Abstract
AbstractWe 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.
Funder
Ministero dellIstruzione, dellUniversitá e della Ricerca
Regione Lombardia
FWF
Vienna Science and Technology Fund
Università degli Studi di Pavia
Publisher
Springer Science and Business Media LLC
Subject
Control and Optimization,Computer Graphics and Computer-Aided Design,Computer Science Applications,Control and Systems Engineering,Software
Reference30 articles.
1. Allaire G, Jouve F, Maillot H (2004) Topology optimization and optimal shape design using homogenization. Struct Multidisc Optim 28:87–98
2. Auricchio F, Bonetti E, Carraturo M, Hömberg D, Reali A, Rocca E (2019) Structural multiscale topology optimization with stress constraint for additive manufacturing. arXiv:1907.06355
3. Auricchio F, Bonetti E, Carraturo M, Hömberg D, Reali A, Rocca E (2020) A phase-field-based graded-material topology optimization with stress constraint. Math Models Methods Appl Sci 30(08):1461–1483
4. Bendsøe MP (1983) On obtaining a solution to optimization problems for solid, elastic plates by restriction of the design space. J Struct Mech 11(4):501–521
5. Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 6(65):635–654
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献