1. Mechanical Behavior of Polyhedral Frames
This research investigates the mechanical behavior of funicular polyhedral frames designed by 3DGS.
Although 3DGS allows exploring static equilibrium of variety of non-conventional funicular solutions in three dimensions, it does not include material properties and self-weight of the members. Therefore, the mechanical behavior of the spatial funicular forms must be evaluated using additional analytical models based on the assigned material properties and various loading cases other than the design loads. The primary objective of this research is to:
validate the results of the applied 3DGS using numerical calculations;
define the type and magnitude of the internal stresses under various loading scenarios their self-weight, ultimate load-bearing capacity, and failure mechanism;
and predict the failure mechanisms and suggest possible improvement in the system
2. Constrained Manipulation of Polyhedral Systems
Modeling or manipulating polyhedral geometry in the context of 3D Graphic Statics and reciprocal polyhedral diagrams, either as the form or force diagram, is not a trivial task. This research presents a method for the manipulation of groups of polyhedral cells that allows geometric transformation while preserving the planarity constraints of the cells and maintaining the equilibrium direction of the edges for the reciprocity of the diagrams. The work expands on previously investigated single-cell manipulations and considers the effects of these transformations in adjacent cells and the whole system. All the transformations addressed in the research maintain the topological relations of the input complex. The result of this research can be applied to both form and force diagrams to investigate various geometric transformations resulting in convex, concave or complex (self-intersecting) polyhedra as a group. The product of this research allows intuitive user interaction in working with form and force diagrams in the early stages of geometric structural design in 3D.
3. 3D Graphic Statics: procedural construction
This research investigates the geometric procedures of 3D Graphic Statics using reciprocal polyhedral diagrams. The concentration is in the procedural construction of the reciprocal form and force diagrams in polyhedral space. The design and analysis methods developed in this research are equivalent to the existing methods of 2D Graphic Statics; it includes the topics such as constrained form finding, funicular polyhedral construction, etc.Triskeles bridge is a conceptual design of a funicular spatial bridge that spans over three support locations in Lauterbrunnen, Switzerland. The structural form of this bridge is derived using 3D Graphic Statics method using reciprocal polyhedral diagrams. The largest span of the bridge is 150 m. The bridge has a depth of 12 m in its deepest part. The funicular form and force diagrams constrained to three support locations include compression (blue spectrum) and tensile members (red). Note that the original form and force diagrams include additional tensile members connecting three supports. reducing these elements from the geometry of form requires additional pre-stressing force to be applied at the supports to guarantee the equilibrium.