲 

分 类 号：O241[理学—计算数学]