Topology and Thickness Optimization of Concrete Thin Shell Structures Based on Weight, Deflection, and Strain Energy

Document Type : Original Article

Authors

1 Department of Architectural Technology, Faculty of Architecture, College of Fine Arts, University of Tehran, Tehran, Iran

2 School of Architecture and Environmental Design, Iran University of Science and Technology, Tehran, Iran

Abstract

This study presents the optimized shape and thickness of thin continuous concrete shell structures, minimizing their weight, deflection, and elastic energy change while meeting the performance requirements and minimizing material usage. Unlike previous studies that focused on single-objective optimization, this research focuses on multi-objective optimization (MOO) by considering three objective functions. This combination of objective functions has not been reflected in previous research, distinguishing this study. The computational design workflow incorporates a parametric model, multiple components for measuring objective functions in the grasshopper of Rhino, and a metaheuristic algorithm, the non-dominated sorting multi-objective genetic algorithm (NSGA-II), as the search tool, which was coded in Python. This workflow allows us to perform form-finding and optimization simultaneously. To demonstrate the effectiveness of this metaheuristic algorithm in structural optimization, we applied it in a case study of a well-known shell designed using the physical prototyping hanging model technique. Interpretations of samples of optimized results indicate that although solution 1 weighs nearly the same as solution 2, it has less deflection and strain energy. Solution 3, with a three-fold mass, has significantly less deflection and strain energy than solution 1 and solution 2, with deflection reductions of over 50 and 17%, respectively. Solutions 3 and 4 show better deflection and strain energy performance. Furthermore, a comparison of the MOO results with the Isler shell revealed that this method found a solution with less weight and deflection while being stiffer, confirming its practicality. The study found that MOO is a reliable method for form-finding and optimization, generating accurate and reasonable results.

Graphical Abstract

Topology and Thickness Optimization of Concrete Thin Shell Structures Based on Weight, Deflection, and Strain Energy

