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.
Combinatorial Representations in Structural Analysis
