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Risk-averse approach for topology optimization of fail-safe structures using the level-set method

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Abstract

This paper presents a risk-averse approach in the context of fail-safe topology optimization. The main novelty is the minimization of two risk functions quantifying the costs inherent to partial or full collapses, whose occurrence is considered as a source of uncertainty. This provides the designer with the flexibility to explicitly incorporate probabilistic information of occurrence of different structural failures, in contrast to the worst case approach, that penalizes all the damage configurations regardless their probability of occurrence. For the first time in the context of fail-safe topology optimization, a level-set method is employed. The level-set function is updated by means of a reaction–diffusion equation incorporating the topological derivative of the two risk-averse functions considered. Finally, the numerical experiments reveal the capability of the proposed formulations to yield redundant structures less sensitive to inherent losses of stiffness resulting from possible failures, whilst allowing designers to assume an acceptable level of risk. The benefits and drawbacks of the formulations proposed are compared against deterministic and fail-safe worst-case formulations.

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Acknowledgements

Project supported by the Autonomous Community of the Region of Murcia, Spain through the programme for the development of scientific and technical research by competitive groups (20911/PI/18), included in the Regional Program for the Promotion of Scientific and Technical Research of Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia. The second author acknowledges the financial support of Fundación Séneca, through the contract with reference number 21132/SF/19 under the programe Subprograma Regional Saavedra Fajardo de incorporación de doctores a Universidades y Centros de investigación de la Región de Murcia.

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  1. Technical University of Cartagena, Campus Muralla del Mar, 30202, Cartagena, Murcia, Spain

    J. Martínez-Frutos & R. Ortigosa

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  1. J. Martínez-Frutos
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  2. R. Ortigosa
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Correspondence to J. Martínez-Frutos.

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Martínez-Frutos, J., Ortigosa, R. Risk-averse approach for topology optimization of fail-safe structures using the level-set method. Comput Mech 68, 1039–1061 (2021). https://doi.org/10.1007/s00466-021-02058-6

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  • DOI: https://doi.org/10.1007/s00466-021-02058-6

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