力学与实践 ›› 2012, Vol. 34 ›› Issue (2): 19-23.DOI: 10.6052/1000-0879-20120203

• 应用研究 • 上一篇    下一篇

用有限积分计算曲率复杂分布下的结构挠度

赵玉星1, 刘洪富1, 吕甲朋2   

  1. 1. 山东建筑大学土木工程学院, 济南 250101;
    2. 青岛建筑设计集团, 青岛 266003
  • 收稿日期:2011-05-09 修回日期:2012-02-22 出版日期:2012-04-15 发布日期:2012-04-16
  • 通讯作者: 赵玉星

DEFLECTIONS OF STRUCTURES WITH COMPLICATED DISTRIBUTION OF CURVATURE CALCULATED BY FINITE INTEGRAL METHOD

ZHAO Yuxing1, LIU Hongfu1, LÜ Jiapeng2   

  1. 1. School of Civil Engineering, Shandong Jianzhu University, Jinan 250101, China ;
    2. Qingdao Architectural Design Group, Qingdao 266003, China
  • Received:2011-05-09 Revised:2012-02-22 Online:2012-04-15 Published:2012-04-16

摘要: 有限积分法是Brown和Trahair在求解微分方程时采用的数值解法, 其核心环节是已知函数z= z(x)的导函数z′ =z′(x)的某些值的情况下数值分析z的方法. 由曲率φ计算挠度, 实质意义上是由z″计算z的数学问题. 基于有限积分法给出的zz″之间及z′与z″之间的数值关系, 通过矩阵运算推导得到了挠曲矩阵,通过引入转换式φ= -z″得到了曲率挠度关系式, 讨论了几种常见边界条件下的曲率挠度关系, 提出了曲率复杂分布情况下结构挠度计算的有限积分方法.

关键词: 挠度计算|有限积分法|曲率挠度分析

Abstract: The finite integral method is a numerical solution by which Brown and Trahair analyzed some differential equations. The kernel mechanism of the finite integral method is how to calculate z = z(x) numerically when some values of z′ = z′(x) are known. Function z′ = z′(x) is the derivative of z = z(x). Essentially, the deflection calculation by curvatures φ is a mathematical process to calculate z from z″. Based on the relations between z-z″ and z′-z″ in the finite integral solutions, the deflection-curvature matrix is derived by matrix operations, and the curvature-deflection equation is derived by the relation φ = - z″. The curvature-deflection equations for some kinds of common boundary conditions are discussed. The finite integral solution for deflections of structures with complicated distribution of curvature is obtained.

Key words: deflection calculation|finite integral method|analysis of curvature and deflection

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