Ayrık Kabuk Tasarımı Çalışmaları için Form Bulma ve Çok Amaçlı Optimizasyon Yaklaşımı
Year 2025,
Volume: 10 Issue: 2, 917 - 937, 27.12.2025
Arda Ağırbaş
,
Seçkin Kutucu
Abstract
Bu çalışma, ayrık kabuk tasarımlarında form bulma, yapısal performans değerlendirmesi ve mimari form ile üretim maliyetinin eş zamanlı olarak optimize edilmesini amaçlayan uyarlanabilir bir hesaplamalı yöntem sunmaktadır. Önerilen yaklaşım, mekansal ve işlevsel gereksinimler dikkate alınarak mimari ve yapısal kısıtlar altında dengeli tasarım alternatifleri üretmektedir. Yöntem kapsamında çok amaçlı evrimsel bir optimizasyon iş akışı geliştirilmiştir. Gevşeme tabanlı form bulma süreci verilen bir başlangıç geometrisinden hareketle denge şekillerini elde ederek ahşap kaset elemanlardan oluşan bir ayrık kabuk tasarlamaktadır. Sonlu eleman analiz modeli ise deformasyon analizi ile düğüm noktalarındaki yer değiştirmeleri değerlendirmektedir. Mekansal kullanım ile ilgili ilgili mimari kısıtlar ve sistem stabilitesine ilişkin yapısal kısıtlar, karar değişkenleri ile birlikte optimizasyon sürecine entegre edilmektedir. Optimizasyon algoritması, üretim maliyetini en aza indirirken, sürekli bir mimari kabuk yüzeyinin geometrik özelliklerine yüksek benzerlik gösteren ayrık kabuk formlarını üretmeyi hedeflemektedir. Yöntemin uygulanabilirliği, iki farklı ayrık kabuk tasarım senaryosu üzerinden test edilerek uygun tasarım alternatifleri ortaya konmuştur.
References
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Adriaenssens, S., Block, P., Veenendaal, D. & Williams, C. (2014). Shell structures for architecture: Form finding and optimization. London: Routledge.
-
Agirbas, A., & Alakavuk, E. (2020). Facade optimization for an education building using multi-objective
evolutionary algorithms. Light & Engineering, (03–2020), 41–50. https://doi.org/10.33383/2020-047
-
Aish, R., Fisher, A., Joyce, S. & Marsh, A. (2012). Progress towards multi-criteria design optimisation using
DesignScript with SMART form, robot structural analysis and Ecotect building performance analysis.
Proceedings of ACADIA, 47–56.
-
Augustynowicz, E. & Aigner, N. (2023). Building from Scrap: Computational Design and Robotic Fabrication
Strategies for Spatial Reciprocal Structures from Plate-shaped Wooden Production Waste. Journal of
Architectural Sciences and Applications, 8(1), 38–53. https://doi.org/10.30785/mbud.1244395
-
Bechert, S., Sonntag, D., Aldinger, L. & Knippers, J. (2021). Integrative structural design and engineering
methods for segmented timber shells—BUGA Wood Pavilion. STRUCTURES, 34, 4814–4833. DOI:
https://doi.org/10.1016/j.istruc.2021.10.032
-
Bletzinger, K. U., Wüchner, R., Daoud, F. & Camprubí, N. (2005). Computational methods for form finding and
optimization of shells and membranes. Computer Methods in Applied Mechanics and Engineering, 194(30–
31), 3438–3452 DOI: https://doi.org/10.1016/j.cma.2004.12.026
-
Block, P. (2009). Thrust Network Analysis: Exploring Three-dimensional Equilibrium (PhD thesis).
Massachusetts Institute of Technology. Access Address (15.07.2025):
https://dspace.mit.edu/handle/1721.1/49539
-
Block, P., Knippers, J., Mitra, N. J. & Wang, W. (2015). Advances in Architectural Geometry 2014. Springer
International Publishing. DOI: https://doi.org/10.1007/978-3-319-11418-7
-
Block, P., Van Mele, T., Liew, A., DeJong, M., Escobedo, D. & Ochsendorf, J. A. (2018). Structural design, fabrication
and construction of the Armadillo vault. The Structural Engineer: Journal of the Institution of Structural
Engineer, 96(5), 10–20. Online ISSN: 1466-5123. Access Address (15.07.2025):
https://dialnet.unirioja.es/servlet/articulo?codigo=6529582
-
Brownlee, A. E. I., & Wright, J. A. (2015). Constrained, mixed-integer and multi-objective optimisation of
building designs by NSGA-II with fitness approximation. Applied Soft Computing, 33, 114–126.
https://doi.org/10.1016/j.asoc.2015.04.010
-
Boylu, E. E. & Ekinci, S. (2024). Examination of Material Selection’s Effect on Lighweightness on Structures.
