Abstract
This work develops a computational method that produces algorithmically generated design forms, able to overcome inherent challenges related to the use of cast glass for the creation of monolithic structural components with light permeability. Structural Topology Optimization (TO) has a novel applicability potential, as decreased mass is associated with shorter annealing times and, thus, considerably improved manufacturability in terms of time, energy, and cost efficiency. However, realistic TO in such structures is currently hindered by existing mathematical formulations and commercial software capabilities. Incorporating annealing constraints into the optimization problem is an essential feature that needs to be accommodated, whereas the brittle nature of glass invokes asymmetric stress failure criteria that cannot be captured by conventional ductile plasticity surfaces or uniform stress constraints. This paper addresses the approximation problems in the evaluation of principal stresses while concurrently incorporating annealing-related manufacturing constraints into a unified TO formulation. A mass minimization objective is articulated, as this is the most critical factor for cast glass structures. To ensure the structural integrity and manufacturability of the component, the applied constraints refer both to the glass material/structural properties and to criteria that ensue from the annealing and fabrication processes. The developed code is based on the penalized artificial density interpolation scheme and the optimization problem is solved with the interior-point method. The proposed formulation is applied in a planar design domain to explore how different glass compositions and structural design strategies affect the final shape. Upon extraction of the optimized shape, the structural performance of the respective 3D structures is validated with respect to performance constraint violations using the Ansys software. Finally, brief guidelines on the practical aspects of the manufacturing process are provided.
C. Andriotis and F. Oikonomopoulou—These authors contributed equally to this work.
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Notes
- 1.
The cooling process consists of phases with different cooling rates [4]. In this paper, only annealing is going to be considered since it is the lengthiest of all cooling phases, thus, having the larger effect on the total time needed.
- 2.
All the variables highlighted in bold refer to vectors and matrices.
- 3.
The geometry of the cantilevers resembles the shape of the classical MBB-Beam problem when similar boundary conditions are imposed [33].
- 4.
Only one of the two monolithic glass components is evaluated structurally in Ansys since the two parts are assumed to perform individually.
- 5.
Although multi-component steel molds can be made for the manufacturing of complex parts, they cannot produce undercuts because the mold must be eventually removed.
References
Oikonomopoulou, F., Bristogianni, T., Barou, L., Veer, F., Nijsse, R.: The potential of cast glass in structural applications. Lessons learned from large-scale castings and state-of-the art load-bearing cast glass in architecture. J. Build. Eng. 20, 213–234 (2018)
Oikonomopoulou, F., Koniari, A., Damen, W., Koopman, D., Stefanaki, I., Bristogianni, T.: Topologically optimized structural glass megaliths: potential, challenges and guidelines for stretching the mass limits of structural cast glass. In: 8th Eighth International Conference on Structural Engineering, Mechanics and Computation (2022)
Damen, W., Oikonomopoulou, F., Bristogianni, T., Turrin, M.: Topologically optimized cast glass: a new design approach for loadbearing monolithic glass components of reduced annealing time. Glass Struct. Eng. (2022)
Shand, E., Armistead, W.: Glass Engineering Handbook, New York (1958)
Schober, H., Schneider, J., Justiz, S., Gugeler, J., Paech, C., Balz, M.: Innovations with Glass, Steel and Cables. Tampere, Finland (2007)
Oikonomopoulou, F.: Unveiling the third dimension of glass. Solid cast glass components and assemblies for structural applications (2019)
Zirker, J.: An Acre of Glass: A History and Forecast of the Telescope. JHU Press (2005)
Oikonomopoulou, F., Bhatia, I., van der Weijst, F., Damen, W., Bristogianni, T.: Rethinking the cast glass Mould. An exploration on novel techniques for generating complex and customized geometries. In: Challenging Glass 7 Conference on Architectural and Structural Applications of Glass (2020)
Langelaar, M.: Topology optimization of 3D self-supporting structures for additive manufacturing. Addit. Manuf. 12, 60–70 (2016)
