Publications
Mixed variational formulations for structural topology optimization based on the phase-field approach
- Author(s)
- Michele Marino, Ferdinando Auricchio, Alessandro Reali, Elisabetta Rocca, Ulisse Stefanelli
- Abstract
We propose a variational principle combining a phase-field functional for structural topology optimization with a mixed (three-field) Hu–Washizu functional, then including directly in the formulation equilibrium, constitutive, and compatibility equations. The resulting mixed variational functional is then specialized to derive a classical topology optimization formulation (where the amount of material to be distributed is an a priori assigned quantity acting as a global constraint for the problem) as well as a novel topology optimization formulation (where the amount of material to be distributed is minimized, hence with no pre-imposed constraint for the problem). Both formulations are numerically solved by implementing a mixed finite element scheme, with the second approach avoiding the introduction of a global constraint, hence respecting the convenient local nature of the finite element discretization. Furthermore, within the proposed approach it is possible to obtain guidelines for settings proper values of phase-field-related simulation parameters and, thanks to the combined phase-field and Hu–Washizu rationale, a monolithic algorithm solution scheme can be easily adopted. An insightful and extensive numerical investigation results in a detailed convergence study and a discussion on the obtained final designs. The numerical results clearly highlight differences between the two formulations as well as advantages related to the monolithic solution strategy; numerical investigations address both two-dimensional and three-dimensional applications.
- Organisation(s)
- Department of Mathematics, Research Platform Accelerating Photoreaction Discovery
- External organisation(s)
- Università degli Studi di Roma "Tor Vergata", Università degli studi di Pavia, Institute of Genetics and Biophysics "Adriano Buzzati-Traverso", CNR
- Journal
- Structural and Multidisciplinary Optimization
- Volume
- 64
- Pages
- 2627-2652
- No. of pages
- 26
- ISSN
- 1615-147X
- DOI
- https://doi.org/10.1007/s00158-021-03017-8
- Publication date
- 10-2021
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101016 Optimisation
- Keywords
- ASJC Scopus subject areas
- Control and Systems Engineering, Software, Computer Science Applications, Computer Graphics and Computer-Aided Design, Control and Optimization
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/mixed-variational-formulations-for-structural-topology-optimization-based-on-the-phasefield-approach(2f2d9031-6e39-4bff-ab6f-5ed561791d57).html