Journal of Architectural Sciences and Applications, 9(2), 798–814. DOI: https://doi.org/10.30785/mbud.1475316
-
Buelow, P. (2002). Using Evolutionary Algorithms to Aid Designer of Architectural Structures. In Creative
Evolutionary Systems, 315–336. DOI: https://doi.org/10.1016/B978-155860673-9/50050-1
-
De Goes, F., Alliez, P., Owhadi, H. & Desbrun, M. (2013). On the equilibrium of simplicial masonry structures. ACM
Transactions on Graphics, 32(4), 1–10. DOI: https://doi.org/10.1145/2461912.2461932
-
Deb, K., Pratap, A., Agarwal, S. & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-
II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197. DOI: https://doi.org/10.1109/4235.996017
-
Echenagucia, T. M. & Block, P. (2015). Acoustic optimization of funicular shells. Proceedings of IASS Annual
Symposia, 2015(13), 1–13.
-
Ertaş, D. G. (2023). A Multi-Dimensional Analysis of The Relationship Between Design and Material in Terms of
Sustainability. Journal of Architectural Sciences and Applications, 8(2), 609–623. DOI:
https://doi.org/10.30785/mbud.1309026
-
Gil-Ureta, F., Pietroni, N. & Zorin, D. (2020). Reinforcement of General Shell Structures. ACM Transactions on
Graphics, 39(5), 1–19. DOI: https://doi.org/10.1145/3375677
-
Huijben, F., Van Herwijnen, F. & Nijsse, R. (2011). Concrete shell structures revisited: Introducing a new ‘low-
tech’construction method using vacuumatics formwork. Textiles Composites and Inflatable Structures V:
Proceedings of the V International Conference on Textile Composites and Inflatable Structures, Barcelona,
Spain. 5-7 October, 2011, 409–420. CIMNE. Access Address (15.07.2025): https://hdl.handle.net/2117/186107
-
Kilian, A. & Ochsendorf, J. (2005). Particle-spring systems for structural form finding. Journal of the
International Association for Shell and Spatial Structures, 46(2), 77–84
-
Krieg, O. D., Schwinn, T., Menges, A., Li, J.-M., Knippers, J., Schmitt, A. & Schwieger, V. (2015). Biomimetic
Lightweight Timber Plate Shells: Computational Integration of Robotic Fabrication, Architectural Geometry
and Structural Design. Advances in Architectural Geometry 2014. DOI: https://doi.org/10.1007/978-3-319-11418-
7_8
-
Liu, Y., Pan, H., Snyder, J., Wang, W. & Guo, B. (2013). Computing self-supporting surfaces by regular
triangulation. ACM Transactions on Graphics, 32(4), 1–10. DOI: https://doi.org/10.1145/2461912.2461927
-
Lozano-Galant, J. A. & Payá-Zaforteza, I. (2011). Structural analysis of Eduardo Torroja’s Frontón de Recoletos’
roof. Engineering Structures. DOI: https://doi.org/10.1016/j.engstruct.2010.12.006
-
Ma, L., He, Y., Sun, Q., Zhou, Y., Zhang, C. & Wang, W. (2019). Constructing 3D Self-Supporting Surfaces with
Isotropic Stress Using 4D Minimal Hypersurfaces of Revolution. ACM Transactions on Graphics, 38(5), 1–13. DOI:
https://doi.org/10.1145/3188735
-
Maden, F. (2015). Novel Design Methodologies for Transfeormable Doubly-Ruled Surface Structures (PhD
thesis) Izmir Institute of Technology. Access Address (15.07.2025):
https://dl.acm.org/doi/abs/10.5555/AAI29205989
-
Miki, M., Adiels, E., Baker, W., Mitchell, T., Sehlström, A. & Williams, C. J. K. (2022). Form-finding of shells
containing both tension and compression using the Airy stress function. International Journal of Space
Structures, 37(4), 261–282. DOI: https://doi.org/10.1177/09560599221102618
-
Miki, M., Mitani, J. & Igarashi, T. (2013). Development of a Grasshopper add-on for interactive exploration of
shapes in equilibrium. Proceedings of IASS Annual Symposia, 2013, 1–6. International Association for Shell and
Spatial Structures (IASS).
