Conceptual Design Technique Employing Graph Theoretic Duality

The work reported in the paper employs a general approach of associating engineering domains with general discrete mathematical models, called – graph representations. Once the engineering system is represented by a graph representation, all the reasoning processes upon the system are substituted by a reasoning of a more mathematical nature over the graph representation. Accordingly, graph representations were shown to be a unified mathematical framework for a variety of engineering domains. One of the strongest features of graph representations is the mathematical duality relation between their different types. It was proved in the previous works that duality relations between the representations, yield relations between engineering systems belonging to similarly unrelated disciplines. These relations will be employed in this paper to establish an efficient design technique, by means of which existing engineering designs are transformed to related engineering disciplines. The idea behind the technique introduced in the paper is first to transform the given design problem to a problem in its dual engineering domain. Then, if a solution exists in the dual domain, it is transformed back to the original engineering domain, yielding the solution to the original problem. This technique has already been applied to solve diverse design problems. The paper introduces two design cases, involving the fields of machine theory, structures and MEMS.