两端任意线弹性支承的压杆稳定性研究

Study on the Stability of a Long Column Supported by Any Linear Elastic Supports at the Two Ends

基于挠曲线近似微分方程,对两端任意线弹性支承的压杆用10个初参数,建立了其处于微弯曲平衡状态时统一的变形方程、静力平衡方程和物理方程。由齐次线性方程组有非零解的条件,导出了求解临界压力的特征方程。验证了在完全理想支承下计算临界压力的欧拉公式仅是本文导出公式的特例,同时以六个非完全理想支承的压杆为例,计算其长度因数。系统地解决了两端任意线弹性支承的压杆临界压力的计算问题。

Based on the approximate differential equation of flexural curve,aiming at the long column supported by any linear elastic supports at the two ends,by 10 initial parameters,under the condition of micro bending equilibrium,thg unified deformation equation,the static equilibrium equations,and the constitutive equation are established,By the condition of homogeneous linear equations with non-zero solution,the characteristic equation to solve critical force is obtained.In the case of completely ideal supports,the Euler’s formula for computing the critical force is verified just a special case of the derived formula in the study,at the same time,taking six long columns of not completely ideal supports as examples,to calculate the factor of length.The problem to calculate the critical pressure of a long colum supported by any linear elastic supports at the two ends is solved systematically.