Algebraic Graph Statics

Van Mele T. and Block P.
Computer-Aided Design
2014
doi: 10.1016/j.cad.2014.04.004

This paper presents a general, non-procedural, algebraic approach to graphical analysis of structures. Using graph theoretical properties of reciprocal graphs, the geometrical relation between the form and force diagrams used in graphic statics are written algebraically. These formulations have been found to be equivalent to the equilibrium equations used in matrix analysis of planar, self-stressed structural systems. The significance and uses of this general approach are demonstrated through several examples and it is shown that it provides a robust back-end for a real-time, interactive and flexible computational implementation of traditional graphic statics.