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力学与实践 ›› 2010, Vol. 32 ›› Issue (2): 35-38.doi: 10.6052/1000-0879-2008-301

• 应用研究 • 上一篇    下一篇

大型圆形贮液池力学分析中的重心插值拟谱法

赵晓伟 王兆清 陈世英   

  1. 山东建筑大学工程结构现代分析与设计研究所 山东建筑大学 山东建筑大学
  • 收稿日期:2008-06-04 修回日期:2009-03-18 出版日期:2010-04-08 发布日期:2010-04-08

BARYCENTRIC INTERPOLATION PSEUDOSPECTRAL METHOD FOR ANALYZING CIRCULAR CONCRETE TANKS WITHOUT PRESTRESSING

Zhao Xiao-Wei ZhaoQing Wang ShiYing Chen   

  • Received:2008-06-04 Revised:2009-03-18 Online:2010-04-08 Published:2010-04-08

摘要: 针对传统大型圆形贮液池力学分析方法计算复杂、精度不高的问题,用拟谱 法对圆形贮液池的线弹性静力问题进行了研究. 采用重心Lagrange插值多项式建立未知函数 的微分矩阵,将池壁的控制方程表示为代数方程组. 通过求解代数方程组,求得池壁各个离 散点挠度,进而采用微分矩阵直接求得池壁内力. 算例表明,该方法原理简单,易于程序实现和数值计算精度高.

关键词: 拟谱法, 微分矩阵, 重心Lagrange插值, 配点法

Abstract: Traditional analyses of circular concrete tanks without prestressing suffer from some drawbacks, such as complicated computation and unsatisfactory accuracy. In this paper, a pseudospectral method based on barycentric Lagrange interpolation for linear elastic static analysis of tank is proposed. The differentiation matrix for the unknown function is constructed by using barycentric Lagrange interpolation. The governing equations of equilibrium, in terms of stress resultants and couples, are put into a generalized displacement form by the use of strain-displacement relationships and constitutive equations. The governing equation of tank wall can be expressed as a set of algebraic equations by the pseudospectral method. With boundary conditions, the algebraic equation system is solved to obtained the deflections at discrete points. The principle of this method is simple and ease to program. The accuracy and the numerical stability are good.

Key words: Pseudospectral method, differentiation Matrix, barycentric Lagrnage interpolation, collocation method