弹性压杆稳定问题的ODE解法

摘要

The ordinary differential equation solver method for the stability problems of elastic compressive bar is presented. It is achieved by transforming the general eigenvalue problem of stability problems of continuously distributed property system into typical boundary value problem of ordinary differential equation (ODE). A series of ODEs, corresponding to the general eigenvalue problem, is formed and then the critical load and corresponding instability mode of column is solved by an general ordinary differential equation solver. An example is taken to illustrate the validity and the availability of this new method.%介绍了一种无限自由度弹性压杆稳定问题的常微分方程求解器(ODE)解法.将计算无限自由度弹性压杆稳定问题转换为典型的常微分方程边值问题,通过构造一系列平凡常微分方程,建立相应的常微分方程组,利用常微分方程求解器予以求解来确定压杆的临界荷载及相应的失稳模态.最后通过数值算例验证了本文方法的正确性及有效性.