Abstract:The counterpart for Euler’s buckling problem is Greenhill’s problem, which studies the forming of a loop in an elastic beam under torsion. In the context of twisted shafts, the optimal shape of the beam along its axis is searched. A priori form of the cross-section remains unknown. For the solution of the actual problem, the stability equations take into account all possible convex and simply connected shapes of the cross-section. The cross-sections are similar geometric figures related by a homothetic transfo… Show more
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