On the Concept of Elastic Stability

Publisher Summary This chapter focuses on the concept of elastic stability. The examples show that the correct approach to the solution of a stability problem depends on the nature of the problem. Unless a problem is purely nongyroscopic, the easy static approaches usually fail and even the kinetic approach frequently is questionable if physical imperfections are neglected. The instances treated are concerned with columns and shafts belong to a relatively narrow field of applications. As most of the stability problems solved in these instances have so far been concerned with comparatively simple load systems of purely nongyroscopic type, the usual static approach has not led to serious troubles. An example that has been studied but abandoned because the static approaches did not supply a satisfactory solution is the problem of a column loaded tangentially over its whole length. Another instance, where the results obtained by the static approach are questionable in certain cases, as the load is not conservative, is the problem of a cylindrical shell subjected to torsion.