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Gradient based biobjective shape optimization to improve reliability and cost of ceramic components

Optimization and Engineering volume 21, pages 1359–1387 (2020)Cite this article

Abstract

We consider the simultaneous optimization of the reliability and the cost of a ceramic component in a biobjective PDE constrained shape optimization problem. A probabilistic Weibull-type model is used to assess the probability of failure of the component under tensile load, while the cost is assumed to be proportional to the volume of the component. Two different gradient-based optimization methods are suggested and compared at 2D test cases. The numerical implementation is based on a first discretize then optimize strategy and benefits from efficient gradient computations using adjoint equations. The resulting approximations of the Pareto front nicely exhibit the trade-off between reliability and cost and give rise to innovative shapes that compromise between these conflicting objectives.

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Acknowledgements

This work was supported by the federal ministry of research and education (BMBF, Grant-No. 05M18PXA ) as a part of the GIVEN consortium.

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Authors and Affiliations

  1. University of Wuppertal, Gaussstraße 20, 42119, Wuppertal, Germany

    O. T. Doganay, H. Gottschalk, C. Hahn, K. Klamroth, J. Schultes & M. Stiglmayr

Authors
  1. O. T. Doganay
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  2. H. Gottschalk
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  3. C. Hahn
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  4. K. Klamroth
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  5. J. Schultes
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  6. M. Stiglmayr
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Correspondence to O. T. Doganay.

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Doganay, O.T., Gottschalk, H., Hahn, C. et al. Gradient based biobjective shape optimization to improve reliability and cost of ceramic components. Optim Eng 21, 1359–1387 (2020). https://doi.org/10.1007/s11081-019-09478-7

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  • DOI: https://doi.org/10.1007/s11081-019-09478-7

Keywords

  • Biobjective shape optimization
  • Shape gradients
  • Probability of failure
  • Descent algorithms

Mathematics Subject Classification

  • 90B50
  • 49Q10
  • 65C50
  • 60G55