Keywords

Main Subjects

References

  1. Adesina A. Recent advances in the concrete industry to reduce its carbon dioxide emissions. Environmental Challenges. 2020;1:100004.
  2. Chilton J, Isler H. Heinz isler: Thomas Telford; 2000.
  3. Goaiz HA, Shamsaldeen HA, Abdulrehman MA, Al-Gasham T. Evaluation of steel fiber reinforced geopolymer concrete made of recycled materials. International Journal of Engineering. 2022;35(10):2018-26.
  4. Farshad M. Design and analysis of shell structures: Springer Science & Business Media; 2013.
  5. Adriaenssens S, Block P, Veenendaal D, Williams C. Shell structures for architecture: form finding and optimization: Routledge; 2014.
  6. Council WGB. New report: The building and construction sector can reach net zero carbon emissions by 2050. World Green Building Council Toronto, ON, Canada; 2019.
  7. IEA U, editor Global status report for buildings and construction 20192019: IEA Paris, France.
  8. Zhong X, Hu M, Deetman S, Steubing B, Lin HX, Hernandez GA, et al. Global greenhouse gas emissions from residential and commercial building materials and mitigation strategies to 2060. Nat Commun. 2021;12(1):6126. 10.1038/s41467-021-26212-z https://www.ncbi.nlm.nih.gov/pubmed/34675192
  9. Block P, Schlueter A, Veenendaal D, Bakker J, Begle M, Hischier I, et al. NEST HiLo: Investigating lightweight construction and adaptive energy systems. J Build Eng. 2017;12:332-41. 10.1016/j.jobe.2017.06.013
  10. Hosseinian SM, Faghani M. Assessing the effect of structural parameters and building site in achieving low carbon building materialization using a life-cycle assessment approach. J Build Eng. 2021;44:103318. 10.1016/j.jobe.2021.103318
  11. Pawar AJ, Suryawanshi SR. Comprehensive Analysis of Stress-strain Relationships for Recycled Aggregate Concrete. International Journal of Engineering. 2022;35(11):1-10. 10.5829/ije.2022.35.11b.05
  12. Sreeman D, Kumar Roy B. Optimization study of isolated building using shape memory alloy with friction pendulum system under near-fault excitations. International Journal of Engineering. 2022;35(11):2176-85.
  13. Talib HY, Al-Salim NHA. Improving Punching Shear in Flat Slab by Replacing Punching Shear Reinforcement by Ultrahigh Performance Concrete. International Journal of Engineering. 2022;35(8):1619-28. 10.5829/ije.2022.35.08b.18
  14. Kotnik T, Schwartz J. The architecture of heinz isler. Journal of the international association for shell and spatial structures. 2011;52(3):185-90.
  15. Kaveh A. Advances in metaheuristic algorithms for optimal design of structures: Springer; 2014.
  16. Talbi E-G. Metaheuristics: from design to implementation: John Wiley & Sons; 2009.
  17. Kaveh A, Ghazaan MI. Meta-heuristic algorithms for optimal design of real-size structures: Springer; 2018.
  18. Mirjalili S, Faris H, Aljarah I. Evolutionary machine learning techniques: Springer; 2019.
  19. Pugnale A, Sassone M. Morphogenesis and structural optimization of shell structures with the aid of a genetic algorithm. Journal of the International Association for Shell and Spatial Structures. 2007;48(3):161-6.
  20. Gokul Santhosh S, Singh A, Abdul Akbar M. Parametric Studies and Optimization of Grid Shell Structures Using Genetic Algorithm. Recent Trends in Civil Engineering: Select Proceedings of ICRACE 2021: Springer; 2022. p. 109-22.
  21. Basso P, Del Grosso AE, Pugnale A, Sassone M. Computational morphogenesis in architecture: Cost optimization of free-form grid shells. Journal of the international association for shell and spatial structures. 2009;50(3):143-50.
  22. Baghdadi A, Doerrie R, Kloft H, editors. Application of different optimisation techniques for material minimisation of individual structural elements. Proceedings of IASS Annual Symposia; 2020: International Association for Shell and Spatial Structures (IASS).
  23. Ansola R, Canales J, Tarrago JA, Rasmussen J. Combined shape and reinforcement layout optimization of shell structures. Struct Multidiscip O. 2004;27(4):219-27. 10.1007/s00158-004-0399-7
  24. Kimura T, Ohmori H. Computational morphogenesis of free form shells. Journal of the International Association for Shell and Spatial structures. 2008;49(3):175-80.
  25. Yang F, Yu T, Bui TQ, editors. Morphogenesis of free-form surfaces by an effective approach based on isogeometric analysis and particle swarm optimization. Structures; 2023: Elsevier.
  26. Tomás A, Martí P. Shape and size optimisation of concrete shells. Engineering Structures. 2010;32(6):1650-8.
  27. Feng RQ, Ge JM. Shape optimization method of free-form cable-braced grid shells based on the translational surfaces technique. Int J Steel Struct. 2013;13(3):435-44. 10.1007/s13296-013-3004-3
  28. Hassani B, Tavakkoli SM, Ghasemnejad H. Simultaneous shape and topology optimization of shell structures. Struct Multidiscip O. 2013;48(1):221-33. 10.1007/s00158-013-0894-9
