Formation of graph models for regular finite element meshes

Abstract

Graph theory has many applications in structural mechanics and there are also numerous topological transformations which make the related problems simpler. The skeleton graph and natural associate graph of finite element models are among such transformations. These transformations can efficiently be used for nodal and element ordering of regular finite element models. Natural associate graph and its mesh basis play a key role in optimal finite element analysis by combinatorial force method. In this paper, an efficient method is presented for generation of skeleton graph, natural associate graph as well as their mesh bases for finite elements models, using graph and digraph products.