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Analysis of a Combined Filtered/Phase-Field Approach to Topology Optimization in Elasticity

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Abstract

We advance a combined filtered/phase-field approach to topology optimization in the setting of linearized elasticity. Existence of minimizers is proved and rigorous parameter asymptotics are discussed by means of variational convergence techniques. Moreover, we investigate an abstract space discretization in the spirit of conformal finite elements. Eventually, stationarity is equivalently reformulated in terms of a Lagrangian.

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Funding

F. Auricchio was partially supported by the Italian Minister of University and Research through the project A BRIDGE TO THE FUTURE: Computational methods, innovative applications, experimental validations of new materials and technologies (No. 2017L7X3CS) within the PRIN 2017 program abd by Regione Lombardia, Regional Law No. 9/2020, Resolution No. 3776/2020. M. Marino was partially supported by the Italian Ministry of University and Research through the project COMETA within the Program for Young Researchers Rita Levi Montalcini (year 2017) and by Regione Lazio through the project BIOPMEAT (No. A0375-2020-36756) within the framework Progetti di Gruppi di Ricerca 2020 (POR FESR LAZIO 2014). I. Mazari is partially supported by the French ANR Project ANR-18-CE40-0013-SHAPO on Shape Optimization and by the Project Analysis and simulation of optimal shapes—application to life sciences of the Paris City Hall. U. Stefanelli is partially supported by the Austrian Science Fund (FWF) through projects F 65, W 1245, I 4354, I 5149, and P 32788, and by the OeAD-WTZ project CZ 01/2021.

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Authors and Affiliations

  1. Department of Civil Engineering and Architecture, University of Pavia, via Ferrata 3, 27100, Pavia, Italy

    Ferdinando Auricchio

  2. Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, via Ferrata 1, 27100, Pavia, Italy

    Ferdinando Auricchio & Ulisse Stefanelli

  3. Department of Civil Engineering and Computer Science, University of Rome Tor Vergata, Via del Politecnico 1, 00133, Rome, Italy

    Michele Marino

  4. Université Paris-Dauphine, Place du Maréchal De Lattre De Tassigny, 75775, Paris CEDEX 16, France

    Idriss Mazari

  5. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Ulisse Stefanelli

  6. Vienna Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währingerstraße 17, 1090, Wien, Austria

    Ulisse Stefanelli

Authors
  1. Ferdinando Auricchio
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  2. Michele Marino
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  3. Idriss Mazari
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  4. Ulisse Stefanelli
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Correspondence to Ulisse Stefanelli.

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Auricchio, F., Marino, M., Mazari, I. et al. Analysis of a Combined Filtered/Phase-Field Approach to Topology Optimization in Elasticity. Appl Math Optim 89, 41 (2024). https://doi.org/10.1007/s00245-024-10104-x

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  • DOI: https://doi.org/10.1007/s00245-024-10104-x

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