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

A theory of generalized statical bases is developed for usein the flexibility methods as applied to skeletal structuralproblems. It is shown that any maximal linearly independentset of cycles of the integral cycle group of a linear graphmodel of the structure may be used in the formation of a staticalbasis. Such a set of simple cycles is found by embedding thisgraph into a two-dimensional polyhedron. Cell complexes areformed so that the simple cycles bounding the 2-cells correspondto 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 setof disks; while in the other the embedding is into an orientablemanifold which is modified to form an admissible complex.