用有限积分计算曲率复杂分布下的结构挠度

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z与z″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.

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

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 curvaturesφis 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 relationφ= -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.