An interactive implementation of algebraic graphic statics for geometry-based teaching and design of structures

Maia Avelino R., Lee J., Van Mele T. and Block P.
Proceedings of the International fib Symposium on the Conceptual Design of Structures 2021
Attisholz Areal, Switzerland
2021
doi: 10.35789/fib.PROC.0055.2021.CDSymp.P054

This paper presents an interactive implementation of graphic statics, which can be integrated into a CAD environment. Graphic statics is a well-known design and analysis method for two-dimensional discrete structures that rely on geometrical rather than an analytical representation of the relation between the structure's geometry and the equilibrium of its internal forces. The method was formalised in the 19th century but slowly disappeared from structural engineering practice over the 20th century. Recent developments have introduced Algebraic Graph Statics (AGS), which formulates the geometrical relationship between the graph representations of the reciprocal form and force diagrams in graphic statics using linear algebra. AGS and its extensions enable automatic construction of force diagrams from given form diagrams and allow a few basic modifications of the force diagram from which the form diagram is updated. This paper builds on the previous work of AGS by implementing a real-time, bi-directional workflow allowing users to impose various constraints, and perform geometrical modifications in either the form or force diagram from which the other is automatically updated by using an iterative geometric solver. The presented implementation of interactive AGS provides a robust computational back-end to harness the advantages of traditional graphic statics for geometry-based teaching and design of structures.