About PolyFrame 2

PolyFrame 2 is a geometry-based, structural form-finding plugin for Rhinoceros3d and Grasshopper implementing polyhedron-based 3D graphic statics. PolyFrame 2 is developed and maintained by Polyhedral Structures Laboratory (PSL) at Weitzman School of Design, University of Pennsylvania.

This new version incorporates a Grasshopper plug-in that not only makes all previous functions available to Grasshopper, but also introduces a variety of new features including tension-compression-combined form-finding, algebraic 3D graphic statics, matrix static and kinematic analysis, scripting interface, built-in examples, and a lot more. The algebraic approach greatly expands the solution space and allows for flexible manipulations of form and force diagrams based on the geometric degrees of freedom. The matrix analysis tools provide additional methods for evaluating the static and kinematic behaviors of the form-finding results.

PolyFrame 2 is built upon the foundational work of PolyFrame by Dr. Andrei Nejur and Dr. Masoud Akbarzadeh.

Team

Yao Lu

Masoud Akbarzadeh

Other Contributors

Dr. Andrei Nejur, Associate Professor of Architecture at the University of Montreal
Dr. Mathias Bernhard, Senior Scientist at ETH Zurich
Dr. Mostafa Akbari, Assistant Professor at Texas A&M
Dr. Márton Hablicsek, Assistant Professor of Mathematics at Leiden University

Lu, Yao, Hablicsek, Márton, and Masoud, Akbarzadeh. "Algebraic 3D Graphic Statics with Edge and Vertex Constraints: A Comprehensive Approach to Extending the Solution Space for Polyhedral Form-Finding".Computer-Aided Design, 166:103620, Jan 2024. doi: 10.1016/j.cad.2023.103620 (1) (Algebraic polyhedral graphic statics, vertex and edge constraints)

@article{Lu_Hablicsek_Akbarzadeh_2024,
    title        = {Algebraic 3D Graphic Statics with Edge and Vertex Constraints: A Comprehensive Approach to Extend the Solution Space for Polyhedral Form-Finding},
    author       = {Lu, Yao and Hablicsek, Márton and Akbarzadeh, Masoud},
    year         = 2024,
    month        = jan,
    journal      = {Computer-Aided Design},
    volume       = 166,
    pages        = 103620,
    doi          = {10.1016/j.cad.2023.103620},
    issn         = {0010-4485},
}

Akbarzadeh, Masoud. 2016. “3D Graphical Statics Using Reciprocal Polyhedral Diagrams.” PhD Thesis. ETH Zurich. doi:10.3929/ETHZ-A-010867338. (1) (Theoretical framework of polyhedral graphic statics)

@phdthesis{Akbarzadeh_2016,
    title        = {3D Graphical Statics Using Reciprocal Polyhedral Diagrams},
    author       = {Akbarzadeh, Masoud},
    year         = 2016,
    pages        = {200 p.},
    doi          = {10.3929/ETHZ-A-010867338},
    url          = {http://hdl.handle.net/20.500.11850/183500},
    rights       = {http://rightsstatements.org/page/InC-NC/1.0/, info:eu-repo/semantics/openAccess},
    school       = {ETH Zurich},
    language     = {en}
}

Nejur, Andrei, and Masoud Akbarzadeh. 2021. “PolyFrame, Efficient Computation for 3D Graphic Statics.” Computer-Aided Design 134 (May): 103003. doi:10.1016/j.cad.2021.103003. (1) (First version of PolyFrame, Rhino commands)

@article{Nejur_Akbarzadeh_2021,
    title        = {PolyFrame, Efficient Computation for 3D Graphic Statics},
    author       = {Nejur, Andrei and Akbarzadeh, Masoud},
    year         = 2021,
    month        = may,
    journal      = {Computer-Aided Design},
    volume       = 134,
    pages        = 103003,
    doi          = {10.1016/j.cad.2021.103003},
    issn         = {0010-4485},
    language     = {en}
}

Hablicsek, Márton, Masoud Akbarzadeh, and Yi Guo. 2019. “Algebraic 3D Graphic Statics: Reciprocal Constructions.” Computer-Aided Design 108 (March): 30–41. doi:10.1016/j.cad.2018.08.003. (1) (Theoretical framework of algebraic polyhedral graphic statics)

@inproceedings{Zhi-2023-Overhang,
    title = {Local optimization of self-supporting shell structures in 3D printing: a skeleton method},
    booktitle = {Proceedings of IASS 2023 symposium Integration of Design and Fabrication},
    author = {Zhi, Yefan and Chai, Hua and Teng, Teng and Akbarzadeh, Masoud},
    year = {2023},
    month = {July 10-14},
    address = {Melbourne, Australia}
}

Akbari, Mostafa, Armin Mirabolghasemi, Mohammad Bolhassani, Abdolhamid Akbarzadeh, and Masoud Akbarzadeh. 2022. “Strut-Based Cellular to Shellular Funicular Materials.” Advanced Functional Materials 32 (14): 2109725. doi:10.1002/adfm.202109725. (1) (Shellular structure made with polyhedral graphic statics)

@article{Akbari_Mirabolghasemi_Bolhassani_Akbarzadeh_Akbarzadeh_2022,
    title        = {Strut-Based Cellular to Shellular Funicular Materials},
    author       = {Akbari, Mostafa and Mirabolghasemi, Armin and Bolhassani, Mohammad and Akbarzadeh, Abdolhamid and Akbarzadeh, Masoud},
    year         = 2022,
    journal      = {Advanced Functional Materials},
    volume       = 32,
    number       = 14,
    pages        = 2109725,
    doi          = {10.1002/adfm.202109725},
    issn         = {1616-3028},
    language     = {en}
}

Acknowledgements

This work is funded by the National Science Foundation CAREER Award (NSF CAREER-1944691) awarded to Dr. Masoud Akbarzadeh, and Thomas Jefferson University Faculty Seed Grant awarded to Dr. Yao Lu.