Developing a polyhedral graphic statics formulation for tetrahedral truss analysis

Abstract

This paper presents procedures to generate tetrahedral truss topologies as an input form for polyhedral graphic statics and develops an algebraic formulation to construct their force diagrams. The recent algebraic 3D graphic statics constructs reciprocal polyhedral diagrams with either form or force as input. However, the input is usually a set of polyhedrons or self-stressed networks. Another implementation of polyhedral graphic statics includes general truss topologies. Nevertheless, the starting geometry is usually the global force diagram and based on its modification or subdivision, a form is constructed. Therefore, currently, there exists no formulation to analyze a spatial truss using polyhedral graphic statics. This paper develops an algorithm to build upon the algebraic 3D graphic statics formulation to construct the force diagram and analyze spatial trusses that are not self-stressed structures. The article also shows how the proper definition of the external spaces between the applied loads and reaction forces and the tetrahedral subdivision of the truss make it possible to construct the reciprocal force diagram.