On the physical realizability of singular structural systems

Unified classification of stability of pin-jointed bar assemblies

“…Although ''statickinematic analysis'' is also called ''geometrical stability'' (e.g. Kuznetsov, 1999Kuznetsov, , 2000, the majority of such studies have begun with purely geometrical views, and not from the viewpoint of structural stability. Research on this issue can be traced back to the work of Maxwell (1890), who defined the static and kinematic behaviour of pin-jointed bars system purely by a simple relationship between number of joints, bars and kinematic constraints.…”

“…It should be noted that Kuznetsov (1999Kuznetsov ( , 2000 presented a novel perspective about the physical realisability and exact computability of such singular system based on mathematic concepts of structural stability (unrelated to structures). In his viewpoints, as the degenerated configurations of geometrically invariant or variant systems, infinitesimal mechanisms are always sensitive to the minute changes of control parameters such as linear and angular sizes of the structural members (i.e.…”

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“…Determination of the finite nature of a mechanism in general requires nonlinear analysis [Tarnai 1989;Calladine and Pellegrino 1992;Salerno 1992;Connelly and Servatius 1994;Tarnai and Szabó 2000;Garcea et al 2005]. Kuznetsov [2000] has stressed the difficulties that may arise with 'singular' (e.g., highly symmetric) configurations, but nonetheless, the behaviour at points of high symmetry is often a useful guide to that of physical systems, where the symmetry may be only approximate. Kangwai and Guest [1999] introduced, for specific symmetric cases, a criterion that could determine the finiteness of a mechanism based on purely first-order analysis combined with a symmetry argument, and has proved to be applicable to a wide variety of structures [Kovács et al 2004;Fowler and Guest 2005].…”

Stability Conjecture in the Theory of Tensegrity Structures

“…An extensive work has been performed in this direction by Kebiche et al 13 Murakami, 21,22 Oppenheim and Williams, 23 Wang, 40 Yuan and Dong, 41 Volokh 33,34 and Volokh et al 39 The intriguing feature of tensegrity structures is their stability at the initial self-stress state (prestressability) in the known computational and practical examples. 18,27 The latter raises general theoretical question: are all tensegrity assemblies with tensioned cables and compressed struts stable independently of their topology, geometry and specific magnitudes of member forces? The positive answer to this question is conjectured in this note.…”