An initially two-dimensional grid of elastic rods may be actuated into a three-dimensional shell-like structure, through buckling, when the end-points of the rods are constrained to a shrunk boundary. The shape of the 3D gridshell is a joint result of elasticity and geometric constraint. We develop a discrete differential geometry-based model of elastic gridshell to investigate their form-finding process. Even though the forward process from 2D footprint to 3D gridshell can be captured by physics-based simulation, the inverse problem of obtaining the original footprint given the 3D deformed shape still lacks a generalized method. In this paper, we propose a genetic algorithm (GA)-based inverse design method to explore the planar footprint of an elastic gridshell as well as the corresponding geometric constraints. Geometric features extracted from the original planar form are encoded into various chromosomes to constitute a population in every generation. With the fitness function constructed based on the deviation of the candidate solution from the 3D target shape, the population evolves gradually until the individual of the smallest fitness value representing the optimal footprint and final boundary constraints is found under seven predefined geometric constraints. Given a series of representative target shapes, e.g., hemispherical cap, paraboloid structure, Gaussian curve shape, and semi-ellipsoid, their original footprints are quantified using a network of 10 elastic rods. Excellent agreement is obtained between the prescribed 3D shape and the simulated buckled structures as small fitness value is obtained and little difference between them is observed, which validates the effectiveness of the proposed GA-based inverse design method.
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This work received financial support from the National Science Foundation (Award No. IIS-1925360) and the Henry Samueli School of Engineering and Applied Science, University of California, Los Angeles.
Conflict of interest
The authors declare that they have no conflict of interest.
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Replication of results
Details of the GA-based inverse design method of elastic gridshells have been described in Section 4, including the geometric constraints, configuration of GA, population initialization, and the definition of fitness function. The corresponding flowcharts can be found in Figs. 6 and 8. Parameters of the designed surfaces in this paper are available in Section 2. As for the forward deformation process, the DER code could be provided upon request. In order to provide more convenient validation and replication of our findings, the optimal chromosomes corresponding to cases I to IV found by the proposed method are provided in Table 2 that encode the geometry information about the 2D footprint and final shrunk boundary. With these data, the footprint, final shrunk constraint boundary, and the corresponding 3D buckled structures can be replicated.
Longhui Qin and Weicheng Huang contributed equally to this work.
The original version of Figure 10 is a repetition of Figure 13 by mistake.
Responsible Editor: Mehmet Polat Saka
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Qin, L., Huang, W., Du, Y. et al. Genetic algorithm-based inverse design of elastic gridshells. Struct Multidisc Optim 62, 2691–2707 (2020). https://doi.org/10.1007/s00158-020-02639-8
- Elastic gridshell
- Buckling instability
- Form finding
- Numerical simulation
- Genetic algorithm