PTAF Polygon Tessellation to Approximate Frame. A Method for the Design and Analysis of Complex Frames

Abstract

Complex frames are difficult to model because there are so many elements and redundant load paths. In order to explore the realm of complex frames, there needs to be a technique for approximate modelling to allow for rapid analysis with dependable accuracy. This thesis proposes the Polygon Tessellation to Approximate Frame (PTAF) method for rapid structural analysis of the Living Architecture Systems (LAS) group’s complex frames.

The PTAF method uses the LAS composition design polygons as inputs for a parametric script that generates a simplified frame model. This model can be used for Finite Element Analysis (FEA) because it has perfect connectivity. By simplifying the model, the analysis can be run quickly on conventional computer hardware. In this way, structural performance can be evaluated without significant time investment. Especially in the early stages of the design process, it is important to quickly receive reasonably accurate predictions of performance because the design is constantly evolving.

To simplify the model, each component of the frame are reduced to a few beam elements that closely approximate the behaviour of much more detailed models. The process of linear FEA relates the force exerted on a model to the displacement it will undergo by its stiffness. The detailed and coarse models were subjected to the same support and loading conditions so that the displacement could be measured, and a function of error between the two displacements could be made. By minimizing the error between detailed and course models, values for the equivalent stiffness of each component can be derived. By enforcing continuity, the behaviour at the component scale can be used to predict behaviour at the global scale. In this way, the global simplified model will approximate the behaviour of the frame.

This research started through a collaboration with the LAS on the Amatria installation at Luddy Hall. The goal of the collaboration was to add value to the project through the addition of structural analysis in the design process. The frame of Amatria was immensely complex, full analysis of the frame would be prohibitively expensive, and add an unreasonable amount of time to the design process. This research was able to benefit the project by analyzing key components to ensure adequate strength and stiffness to facilitate ease of construction. Lessons learned from this projected helped inform this method’s development.

This research provided the possibility of self-supporting LAS structures, based on the system of components currently being used in LAS testbeds. A pavilion study was used as a thought experiment of how the combination of parametric modeling and approximate analysis could be used to design a free standing pavilion with LAS component construction. Participation in future testbeds will undoubtedly provide invaluable information to refine this method.