-
Millar, C., Mitchell, T., Mazurek, A., Chhabra, A., Beghini, A., Clelland, J. N., McRobie, A. & Baker, W. F. (2023). On
designing plane-faced funicular gridshells. International Journal of Space Structures, 38(1), 40–63. DOI:
https://doi.org/10.1177/09560599221126656
-
Mueller, C., Fivet, C. & Ochsendorf, J. (2015). Graphic statics and interactive optimization for engineering
education. Structures Congress 2015 - Proceedings of the 2015 Structures Congress. DOI:
https://doi.org/10.1061/9780784479117.223
-
Otter, J. R. H., Cassell, A. C. & Hobbs, R. E. (1967). Dynamic Relaxation. Proceedings of the Institution of Civil
Engineers. DOI: https://doi.org/10.1680/iicep.1967.8278
-
Panozzo, D., Block, P. & Sorkine-Hornung, O. (2013). Designing unreinforced masonry models. ACM
Transactions on Graphics, 32(4), 1–12. DOI: https://doi.org/10.1145/2461912.2461958
-
Piker, D. (2013). Kangaroo: Form finding with computational physics. Architectural Design, 83(2), 136–137. DOI:
https://doi.org/10.1002/ad.1569
-
Preisinger, C. & Heimrath, M. (2014). Karamba—A Toolkit for Parametric Structural Design. Structural
Engineering International, 24(2), 217–221. DOI: https://doi.org/10.2749/101686614X13830790993483
-
Rippmann, M. (2016). Funicular Shell Design: Geometric approaches to form finding and fabrication of
discrete funicular structures (PhD thesis) ETH Zurich. Access Address (15.07.2025): https://www.research-
collection.ethz.ch/bitstream/handle/20.500.11850/116926/eth-49131-02.pdf
-
Robeller, C. & Von Haaren, N. (2020). Recycleshell: Wood-only shell structures made from cross-laminated
timber (CLT) production waste. Journal of the International Association for Shell and Spatial Structures, 61(2),
125–139. DOI: https://doi.org/10.20898/j.iass.2020.204.045
-
Schek, H. J. (1974). The force density method for form finding and computation of general networks.
Computer Methods in Applied Mechanics and Engineering. https://doi.org/10.1016/0045-7825(74)90045-0
-
Svoboda, L., Novák, J., Kurilla, L. & Zeman, J. (2014). A framework for integrated design of algorithmic
architectural forms. Advances in Engineering Software, 72, 109–118. DOI:
https://doi.org/10.1016/j.advengsoft.2013.05.006
-
Tang, C., Sun, X., Gomes, A., Wallner, J. & Pottmann, H. (2014). Form-finding with polyhedral meshes made
simple. ACM Transactions on Graphics, 33(4), 1–9. DOI: https://doi.org/10.1145/2601097.2601213
-
TSE. (2022). Yapılar üzerindeki etkiler—Bölüm 1-4: Genel etkiler—Rüzgâr etkileri (eurocode 1) (CEN No. TS EN
1991-1-4/D2). Ankara.
-
Vatandoost, M., Ekhlassi, A., Golabchi, M., Rahbar, M. & von Buelow, P. (2024). Fabrication methods of shell
structures. Automation in Construction, 165, 105570. DOI: https://doi.org/10.1016/j.autcon.2024.105570
-
Vouga, E., Höbinger, M., Wallner, J. & Pottmann, H. (2012). Design of self-supporting surfaces. ACM
Transactions on Graphics, 31(4), 1–11. DOI: https://doi.org/10.1145/2185520.2185583
-
Wang, Z., Song, P., Isvoranu, F. & Pauly, M. (2019). Design and structural optimization of topological interlocking
assemblies. ACM Transactions on Graphics, 38(6), 1–13. DOI: https://doi.org/10.1145/3355089.3356489
-
Whiting, E., Ochsendorf, J. & Durand, F. (2009). Procedural modeling of structurally-sound masonry buildings.
ACM SIGGRAPH Asia 2009 Papers, 1–9. DOI: https://doi.org/10.1145/1661412.1618458
-
Whiting, E., Shin, H., Wang, R., Ochsendorf, J. & Durand, F. (2012). Structural optimization of 3D masonry
buildings. ACM Transactions on Graphics, 31(6), 1–11. DOI: https://doi.org/10.1145/2366145.2366178
-
Zhang, Y., & Wang, R. (2025). Multi-objective optimization of construction based on genetic algorithm NSGA-II.
