The Odd Stability of the Euler Beam

摘要

In this part of the lecture notes we investigate a classical chapter of elastic stability from a new perspective. We show that even the first buckling mode in Euler's problem becomes unstable at a second critical load parameter P_L = 2.183P_(Euler) and the only stable solution for P > P_L is the straight bar in tension. We also show that if we discretize the beam into a sequence of n rigid links coupled by linear torsional springs, the described stability behaviour is only reflected correctly if n is an odd number.