A Problem in Applied Topology: on the Selection of Cycles for the Flexibility Analysis of Skeletal Structures

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Abstract
A theory of generalized statical bases is developed for use in the flexibility methods as applied to skeletal structural problems. It is shown that any maximal linearly independent set of cycles of the integral cycle group of a linear graph model of the structure may be used in the formation of a statical basis. Such a set of simple cycles is found by embedding this graph into a two-dimensional polyhedron. Cell complexes are formed so that the simple cycles bounding the 2-cells correspond to substructures on which a statical basis may be constructed. Two methods are given for the construction of the embeddings. In one a collapsible complex is formed from a union of a set of disks; while in the other the embedding is into an orientable manifold which is modified to form an admissible complex.

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