International Journal of Architectural Computing. 2025;0(0). https://doi.org/10.1177/14780771251335107
A Form-Finding and Multi-Objective Optimization Approach for Discrete Shell Design Studies
Year 2025,
Volume: 10 Issue: 2, 917 - 937, 27.12.2025
Arda Ağırbaş
,
Seçkin Kutucu
Abstract
This study presents an adaptive computational technique that applies form-finding, assesses structural performance, and optimizes architectural form and production cost for discrete shell design. The approach generates design alternatives that balance objectives under architectural and structural constraints, considering spatial and functional needs. To realize the method, a multi-objective evolutionary optimization workflow is formulated. The relaxation-based design method explores equilibrium shapes corresponding to an input geometry to create a discrete shell consisting of timber cassette elements. The finite element analytical model evaluates nodal displacements through large deformation analysis. The architectural constraints related to spatial use and structural constraints regarding system stability are introduced to the optimization workflow alongside the decision variables. The optimization algorithm minimizes production cost while generating a resembling discrete approximation of a continuum architectural surface. The viability of the approach is demonstrated in two distinct cases of discrete shell design problems to create suitable design alternatives.
Ethical Statement
This article, Yasar University, Graduate School of Architecture, produced from ongoing doctoral thesis. The authors would like to express their gratitude to Yasar University for providing the academic environment and resources that supported the development of this work.
The article complies with national and international research and publication ethics. Ethics committee approval was not required for the study.
References
-
Adriaenssens, S., Block, P., Veenendaal, D. & Williams, C. (2014). Shell structures for architecture: Form finding and optimization. London: Routledge.
-
Agirbas, A., & Alakavuk, E. (2020). Facade optimization for an education building using multi-objective
evolutionary algorithms. Light & Engineering, (03–2020), 41–50. https://doi.org/10.33383/2020-047
-
Aish, R., Fisher, A., Joyce, S. & Marsh, A. (2012). Progress towards multi-criteria design optimisation using
DesignScript with SMART form, robot structural analysis and Ecotect building performance analysis.
Proceedings of ACADIA, 47–56.
-
Augustynowicz, E. & Aigner, N. (2023). Building from Scrap: Computational Design and Robotic Fabrication
Strategies for Spatial Reciprocal Structures from Plate-shaped Wooden Production Waste. Journal of
Architectural Sciences and Applications, 8(1), 38–53. https://doi.org/10.30785/mbud.1244395
-
Bechert, S., Sonntag, D., Aldinger, L. & Knippers, J. (2021). Integrative structural design and engineering
methods for segmented timber shells—BUGA Wood Pavilion. STRUCTURES, 34, 4814–4833. DOI:
https://doi.org/10.1016/j.istruc.2021.10.032
-
Bletzinger, K. U., Wüchner, R., Daoud, F. & Camprubí, N. (2005). Computational methods for form finding and
optimization of shells and membranes. Computer Methods in Applied Mechanics and Engineering, 194(30–
31), 3438–3452 DOI: https://doi.org/10.1016/j.cma.2004.12.026
-
Block, P. (2009). Thrust Network Analysis: Exploring Three-dimensional Equilibrium (PhD thesis).
Massachusetts Institute of Technology. Access Address (15.07.2025):
https://dspace.mit.edu/handle/1721.1/49539
-
Block, P., Knippers, J., Mitra, N. J. & Wang, W. (2015). Advances in Architectural Geometry 2014. Springer
International Publishing. DOI: https://doi.org/10.1007/978-3-319-11418-7
-
Block, P., Van Mele, T., Liew, A., DeJong, M., Escobedo, D. & Ochsendorf, J. A. (2018). Structural design, fabrication
and construction of the Armadillo vault. The Structural Engineer: Journal of the Institution of Structural
Engineer, 96(5), 10–20. Online ISSN: 1466-5123. Access Address (15.07.2025):
https://dialnet.unirioja.es/servlet/articulo?codigo=6529582
-
Brownlee, A. E. I., & Wright, J. A. (2015). Constrained, mixed-integer and multi-objective optimisation of
building designs by NSGA-II with fitness approximation. Applied Soft Computing, 33, 114–126.
https://doi.org/10.1016/j.asoc.2015.04.010
-
Boylu, E. E. & Ekinci, S. (2024). Examination of Material Selection’s Effect on Lighweightness on Structures.
