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Topology Optimization of 3D-printed joints under crash loads using Evolutionary Algorithms

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A Correction to this article was published on 18 October 2021

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Abstract

In order to take full advantage of the enormous design freedom offered by Additive Manufacturing (AM) technologies, the use of Topology Optimization (TO) methods becomes essential. Although TO is well-established in many disciplines, the problems in vehicle crashworthiness pose severe difficulties for standard, gradient-based approaches, due to high noisiness, multi-modality, and discontinuous nature of the nonlinear simulation responses considered typically as objectives and constraints. In this article, we propose to use Evolutionary Algorithms (EAs) together with a suitable low-dimensional representation in an extended version of the Evolutionary Level Set Method (EA-LSM), able to address complex 3D crash TO problems. The method is used to optimize a 3D-printed metal joint in a hybrid S-rail structure under axial crash loading, inspired by novel frame design concepts in industry. The obtained results show that the method is capable of handling optimization problems with multiple constraints, including challenging acceleration responses, and yields significantly better solutions than the state-of-the-art methods. Finally, the robustness of the obtained designs is studied, demonstrating the ability of EA-LSM to find designs of low sensitivity w.r.t. small variations of the loading conditions, which is crucial from the perspective of industrial applications of the proposed method.

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Notes

  1. Solid Isotropic Material with Penalization (Bendsøe and Sigmund 2004).

  2. The local level set basis function is referred to as a Topology Description Function (TDF) (Guo et al. 2016; de Ruiter and van Keulen 2004; Zhang et al. 2016), as well.

  3. Please note that the deletion of the finite elements in a given model is related exclusively to the layout and the shape of MMCs. Hence, elements deleted from the model in earlier optimization iterations can be present in the finite element models in later phases of the optimization process.

  4. According to a popular rule of thumb for ESs (Bäck 2014), the convergence velocity of the algorithm can be estimated as \({c\sim \mu \ln \left( \frac{\lambda }{\mu }\right) }\), where \({\lambda }\) is the number of offspring individuals and \({\mu }\) is the number of parents in the population.

  5. Another rule of thumb (Bäck 2014) states that \({c\sim \frac{1}{n}}\), where n is the dimensionality of the optimization problem.

  6. Please note that more complex design domains can be considered in a similar way.

  7. http://www.3i-print.com (accessed 8 April 2021).

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Authors and Affiliations

  1. Honda Research Institute Europe GmbH, Carl-Legien-Str. 30, 63073, Offenbach/Main, Germany

    Mariusz Bujny, Markus Olhofer & Nikola Aulig

  2. Faculty of Civil, Geo, and Environmental Engineering, Technische Universität München, Arcisstr. 21, 80333, Munich, Germany

    Fabian Duddeck

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  1. Mariusz Bujny
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  2. Markus Olhofer
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  3. Nikola Aulig
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  4. Fabian Duddeck
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Correspondence to Mariusz Bujny.

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Bujny, M., Olhofer, M., Aulig, N. et al. Topology Optimization of 3D-printed joints under crash loads using Evolutionary Algorithms. Struct Multidisc Optim 64, 4181–4206 (2021). https://doi.org/10.1007/s00158-021-03053-4

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  • DOI: https://doi.org/10.1007/s00158-021-03053-4

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