Algebraic and Combinatorial Graph Theory for Optimal Structural Analysis

Abstract

For an efficient analysis of structures, the corresponding matrices should be sparse, well conditioned, and well structured. Analysis having these properties for structural matrices is called an optimal analysis. Such analysis becomes more and more important as the number of nodes and members of the structure increases. In this paper, applications of graph theory, algebraic graph theory, and matroids are presented for optimal analysis of the structures. These methods are used either separately or in hybrid forms. Applications are extended to finite element nodal ordering using ten topological transformations.