Network Graph Theory Perspective on Skeletal Structures for Theoretical and Educational Purposes

Abstract

The paper introduces an approach to the analysis of skeletal structures in which they are represented by a discrete mathematical model called graph representation. The paper shows that the reasoning upon the structure can be performed solely upon the representation, which, besides the theoretical value, presents a powerful educational tool. Students can learn skeletal structures entirely through the graph representations and derive advanced structural topics, including the conjugate theorem and the unit force method from the theorems and principles of network graph theory. The graph representations used in the paper for structures have also been applied to represent systems from different engineering disciplines. This provides students with a multidisciplinary perspective on analysis of engineering systems in general, and skeletal structures in particular.