阶梯形变截面压杆临界荷载的一种较精确算法

A more precise calculating method of critical load for compression member with various ladder sections

用瑞利-里兹法计算压杆临界荷载时,需要假设挠曲线函数。对于阶梯形变截面压杆,若对整个结构取一个统一的挠曲线函数,虽然在截面突变点位移和转角保持连续,但弯矩不连续,导致计算精度不高。通过在压杆不同等截面杆段,分别假设不同的挠曲线函数,即分段挠曲线函数,可以同时满足以上三种连续条件,其精度较整个结构取一个统一的挠曲线函数有大幅度提高,是计算阶梯形变截面压杆临界荷载的一种较精确方法。

It is needed to assume the flexural function when the critical load of compressive member is calculated by Rayleigh-Ritz method.A unified flexural function was taken for the entire structure of the various ladder pressure members,although the displacement and the angle are kept continuous in section mutation points,but the bending moment is kept discontinuity.It would cause the less calculation accuracy.The different flexural functions are assumed respectively on the difference equal section area of compressive member,that is the piecewise flexural function.This method can satisfy the above three kinds of continuous conditions at the same time.Its precision has increased significantly compared with a unified flexural function for the entire structure.Above method is a more accurate method of critical load for the compression member with various ladder sections.