Volume 28, 2022
|Number of page(s)||40|
|Published online||07 July 2022|
Topology optimization for quasistatic elastoplasticity
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, via Cintia, 80126 Napoli, Italy
2 Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
3 Vienna Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währingerstraße 17, 1090 Wien, Austria
4 Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, via Ferrata 1, 27100 Pavia, Italy
* Corresponding author: firstname.lastname@example.org
Accepted: 2 May 2022
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic medium under kinematic hardening. We adopt a phase-field approach and argue by subsequent approximations, first by discretizing time and then by regularizing the flow rule. Existence of optimal shapes is proved both at the time-discrete and time-continuous level, independently of the regularization. First order optimality conditions are firstly obtained in the regularized time-discrete setting and then proved to pass to the nonregularized time-continuous limit. The phase-field approximation is shown to pass to its sharp-interface limit via an evolutive variational convergence argument.
Mathematics Subject Classification: 74C05 / 74P10 / 49Q10 / 49J20 / 49K20
Key words: Topology optimization / elastoplasticity / first-order conditions
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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