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Adjoint Method for Topological Derivatives for Optimization Tasks with Material and Geometrical Nonlinearities

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EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization (EngOpt 2018)

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Abstract

In this paper the Topological Derivative for crash loaded structures is derived with the adjoint sensitivity analysis. The main idea of the adjoint sensitivity analysis is to circumvent the direct calculation of the sensitivity of the displacement field. Instead, the adjoint equilibrium equation has to be solved. In this approach, material derivation and partial integration in the time domain are applied to the Topological Derivative. This ensures, that the inertial effects are kept, as they are important for a reliable crash simulation. The result is a backward integration scheme for the adjoint state.

With implicit time integration, a numerical scheme to solve the primal and the adjoint problem is demonstrated. The specific adjoint equation as well as the Topological Derivative for a displacement functional and the internal energy are presented.

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Acknowledgment

The authors express their tanks to the German Research Foundation (DFG) for the support of the research project “Topological derivatives for layout generation of crash-loaded structures” (DFG-No. Schu915/4-1, project number 350645830).

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Authors and Affiliations

  1. Chair for Optimization of Mechanical Structures, University of Wuppertal, Gaußstr. 20, 42119, Wuppertal, Germany

    Katrin Weider & Axel Schumacher

Authors
  1. Katrin Weider
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  2. Axel Schumacher
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Corresponding author

Correspondence to Katrin Weider .

Editor information

Editors and Affiliations

  1. Mechanical Engineering Department, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal

    H.C. Rodrigues

  2. Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    J. Herskovits

  3. Instituto Superior Tecnico, University of Lisbon, Lisbon, Portugal

    C.M. Mota Soares

  4. Instituto Superior Tecnico, University of Lisbon, Lisbon, Portugal

    A.L. Araújo

  5. Instituto Superior Tecnico, University of Lisbon, Lisbon, Portugal

    J.M. Guedes

  6. Instituto Superior Tecnico, University of Lisbon, Lisbon, Portugal

    J.O. Folgado

  7. Instituto Superior Tecnico, University of Lisbon, Lisbon, Portugal

    F. Moleiro

  8. IST, IDMEC – Instituto de Engenharia Mecânica, Lisbon, Portugal

    J. F. A. Madeira

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Weider, K., Schumacher, A. (2019). Adjoint Method for Topological Derivatives for Optimization Tasks with Material and Geometrical Nonlinearities. In: Rodrigues, H., et al. EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization. EngOpt 2018. Springer, Cham. https://doi.org/10.1007/978-3-319-97773-7_75

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  • DOI: https://doi.org/10.1007/978-3-319-97773-7_75

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-97772-0

  • Online ISBN: 978-3-319-97773-7

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