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On speeding up an asymptotic-analysis-based homogenisation scheme for designing gradient porous structured materials using a zoning strategy

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Abstract

Gradient porous structured materials possess significant potential of being applied in many engineering fields. To accelerate the design process of infill graded microstructures of uniform local density, a novel asymptotic homogenisation topology optimisation method was proposed by Zhu et al. (J Mech Phys Solids 124:612–633, 2019), aiming for (1) significantly enriching the pool of representable graded microstructures; and (2) deriving an homogenised formulation for stress analysis in consistency with fine-scale results. But the work is severely confined from being widely applied, mainly due to the following two reasons. Firstly, to circumvent macroscopically pointwise computation for solving various microscopic cell problems, linearisation had to be adopted for its numerical implementation, and this significantly reduces the design freedom. Secondly, lacking of sensitive analysis, genetic algorithm was chosen for optimisation, inevitably decreasing the computational efficiency. To address these bottleneck challenging issues, a zoning scheme empowered by computational parallelism is introduced, and the sensitivity analysis associated with the new asymptotic framework is conducted. Through comparisons with fine-scale simulation results, the proposed algorithm is shown to be an effective tool for evaluating the mechanical behaviour of graded microstructures. As an optimisation tool, the mapping function takes a concise and explicit form. But its parameterisation still needs further investigation, so as to improve the solution optimality of the present approach, especially in comparison with another recently proposed method (Groen and Sigmund, Internat J Numer Methods Engrg 113(8):1148–1163, 2018). Optimisation results for three-dimensional graded microstructures are also shown, which are not frequently discussed in literature, possibly because of the high computational cost generated.

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Acknowledgements

We thank Ole Sigmund and Jeroen Groen for providing the comparative simulation example shown in Fig. 12. We also thank Ole Sigmund for many valuable comments, without which the article cannot reach the present stage. The comments from (anonymous) reviewers during the previous rounds of review process are also appreciated.

Funding

This study was financially supported by the National Key Research and Development Plan (2016YFB0201601) from the Ministry of Science and Technology of the People’s Republic of China, the National Natural Science Foundation of China (11772076, 11732004, 11821202), the Fundamental Research Funds for the Central Universities (DUT16RC(3)091), and Program for Chang-jiang Scholars, Innovative Research Team in University (PCSIRT).

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  1. Dingchuan Xue

    Present address: Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, State College, PA, 16802, USA

Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116023, People’s Republic of China

    Dingchuan Xue, Yichao Zhu, Shaoshuai Li, Chang Liu, Weisheng Zhang & Xu Guo

  2. International Research Center for Computational Mechanics, Dalian University of Technology, Dalian, People’s Republic of China

    Dingchuan Xue, Yichao Zhu, Shaoshuai Li, Chang Liu, Weisheng Zhang & Xu Guo

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  1. Dingchuan Xue
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Correspondence to Yichao Zhu or Xu Guo.

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All the data underlying the argument in the article are generated by locally devised MATLAB codes consisting of a set of systematically arranged sub-function modules (such as homogenisation). We are willing to satisfy the reasonable and responsible demand for the data and the source codes underpinning the present article.

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Xue, D., Zhu, Y., Li, S. et al. On speeding up an asymptotic-analysis-based homogenisation scheme for designing gradient porous structured materials using a zoning strategy. Struct Multidisc Optim 62, 457–473 (2020). https://doi.org/10.1007/s00158-020-02655-8

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