Representing and analysing integrated engineering systems through combinatorial representations

Abstract

The current paper introduces a systematic method for representing and analysing coupled integrated engineering systems by means of general discrete mathematical models, called Combinatorial Representations, that can be conveniently implemented in computers. The combinatorial representation of this paper, which is based on graph theory, was previously shown to be useful in representing engineering systems from different engineering domains. Once all of the subsystems of an integrated multidisciplinary system are brought up to the common level of the combinatorial representation, they cease to be separated from one another and the analysis process is applied to all of the engineering elements disregarding the domain to which they belong.During the development of the representation and study of its inherent properties, special attention was dedicated to developing an efficient analysis method. A vectorial extension of the mixed variable method known from electrical network theory was found to be the most suitable choice for this purpose.In the paper, the approach is implemented by representing and analysing two systems: one that is a macro system comprised of truss, dynamic and electric elements, and another that is a comb-driven micro-resonator. The techniques presented in the paper are not limited to analysis only, but can be applied to many other aspects of engineering research. Among them is a systematic derivation of new ways of presenting engineering elements, one of which – the process of derivation of a new type of force representation entitled “face force” – is described in the paper.