Instability of Continuous Systems pp 295-301 | Cite as
Optimal Structural Design in Non-conservative Problems of Elastic Stability
Abstract
The problem of optimal shape of an elastic column subject to buckling under a compressive force with constant direction (Eulerian force) was formulated by Lagrange; basic solutions were given by Clausen, Blasius, Nicolai and Tchentsov. Such a behaviour of force corresponds to the existence of a potential and the system is conservative. In many cases, however, the behaviour of applied loading leads to non-conservative problems of elastic stability. One of the simplest examples — prismatic bar compressed by a tangential (follower) force — was solved by M. Beck [1] who used the kinetic criterion of stability. Z. Kordas and M. Zyczkowski [2] generalized this solution for any value of the tangency coefficient η, determined by Fig. 1.
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