Deriving structural theorems and methods using Tellegen's theorem and combinatorial representations

Abstract The paper shows that there are theorems and methods in structural engineering that can be derived from Tellegen's theorem of network graphs. This is demonstrated by deriving from this theorem, Betti's law and the known method for analyzing displacements of truss joints. This work is a part of a general research approach in accordance with which combinatorial representations (CR) were developed and then applied to represent various engineering systems. In doing so, new connections between engineering fields that traditionally are considered to be unrelated are found. These connections enable augmentation of engineering knowledge in one engineering field by using analogous knowledge from another. This issue is demonstrated in the paper by applying knowledge and methods from electricity to structural mechanics and from machine theory to truss analysis on the basis of the connections between the corresponding CR of these fields.

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