Journal of Architectural Sciences and Applications, 9(2), 798–814. DOI: https://doi.org/10.30785/mbud.1475316
-
Buelow, P. (2002). Using Evolutionary Algorithms to Aid Designer of Architectural Structures. In Creative
Evolutionary Systems, 315–336. DOI: https://doi.org/10.1016/B978-155860673-9/50050-1
-
De Goes, F., Alliez, P., Owhadi, H. & Desbrun, M. (2013). On the equilibrium of simplicial masonry structures. ACM
Transactions on Graphics, 32(4), 1–10. DOI: https://doi.org/10.1145/2461912.2461932
-
Deb, K., Pratap, A., Agarwal, S. & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-
II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197. DOI: https://doi.org/10.1109/4235.996017
-
Echenagucia, T. M. & Block, P. (2015). Acoustic optimization of funicular shells. Proceedings of IASS Annual
Symposia, 2015(13), 1–13.
-
Ertaş, D. G. (2023). A Multi-Dimensional Analysis of The Relationship Between Design and Material in Terms of
Sustainability. Journal of Architectural Sciences and Applications, 8(2), 609–623. DOI:
https://doi.org/10.30785/mbud.1309026
-
Gil-Ureta, F., Pietroni, N. & Zorin, D. (2020). Reinforcement of General Shell Structures. ACM Transactions on
Graphics, 39(5), 1–19. DOI: https://doi.org/10.1145/3375677
-
Huijben, F., Van Herwijnen, F. & Nijsse, R. (2011). Concrete shell structures revisited: Introducing a new ‘low-
tech’construction method using vacuumatics formwork. Textiles Composites and Inflatable Structures V:
Proceedings of the V International Conference on Textile Composites and Inflatable Structures, Barcelona,
Spain. 5-7 October, 2011, 409–420. CIMNE. Access Address (15.07.2025): https://hdl.handle.net/2117/186107
-
Kilian, A. & Ochsendorf, J. (2005). Particle-spring systems for structural form finding. Journal of the
International Association for Shell and Spatial Structures, 46(2), 77–84
-
Krieg, O. D., Schwinn, T., Menges, A., Li, J.-M., Knippers, J., Schmitt, A. & Schwieger, V. (2015). Biomimetic
Lightweight Timber Plate Shells: Computational Integration of Robotic Fabrication, Architectural Geometry
and Structural Design. Advances in Architectural Geometry 2014. DOI: https://doi.org/10.1007/978-3-319-11418-
7_8
-
Liu, Y., Pan, H., Snyder, J., Wang, W. & Guo, B. (2013). Computing self-supporting surfaces by regular
triangulation. ACM Transactions on Graphics, 32(4), 1–10. DOI: https://doi.org/10.1145/2461912.2461927
-
Lozano-Galant, J. A. & Payá-Zaforteza, I. (2011). Structural analysis of Eduardo Torroja’s Frontón de Recoletos’
roof. Engineering Structures. DOI: https://doi.org/10.1016/j.engstruct.2010.12.006
-
Ma, L., He, Y., Sun, Q., Zhou, Y., Zhang, C. & Wang, W. (2019). Constructing 3D Self-Supporting Surfaces with
Isotropic Stress Using 4D Minimal Hypersurfaces of Revolution. ACM Transactions on Graphics, 38(5), 1–13. DOI:
https://doi.org/10.1145/3188735
-
Maden, F. (2015). Novel Design Methodologies for Transfeormable Doubly-Ruled Surface Structures (PhD
thesis) Izmir Institute of Technology. Access Address (15.07.2025):
https://dl.acm.org/doi/abs/10.5555/AAI29205989
-
Miki, M., Adiels, E., Baker, W., Mitchell, T., Sehlström, A. & Williams, C. J. K. (2022). Form-finding of shells
containing both tension and compression using the Airy stress function. International Journal of Space
Structures, 37(4), 261–282. DOI: https://doi.org/10.1177/09560599221102618
-
Miki, M., Mitani, J. & Igarashi, T. (2013). Development of a Grasshopper add-on for interactive exploration of
shapes in equilibrium. Proceedings of IASS Annual Symposia, 2013, 1–6. International Association for Shell and
Spatial Structures (IASS).
