Singular configurations of structural systems

A singular con_guration of a structural system is characterized by rank de_ciency of the equilibrium matrix and kinematic matrix "the rank is lower than both the number of degrees of freedom and the number of constraints#[ Such con_gurations exist only in systems that are not geometrically invariant "underconstrained structural systems#[ Most interesting among them are systems with in_nitesimal mobility which attracted attention of many prominent researchers[ This paper puts the entire issue in a di}erent perspective by addressing a critical\ yet so far unexplored\ aspect of singular con_gurations*their real! izability[ It turns out that the only generic\ physically realizable type of a singular con_guration is a system with _rst!order in_nitesimal mobility\ and even this cannot be constructed without inducing prestress of _nite magnitude[ All other singular con_gurations "unprestressable _rst!order mechanisms^ higher!order mechanisms^ and singular con_gurations of _nite mechanisms# are unrealizable[ Moreover\ short of exact or symbolic calculation\ they are also noncomputable and are just formal analytical constructs