变截面箱形薄壁立柱屈曲荷载的近似分析解

变截面箱形薄壁立柱弯扭屈曲的三个控制方程是二阶或四阶变系数的常微分方程,很难用解析的方法求解。本文用多项式来近似截面的几何特性和微分方程的某些系数,用能量原理和伽辽金法分别导出了计算这种立柱弯曲和扭转屈曲荷载的近似公式,用数值算例来验证了所给解答的正确性。本文的计算结果为论证变截面箱形薄壁立柱的稳定性提供了依据。本文具有实用价值。

The Approximate Analytical Solution for the Buckling Loads of a Thin_Walled Box Column with Variable Cross_section

For a thin-walled box column with variable cross-section,the three governing equations for torsional-flexural buckling are ordinary differential equations of the second or fourth order with variable coefficients,so it is very difficult to solve them by means of an analytic method.In this paper,Polynomials are used to approximate the geometric properties of cross-section and certain coefficients of the differential equations.Based on the energy principle and the Galerkinc's method,the approximate formulas for calculating the flexural and torsional buckling loads of this kind of columns are developed respectively,and numerical examples are used to verify the correctness of the solutions obtained. The results calculated in this paper provide the basis for demonstrating the stability of thin-walled box columns with variable cross-section.This paper is of practical value.