Expansion Process in Mathematics and Structural Mechanics

The idea of expansion has a long history in mathematics and structural mechanics. In mathematics, Whitehead [1] used an expansion process for the characterization of topological spaces. In structural mechanics, Müller Breslau and Henneberg [2,3] employed simple expansion for the classification of trusses. In this paper, the latter idea is generalized and applied to the calculation of degree of statical indeterminacy (DSI) and degree of kinematical indeterminacy (DKI) of different types of skeletal structures, such as rigid-jointed planar and space frames, pin-jointed planar trusses and ball-jointed space trusses. Such a calculation not only simplifies the evaluation of DSI and DKI, but it also provides an insight to the problem of the formation of sparse statical and kinematical basis matrices required for efficient analysis of structures by the force method and displacement approach, respectively.