Derivation of methods and knowledge in structures by combinatorial representations

The paper develops an isomorphic discrete mathematical model (combinatorial representation), for skeletal structures on the basis of the graph theory. The main advantage offered by establishing such a representation for an engineering system is that once the graph representation is constructed, the knowledge embedded in it becomes available for use by the engineering community. In the paper, an analysis method for skeletal structures is derived from the known method in graph theory, called - mixed variable method, while for the first time being applied to multidimensional systems. Known methods in structural mechanics can also be derived, and it is demonstrated by showing that the conjugate frame and beam theorems are special cases of the duality property in graph theory. The paper discusses new avenues of research and practical applications that are provided by this approach.

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