  29. Richardson JN, Adriaenssens S, Coelho RF, Bouillard P. Coupled form-finding and grid optimization approach for single layer grid shells. Engineering Structures. 2013;52:230-9. 10.1016/j.engstruct.2013.02.017
  30. Shimoda M, Liu Y. A non-parametric free-form optimization method for shell structures. Struct Multidiscip O. 2014;50(3):409-23. 10.1007/s00158-014-1059-1
  31. Kaveh A, Amirsoleimani P, Eslamlou AD, Rahmani P, editors. Frequency-constrained optimization of large-scale dome-shaped trusses using chaotic water strider algorithm. Structures; 2021: Elsevier.
  32. Tomei V, Grande E, Imbimbo M. Design optimization of gridshells equipped with pre-tensioned rods. J Build Eng. 2022;52:104407. 10.1016/j.jobe.2022.104407
  33. Ansola R, Canales J, Tarrago J, Rasmussen J. On simultaneous shape and material layout optimization of shell structures. Struct Multidiscip O. 2002;24:175-84.
  34. Gythiel W, Schevenels M. Gradient-based size, shape, and topology optimization of single-layer reticulated shells subject to distributed loads. Struct Multidiscip O. 2022;65(5):144. 10.1007/s00158-022-03225-w
  35. Teimouri M, Asgari M. Developing an efficient coupled function-based topology optimization code for designing lightweight compliant structures using the BESO algorithm. Optim Eng. 2023:1-29. 10.1007/s11081-023-09808-w
  36. Zhang ZJ, Kanno Y, Feng RQ. Collapse-resistance optimization of fabricated single-layer grid shell based on sequential approximate optimization. Struct Multidiscip O. 2023;66(7):153. 10.1007/s00158-023-03604-x
  37. Emami N, Giles H, von Buelow P. Structural, daylighting, and energy performance of perforated concrete shell structures. Automat Constr. 2020;117:103249. 10.1016/j.autcon.2020.103249
  38. Liuti A, Pugnale A, Erioli A, editors. Computational morphogenesis in architecture: Structure and light as a multi-objective design/optimization problem. Proceedings of the 2nd International Conference on Structures and Architecture (ICSA 2013), Guimaraes, Portugal; 2013.
  39. Emami N, editor Structure and daylighting performance comparisons of Heinz Isler’s roof shell based on variations in parametrically derived multi opening topologies. Proceedings of IASS Annual Symposia; 2015: International Association for Shell and Spatial Structures (IASS).
  40. Pugnale A. Integrating Form, Structure and Acoustics: A Computational Reinterpretation of Frei Otto's Design Method and Vision. Journal of the International Association for Shell and Spatial Structures. 2018;59(1):75-86. 10.20898/j.iass.2018.195.901.
  41. Turrin M, von Buelow P, Stouffs R. Design explorations of performance driven geometry in architectural design using parametric modeling and genetic algorithms. Adv Eng Inform. 2011;25(4):656-75. 10.1016/j.aei.2011.07.009
  42. Puppa GD, Trautz M, editors. Multi-objective shape optimization of shell structures based on buckling forms. Proceedings of IASS Annual Symposia; 2015: International Association for Shell and Spatial Structures (IASS).
  43. Nagata K, Honma T, editors. Multi-objective Optimization for Free Form Surface Shell Using Swarm Intelligence with Decent Solutions Search. Proceedings of IASS Annual Symposia; 2016: International Association for Shell and Spatial Structures (IASS).
  44. Wang XY, Zhu SJ, Zeng Q, Guo XN. Improved multi-objective Hybrid Genetic Algorithm for Shape and Size Optimization of Free-form latticed structures. J Build Eng. 2021;43:102902. https://doi.org/10.1016/j.jobe.2021.102902
  45. Henriksson V, Lomax S, Richardson JN, editors. Multi-Objective Optimization of a Concrete Shell. Proceedings of IASS Annual Symposia; 2019: International Association for Shell and Spatial Structures (IASS).
  46. Veenendaal D. DESIGN AND FORM FINDING OF FLEXIBLY FORMED CONCRETE SHELL STRUCTURES: ETH Zuric; 2017.
  47. Veenendaal D, Bakker J, Block P. Structural Design of the Flexibly Formed, Mesh-Reinforced Concrete Sandwich Shell Roof of Nest Hilo. Journal of the International Association for Shell and Spatial Structures. 2017;58(1):23-38. 10.20898/j.iass.2017.191.847
  48. Zhao ZW, Wu JJ, Qin Y, Liang B. The strong coupled form-finding and optimization algorithm for optimization of reticulated structures. Adv Eng Softw. 2020;140:102765. 10.1016/j.advengsoft.2019.102765
  49. Vargas DEC, Lemonge ACC, Barbosa HJC, Bernardino HS. Differential evolution with the adaptive penalty method for structural multi-objective optimization. Optim Eng. 2019;20(1):65-88. 10.1007/s11081-018-9395-4
  50. Mirra G, Pugnale A, editors. Comparison between human-defined and AI-generated design spaces for the optimisation of shell structures. Structures; 2021: Elsevier.
  51. Nishei T, Fujita S, editors. Structural optimization of latticed shells considering strain energy and collapse load factor. Proceedings of IASS Annual Symposia; 2020: International Association for Shell and Spatial Structures (IASS).
