PolyFrame, Efficient Computation for 3D Graphic Statics. (May 2021) - Nejur, Andrei; Akbarzadeh, Masoud
Abstract: In this paper, we introduce a structural form finding plugin called PolyFrame for the Rhinoceros software. This plugin is developed based on the methods of 3D Graphic Statics and Polyhedral Reciprocal Diagrams. The computational framework of this plugin uses new robust and efficient algorithms for the creation and modification of complex funicular, compression-only structural forms and is freely available for students, designers, researchers, and practitioners in the fields of architecture, structural engineering, mechanical engineering, and material science. The geometry-based structural design methods are one of the most intuitive yet powerful structural design methods that have recently been extended to 3D based on the Principles of the Equilibrium of Polyhedral Frames. Still, the increased geometrical complexities of the polyhedral diagrams hinder more in-depth practical applications and the research in this field. The framework proposed in this paper can manage, in near real-time, the creation and transformation of reciprocal polyhedral diagrams with a large number of elements as form and force diagrams for structural design purposes. The paper also introduces a hybrid object-oriented data structure that extends and generalizes the previously proposed approaches and thus allows the users to incorporate a variety of different geometric constraints, including edge lengths and the location of the supports from the initial stages of design. Additionally, a new parallel manipulation algorithm is introduced that is capable of transforming polyhedral diagrams while preserving the edge directions and face normal. As a result, a designer can effectively manipulate both structural form and its force distribution without breaking their reciprocity. Highlights: A robust iterative method is provided for compression-only form finding of 3D graphic statics The framework can handle convex polyhedral cells with a large number (100k) of face elements An object-oriented, hybrid data structure allows for an effective access to various components Proposed algorithm constructs diagrams with multiple competing geometric constraints The algorithm uses a new damping function that can significantly reduce self-intersections The parallel manipulation algorithm transformations polyhedral systems without breaking reciprocity