考虑轴向均布载荷时线弹性支承压杆的稳定性计算

Stability Calculation of Long Column under Linear Elastic Supports and Extra Axial Uniform Load

摘要: 为了计算考虑轴向均布载荷时线弹性支承压杆的稳定性，首先用压杆微元段的静力平衡条件，建立了其变形和内力的近似方程；接着由变形边界条件、内力边界条件、内力与外力的关系、外力与变形的关系，确定了一个包含12个初参数的齐次线性方程组，由方程组有非零解的条件，导出了临界载荷的特征方程；最后以6个线弹性支承的压杆为例，进行了稳定性计算，绘制了轴向均布载荷与集中载荷的近似关系曲线，给出了这些曲线在坐标轴上的截距的数值解，发现每条曲线的走势以及它们所代表的压杆的稳定性排序关系，较符合理论预期。

Abstract: For calculating the stability of long column under linear elastic supports and extra axial uniform load, first of all, with the static equilibrium conditions of the micro section of long column, the ap-proximate equations of deformations and internal forces are established; The next, by the boundary conditions of deformations and internal forces, and the relationship between internal forces and external forces, and the relationship between external forces and deformations, the homogeneous linear equations of containing 12 initial parameters are established, by the conditions of equations with non-zero solution, the characteristic equation of critical load are derived; The last, taking 6 linear elastic supports long columns as example, the stability is calculated, the approximate relation curves between axial uniform load and concentrated load are drawn, and the numerical solutions of intercepts on Cartesian coordinate system are given, and found that the trend of each curve, and the relationship of sorting to stability represented by them, are more consistent with theoretical expectations.