  52. Wang H, Li PC, Wang J. Shape optimization and buckling analysis of novel two-way aluminum alloy latticed shells. J Build Eng. 2021;36:102100. 10.1016/j.jobe.2020.102100
  53. Kostura Z, Clark MC, Olson JR, editors. Design of a 500,000 m2 Iconic Roof for the New International Airport for Mexico City. Proceedings of IASS Annual Symposia; 2018: International Association for Shell and Spatial Structures (IASS).
  54. Jiang B, Zhang J, Ohsaki M, editors. Shape optimization of free-form shell structures combining static and dynamic behaviors. Structures; 2021: Elsevier.
  55. Cao Z, Wang Z, Zhao L, Fan F, Sun Y. Multi-constraint and multi-objective optimization of free-form reticulated shells using improved optimization algorithm. Engineering Structures. 2022;250:113442.
  56. Desai R. Structural Optimization Using Genetic Algorithm. Handbook of AI-based Metaheuristics: CRC Press; 2021. p. 73-116.
  57. Reisinger J, Zahlbruckner MA, Kovacic I, Kán P, Wang-Sukalia X, Kaufmann H. Integrated multi-objective evolutionary optimization of production layout scenarios for parametric structural design of flexible industrial buildings. J Build Eng. 2022;46:103766.
  58. Preisinger C. Karamba3D. Vienna: Bollinger und Grohmann ZT GmbH. 2018.
  59. Vatandoost M, Yazdanfar S, Ekhlassi A. Computer-Aided Design: Classification of Design problems in Architecture. Journal of Information and Computational Science. 2019;9(10):605-25.
  60. Mirjalili S, Dong JS. Multi-objective optimization using artificial intelligence techniques: Springer; 2020.
  61. Rao SS. Engineering optimization: theory and practice: John Wiley & Sons; 2019.
  62. Yi YK, Tariq A, Park J, Barakat D. Multi-objective optimization (MOO) of a skylight roof system for structure integrity, daylight, and material cost. J Build Eng. 2021;34:102056. 10.1016/j.jobe.2020.102056
  63. Smith G, Rivlin R. The strain-energy function for anisotropic elastic materials. Collected Papers of RS Rivlin: Volume I and II. 1997:541-59.
  64. Al-Tashi Q, Mirjalili S, Wu J, Abdulkadir SJ, Shami TM, Khodadadi N, et al. Moth-Flame Optimization Algorithm for Feature Selection: A Review and Future Trends. Handbook of Moth-Flame Optimization Algorithm. 2022:11-34.
  65. Vatandoost M, Ekhlassi A, Yazdanfar S. Computer-aided architectural design: classification and application of optimization algorithms. Journal of Information and Computational Science. 2020;10(6):18-43.
  66. Chatterjee S, Sarkar S, Dey N, Ashour AS, Sen S. Hybrid non-dominated sorting genetic algorithm: II-neural network approach. Advancements in Applied Metaheuristic Computing: IGI Global; 2018. p. 264-86.
  67. Sayyaadi H. Modeling, assessment, and optimization of energy systems: Academic Press; 2020.
  68. Deb K, Agrawal S, Pratap A, Meyarivan T, editors. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. Parallel Problem Solving from Nature PPSN VI: 6th International Conference Paris, France, September 18–20, 2000 Proceedings 6; 2000: Springer.
  69. Yang X-S. Nature-inspired optimization algorithms: Academic Press; 2020.
  70. Baghdadi A, Heristchian M, Kloft H, editors. Displacement-based seismic assessment of Heinz Isler’s shell structures. Proceedings of IASS Annual Symposia; 2020: International Association for Shell and Spatial Structures (IASS).
  71. Vu-Bac N, Duong TX, Lahmer T, Zhuang X, Sauer RA, Park HS, et al. A NURBS-based inverse analysis for reconstruction of nonlinear deformations of thin shell structures. Comput Method Appl M. 2018;331:427-55. 10.1016/j.cma.2017.09.034
  72. Zhang XK, Jin CN, Hu P, Zhu XF, Hou WB, Xu JT, et al. NURBS modeling and isogeometric shell analysis for complex tubular engineering structures. Comput Appl Math. 2017;36(4):1659-79. 10.1007/s40314-016-0312-1
  73. Baghdadi A, Heristchian M, Kloft H. Structural assessment of remodelled shells of Heinz Isler. International Journal of Advanced Structural Engineering. 2019;11(4):491-502.
  74. Piker D. Kangaroo Form Finding with Computational Physics. Archit Design. 2013;83(2):136-7. 10.1002/ad.1569
  75. Sassone M, Pugnale A, editors. Evolutionary Structural Optimization in Shell Design. Advanced Numerical Analysis of Shell-like Structures: Special Workshop, Zagreb, 26-28 September 2007; 2007.
  76. Ramavath S, Suryawanshi S. Optimal Prediction of Shear Properties in Beam-Column Joints Using Machine Learning Approach. International Journal of Engineering. 2024;37(1):67-82.
  77. El Alaoui M, Chahidi LO, Rougui M, Lamrani A, Mechaqrane A. Prediction of Energy Consumption of an Administrative Building using Machine Learning and Statistical Methods. Civil Engineering Journal. 2023;9(5):1007-22.
  78. Bessa M, Pellegrino S. Design of ultra-thin shell structures in the stochastic post-buckling range using Bayesian machine learning and optimization. International Journal of Solids and Structures. 2018;139:174-88.
International Journal of Engineering
Volume 37, Issue 7
TRANSACTIONS A: Basics
July 2024
Pages 1369-1383

Files

Share

How to cite

Statistics