![Sample our Geography journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5937/TOC-Subject-Sample-2021-Geography.jpg"})
Abstract
Most finite elements have variables associated with corner nodes. However, families of equilibrium and hybrid elements exist that have connections on sides, or interfaces, and retain the corner nodes only to describe the geometry. The aim of this paper is to combine concepts from finite elements and graph-theory so that models composed of such elements can be rigorously derived. Two tree graphs are introduced to each element to represent two distinct types of generalized through (forces and moments) and across (translations and rotations) variables. These variables are termed basic and higher-order and are associated with element properties in the form of mukiterminal representations. The terminal equations couple the variables from the two graphs, and are based on weak integral forms, although discrete versions based on graph-theoretic models are also possible. The variables satisfy vertex and circuit laws for each system graph as built up from connected elements, along with driver edges that represent specified loads and displacements. Graph-theory issues are invoked to obtain independent equations for stiffness and flexibility methods of analysis.