矩阵法求解压杆稳定的有限差分欧拉方程

摘要

Euler equation of column stability can be expressed in the form of finite differential .According to the require‐ments of column stability ,coefficient matrices the differential equations are solved with the method of matrices calcula‐tion .Subsequently ,the critical stress of column stability of constant section of the simply supported beams is obtained . The results are compared with the analytical results .Also presented in the paper is an error analysis including the causes of the error and measures for diminishing it .The method proposed has positive value for the variable section beams .%将压杆稳定的欧拉方程用差分的形式表达后，根据压杆稳定的实际要求，通过矩阵的方法求解该差分方程的系数矩阵，最后求出简支梁等截面直杆的压杆稳定临界应力。将求出的结果与解析解进行对比并进行误差分析，找出产生误差的原因和减小误差的措施，并指出该方法在解决变截面杆的实际意义。