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 and methods embedded in each representation and the connections between them were investigated thoroughly, after which they were associated with various engineering systems to solve related engineering problems. The CR developed up until now are based on graph theory, matroid theory, and discrete linear programming, whereas the current paper employs only the first two. The approach opens up new ways of working with representations, reasoning and design, some of which are reported in the paper, as follows: 1) Integrated multidisciplinary representation—systems which contain interrelating elements from different disciplines are represented by the same CR. Consequently, a uniform analysis process is performed on the representation, and thus on the whole system, irrespective of the specific disciplines, to which the elements belong. 2) 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 the CR. This enables development of a meta-representation for engineering as a whole, through which the engineering reasoning becomes convenient. In the current paper, this issue is illustrated on structural analysis. 3) Deriving novel connections between remote fields—new connections are derived on the basis of the relations between the 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 several new avenues of research, since knowledge and algorithms from machine theory are now available for use in structural analysis and vice versa. Furthermore, it has opened opportunities for developing new design methods, in which, for instance, structures with special properties are developed on the basis of known mechanisms with special properties, as demonstrated in this paper. Conversely, one can use these techniques to develop special mechanisms from known trusses.