The multidisciplinary combinatorial approach (MCA) and its applications in engineering

ABSTRACT. The current paper describes the Multidisciplinary Combinatorial Approach (MCA), the idea of which is to develop discrete mathematical representations, called “Combinatorial Representations” (CR) and to represent with them various engineering systems. During the research, the properties of each representation and the connections between them were investigated thoroughly, after that they were associated with various engineering systems in order to solve related engineering problems. The CR developed up until now are based on graph theory, matroid theory and discrete linear programming. The approach opens up new ways of working with representations, reasoning and design, some of which are reported in the paper, as follows: Multidisciplinary representation – systems which contain elements from different fields are represented by the same CR. Consequently, a uniform analysis process is performed on the representation, and thus on the whole system, without concerning about the specific disciplines the elements belong to. Deriving known methods and theorems – new proofs to known methods and theorems are derived in a new way, this time on the basis of the combinatorial theorems embedded in CR. This enables to develop a meta representation of engineering as a whole, through which the engineering reasoning will become convenient. In the current paper this issue is illustrated on structural analysis. Deriving novel connections between remote fields – new connections are derived on the basis of the relations between different combinatorial representations. An innovative connection between mechanisms and trusses, shown in the paper, has been derived on the basis of the mutual dualism between their corresponding CR. This new connection alone has opened new avenues of research, since knowledge and algorithms from machine theory are now available for usage in structural analysis and vice versa. Furthermore, it opened opportunities for developing new design methods, in which structures with special properties are developed based on known mechanisms with special properties and vice versa, as demonstrated in the paper.