Geometric Degrees of Freedom and Non-conventional Spatial Structural Forms

This paper expands on the Geometric Degrees of Freedom (GDoF) in the context of geometry-based structural form finding and emphasizes its importance in finding non-conventional architectural structures in three-dimensional space. Using GDoF allows a designer to find various iterations of a network, each representing a unique design within the state of equilibrium and explore the non-conventional solutions particularly for funicular polyhedrons of 3D graphic statics. The paper briefly explains a method to find the GDoF of a given network consisting of closed polygons in 2D or 3D and applies the same method in finding the GDoF of reciprocal polyhedral diagrams of 3D graphic statics and expands on their non-trivial geometric transformations with their planarity constraints. The paper goes beyond the GDoF and provides a method to parameterize all the members of a network by assigning weights to all edges in a network to control the design properties of the solutions. For instance, a synclastic, compression-only shell can turn into an anticlastic compression-and-tension combined shell with the same magnitude of internal forces and external loads reciprocal to the same force distribution/diagram (Fig. 1). Using this technique in the context of 3D graphic statics allows a designer to find non-conventional spatial structural solutions with both compression and tension members with planar faces for architectural/structural design purposes.