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Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model

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Abstract

Using a quantified measure for non-probab ilistic reliability based on the multi-ellipsoid convex model, the topology optimization of continuum structures in presence of uncertain-but-bounded parameters is investigated. The problem is formulated as a double-loop optimization one. The inner loop handles evaluation of the non-probabilistic reliability index, and the outer loop treats the optimum material distribution using the results from the inner loop for checking feasibility of the reliability constraints. For circumventing the numerical difficulties arising from its nested nature, the topology optimization problem with reliability constraints is reformulated into an equivalent one with constraints on the concerned performance. In this context, the adjoint variable schemes for sensitivity analysis with respect to uncertain variables as well as design variables are discussed. The structural optimization problem is then solved by a gradient-based algorithm using the obtained sensitivity. In the present formulation, the uncertain-but bounded uncertain variations of material properties, geometrical dimensions and loading conditions can be realistically accounted for. Numerical investigations illustrate the applicability and the validity of the present problem statement as well as the proposed numerical techniques. The computational results also reveal that non-probabilistic reliability-based topology optimization may yield more reasonable material layouts than conventional deterministic approaches. The proposed method can be regarded as an attractive supplement to the stochastic reliability-based topology optimization.

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Yangjun Luo & Zhan Kang

  2. School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW, 2006, Australia

    Zhen Luo

  3. Laboratoire de Génie Civil, GRESPI, Université de Reims Champagne-Ardenne, Rue des Crayères, BP 1035, 51687, Reims, France

    Alex Li

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  1. Yangjun Luo
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  2. Zhan Kang
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  3. Zhen Luo
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  4. Alex Li
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Correspondence to Zhan Kang.

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Luo, Y., Kang, Z., Luo, Z. et al. Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model. Struct Multidisc Optim 39, 297–310 (2009). https://doi.org/10.1007/s00158-008-0329-1

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  • DOI: https://doi.org/10.1007/s00158-008-0329-1

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