引用本文: 赵玉星, 刘洪富, 吕甲朋. 用有限积分计算曲率复杂分布下的结构挠度[J]. 力学与实践, 2012, 34(2): 19-23.
ZHAO Yuxing, LIU Hongfu, LÜ Jiapeng. DEFLECTIONS OF STRUCTURES WITH COMPLICATED DISTRIBUTION OF CURVATURE CALCULATED BY FINITE INTEGRAL METHOD[J]. MECHANICS IN ENGINEERING, 2012, 34(2): 19-23.
 Citation: ZHAO Yuxing, LIU Hongfu, LÜ Jiapeng. DEFLECTIONS OF STRUCTURES WITH COMPLICATED DISTRIBUTION OF CURVATURE CALCULATED BY FINITE INTEGRAL METHOD[J]. MECHANICS IN ENGINEERING, 2012, 34(2): 19-23.

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

• 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.

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.

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