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On the consistency of adjoint sensitivity analysis for structural optimization of linear dynamic problems

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Abstract

Gradient-based topology optimization typically involves thousands or millions of design variables. This makes efficient sensitivity analysis essential and for this the adjoint variable method (AVM) is indispensable. For transient problems it has been observed that the traditional AVM, based on a differentiate-then-discretize approach, may lead to inconsistent sensitivities. Herein this effect is explicitly demonstrated for a single dof system and the source of inconsistency is identified. Additionally, we outline an alternative discretize-then-differentiate AVM that inherently produces consistent sensitivities.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Technical Universityof Denmark, 2800, Kgs. Lyngby, Denmark

    Jakob S. Jensen

  2. Department of Mechanical Science and Engineering, Universityof Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Praveen B. Nakshatrala & Daniel A. Tortorelli

Authors
  1. Jakob S. Jensen
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  2. Praveen B. Nakshatrala
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  3. Daniel A. Tortorelli
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Correspondence to Jakob S. Jensen.

Additional information

The work of Jakob S. Jensen work was supported via ERC-starting grant 279529.

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Jensen, J.S., Nakshatrala, P.B. & Tortorelli, D.A. On the consistency of adjoint sensitivity analysis for structural optimization of linear dynamic problems. Struct Multidisc Optim 49, 831–837 (2014). https://doi.org/10.1007/s00158-013-1024-4

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  • DOI: https://doi.org/10.1007/s00158-013-1024-4

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