On the physical realizability of singular structural systems

Analytical models of structural systems allow for exceptional, singular geometric con®gurations, characterized by rank de®ciency of the equilibrium and kinematic matrix. The feasibility of physical and numerical realization of such con®gurations depends on the type of singularity±generic vs. nongeneric. It turns out that some interesting, theoretically predicted and thoroughly studied, types of singular con®gurations (systems with simultaneous statical and kinematic indeterminacy; unprestressable ®rst-order mechanisms; all higher-order mechanisms; singular con®gurations of ®nite mechanisms; and kinematically mobile closed polyhedral surfaces) are nongeneric, hence, physically unrealizable and noncomputable (except for exact or symbolic calculation). Thus, in spite of their sometimes remarkable theoretical features, these systems and con®gurations are just purely formal constructs. Moreover, their attempted implementation would produce a generic prototype with `essentiallyʹ di€erent properties, including structural response. A few of the somewhat unexpected implications of this observation are discussed and a complete set of analytical criteria for the four statical-kinematic types of realizable structural systems is presented.