The Odd Stability of the Euler Beam
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.
KeywordsBoundary Value Problem Bifurcation Diagram Initial Value Problem Equilibrium Path Rigid Body Rotation
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- Euler, L. (1744). Additamentum I de curvis elasticis, methodus inveniendi lineas curvas maximi minimivi proprietate gaudentes. In Opera Omnia., vol. 24. Lausanne: Bousquet. 231–297.Google Scholar