Luo, Y., Sigmund, O., Li, Q., Liu, S.: Additive manufacturing oriented topology optimization of structures with self-supported enclosed voids. Comput. Methods Appl. Mech. Eng. 372 (2020)
Duysinx, P., Sigmund, O.: New developments in handling stress constraints in optimal material distributions. In: 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization (1998)
Le, C., Norato, J., Bruns, T., Ha, C., Tortorelli, D.: Stress-based topology optimization for continua. Struct. Multidiscip. Optim. 41, 605–620 (2010)
Paris, J., Navarrina, F., Colominas, I., Casteleiro, M.: Topology optimization of continuum structures with local and global stress constraints. Struct. Multidiscip. Optim. 39, 419–437 (2009)
Yang, R., Chen, C.: Stress-based topology optimization techniques. Struct. Optimiz. 12, 98–105 (1996)
Duysinx, P., Bendsoe, M.: Topology optimization of continuum structures with local stress constraints. Int. J. Numer. Meth. Eng. 43, 1453–1458 (1998)
Giraldo-Londoño, O., Paulino, G.: A unified approach for topology optimization with local stress constraints considering various failure criteria: von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler–Pister and Willam–Warnke. Proc. Roy. Soc. A 476 (2020)
Senhora, F.V., Giraldo-Londoño, O., Menezes, I.F.M., Paulino, G.H.: Topology optimization with local stress constraints: a stress aggregation-free approach. Struct. Multidiscip. Optim. 62(4), 1639–1668 (2020). https://doi.org/10.1007/s00158-020-02573-9
Bruggi, M.: On an alternative approach to stress constraints relaxation in topology optimization. Struct. Multidiscip. Optim. 36, 125–141 (2008)
Bruggi, M., Duysinx, P.: Topology optimization for minimum weight with compliance and stress constraints. Struct. Multidiscip. Optim. 46, 369–384 (2012)
Luo, Y., Kang, Z.: Topology optimization of continuum structures with Drucker-Prager yield stress constraints. Comput. Struct. 90–91, 65–75 (2012)
Bruggi, M., Duysinx, P.: A stress–based approach to the optimal design of structures with unilateral behavior of material or supports. Struct. Multidiscip. Optim. 48, 311–326 (2013)
Bendsoe, M.: Optimal shape design as a material distribution problem. Struct. Optim. 1, 193–202 (1989)
Sigmund, O., Petersson, J.: Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct. Optim. 16, 68–75 (1998)
Bendsøe, M.P., Sigmund, O.: Topology Optimisation. Theory, Methods and Applications. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-662-05086-6
Sigmund, O.: A 99 line topology optimization code written in Matlab. Struct. Multidiscip. Optim. 21(2), 120–127 (2001). https://doi.org/10.1007/s001580050176
Guest, J.: Imposing maximum length scale in topology optimization. Struct. Multidiscip. Optim. 37, 463–473 (2009)
Cheng, G., Guo, X.: Ε-relaxed approach in structural topology optimization. Struct. Optim. 13, 258–266 (1997)
Koniari, A.M.: Just Glass. Development of a Topology Optimization Algorithm for a Mass-Optimized Cast Glass Component. Delft University of Technology (2022)
Stefanaki, I.M.: Glass Giants. Mass-Optimized Massive Cast Glass Slab. Delft University of Technology (2020)
Bristogianni, T., Oikonomopoulou, F., Yu, R., Veer, F., Nijsse, R.: Exploratory study on the fracture resistance of cast glass. Int. J. Struct. Glass Adv. Mater. Res. 5 (2021)
Giesecke, R., Dillenburger, B.: Three-dimensionally (3D) printed sand molds for custom glass parts. Glass Struct. Eng. 7, 231–251 (2022)
Jipa, A., Bernhard, M., Meibodi, M., Dillenburger, B.: 3D‐printed stay‐in‐place formwork for topologically optimized concrete slabs. In: TxA Emerging Design + Technology Conference, San Antonio, Texas, USA (2016)
Liu, K., Tovar, A.: An efficient 3D topology optimization code written in Matlab. Struct. Multidiscip. Optim. 50, 1175–1196 (2014)
Acknowledgements
The authors would like to thank ir. Hans Hoogenboom (Digital Technologies section) at the VR-lab at TU Delft Faculty of Architecture & the Built Environment and Aytac Balci (@Hok Student ICT Support) for offering the facilities and support for the computational needs of this research. Dr. Andriotis would further like to acknowledge the support by the TU Delft AI Labs program.
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Koniari, A.M., Andriotis, C., Oikonomopoulou, F. (2023). Minimum Mass Cast Glass Structures Under Performance and Manufacturability Constraints. In: Turrin, M., Andriotis, C., Rafiee, A. (eds) Computer-Aided Architectural Design. INTERCONNECTIONS: Co-computing Beyond Boundaries. CAAD Futures 2023. Communications in Computer and Information Science, vol 1819. Springer, Cham. https://doi.org/10.1007/978-3-031-37189-9_29
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