On the physical realizability of singular structural systems

Abstract

Analytical models of structural systems allow for exceptional, singular geometric configurations, characterized by rank deficiency of the equilibrium and kinematic matrix. The feasibility of physical and numerical realization of such configurations depends on the type of singularity–generic vs. nongeneric. It turns out that some interesting, theoretically predicted and thoroughly studied, types of singular configurations (systems with simultaneous statical and kinematic indeterminacy; unprestressable first-order mechanisms; all higher-order mechanisms; singular configurations of finite 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 configurations are just purely formal constructs. Moreover, their attempted implementation would produce a generic prototype with `essentially' different 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.