-
Millar, C., Mitchell, T., Mazurek, A., Chhabra, A., Beghini, A., Clelland, J. N., McRobie, A. & Baker, W. F. (2023). On
designing plane-faced funicular gridshells. International Journal of Space Structures, 38(1), 40–63. DOI:
https://doi.org/10.1177/09560599221126656
-
Mueller, C., Fivet, C. & Ochsendorf, J. (2015). Graphic statics and interactive optimization for engineering
education. Structures Congress 2015 - Proceedings of the 2015 Structures Congress. DOI:
https://doi.org/10.1061/9780784479117.223
-
Otter, J. R. H., Cassell, A. C. & Hobbs, R. E. (1967). Dynamic Relaxation. Proceedings of the Institution of Civil
Engineers. DOI: https://doi.org/10.1680/iicep.1967.8278
-
Panozzo, D., Block, P. & Sorkine-Hornung, O. (2013). Designing unreinforced masonry models. ACM
Transactions on Graphics, 32(4), 1–12. DOI: https://doi.org/10.1145/2461912.2461958
-
Piker, D. (2013). Kangaroo: Form finding with computational physics. Architectural Design, 83(2), 136–137. DOI:
https://doi.org/10.1002/ad.1569
-
Preisinger, C. & Heimrath, M. (2014). Karamba—A Toolkit for Parametric Structural Design. Structural
Engineering International, 24(2), 217–221. DOI: https://doi.org/10.2749/101686614X13830790993483
-
Rippmann, M. (2016). Funicular Shell Design: Geometric approaches to form finding and fabrication of
discrete funicular structures (PhD thesis) ETH Zurich. Access Address (15.07.2025): https://www.research-
collection.ethz.ch/bitstream/handle/20.500.11850/116926/eth-49131-02.pdf
-
Robeller, C. & Von Haaren, N. (2020). Recycleshell: Wood-only shell structures made from cross-laminated
timber (CLT) production waste. Journal of the International Association for Shell and Spatial Structures, 61(2),
125–139. DOI: https://doi.org/10.20898/j.iass.2020.204.045
-
Schek, H. J. (1974). The force density method for form finding and computation of general networks.
Computer Methods in Applied Mechanics and Engineering. https://doi.org/10.1016/0045-7825(74)90045-0
-
Svoboda, L., Novák, J., Kurilla, L. & Zeman, J. (2014). A framework for integrated design of algorithmic
architectural forms. Advances in Engineering Software, 72, 109–118. DOI:
https://doi.org/10.1016/j.advengsoft.2013.05.006
-
Tang, C., Sun, X., Gomes, A., Wallner, J. & Pottmann, H. (2014). Form-finding with polyhedral meshes made
simple. ACM Transactions on Graphics, 33(4), 1–9. DOI: https://doi.org/10.1145/2601097.2601213
-
TSE. (2022). Yapılar üzerindeki etkiler—Bölüm 1-4: Genel etkiler—Rüzgâr etkileri (eurocode 1) (CEN No. TS EN
1991-1-4/D2). Ankara.
-
Vatandoost, M., Ekhlassi, A., Golabchi, M., Rahbar, M. & von Buelow, P. (2024). Fabrication methods of shell
structures. Automation in Construction, 165, 105570. DOI: https://doi.org/10.1016/j.autcon.2024.105570
-
Vouga, E., Höbinger, M., Wallner, J. & Pottmann, H. (2012). Design of self-supporting surfaces. ACM
Transactions on Graphics, 31(4), 1–11. DOI: https://doi.org/10.1145/2185520.2185583
-
Wang, Z., Song, P., Isvoranu, F. & Pauly, M. (2019). Design and structural optimization of topological interlocking
assemblies. ACM Transactions on Graphics, 38(6), 1–13. DOI: https://doi.org/10.1145/3355089.3356489
-
Whiting, E., Ochsendorf, J. & Durand, F. (2009). Procedural modeling of structurally-sound masonry buildings.
ACM SIGGRAPH Asia 2009 Papers, 1–9. DOI: https://doi.org/10.1145/1661412.1618458
-
Whiting, E., Shin, H., Wang, R., Ochsendorf, J. & Durand, F. (2012). Structural optimization of 3D masonry
buildings. ACM Transactions on Graphics, 31(6), 1–11. DOI: https://doi.org/10.1145/2366145.2366178
-
Zhang, Y., & Wang, R. (2025). Multi-objective optimization of construction based on genetic algorithm NSGA-II.
International Journal of Architectural Computing. 2025;0(0). https://doi.org/10.1177/14780771251335107