弹性压杆稳定问题的精确解法

对于杆系结构的静力问题能够通过有限单元法得到精确解答,但是对于稳定问题常规有限元法则很难得到精确解答。本文提出一种新的有限元列式,能够精确求解弹性压杆稳定问题。即通过对弹性压杆稳定问题控制微分方程进行分析,建立了新的精确单元形函数,提出一种新的弹性压杆稳定有限单元,利用迭代算法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。

Exact Solution of Stable Reliability Problem of Elastic Compressive Bar

The exact solution of static problem of pole series can be found by the FEM,but it is very difficult for stable reliability problem by the normal FEM.This paper presents a new formula for the exact solution of stable reliability of compressive bar by the FEM.The new exact shape function is presented by analyzing the governing differential equation,and critical load and buckling mode are calculated by the iteration method.An example is taken to illustrate the validity and the availability of this new method.