Phase Field: A Variational Method for Structural Topology Optimization

By Michael Y. Wang, Shiwei Zhou. 2004

161 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering

View Paper: https://www.semanticscholar.org/paper/68fa245cac311a2afc15e94c7f67886ee96546f9

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In Civil and Structural Engineering

Citations in the corpus

A topology optimization method based on the level set method incorporating a fictitious interface energy (2010, methodology): “Burger and Stainko [38], Wang and Zhou [33,37] and Zhou and Wang [34,35] proposed an alternative regularization method using the Tikhonov regularization method [82].”
Isogeometric Analysis for Topology Optimization with a Phase Field Model (2012, methodology): “The definition of topology optimization problems in a multiphase approach has recently been introduced for design dependent loads in [20] (and [21]), for problems with stress constraints in [23] and for the minimum compliance case in [107, 115]; further extensions are also considered in [102].”
Topology optimization approaches (2013, background): “A number of other approaches (Bourdin and Chambolle 2003; Wang and Zhou 2004; Burger and Stainko 2006) minimize the functional (15) directly, without the use of the auxiliary field μ but with an added volume constraint, hence they cannot be categorized as “true” phase field solutions.”
Multi-material topology optimization using ordered SIMP interpolation (2016, methodology): “Recently, the phase field method (Wang and Zhou 2004) and the level set method (Guo et al.”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “…further explored the idea by using van der Waals-Cahn-Hilliard phase transition theory and a numerical method based on the theory of -convergence to solve the variational system for mean compliance minimization of bi-material phases of solids and later for three-phase systems (Wang and Zhou 2004b).”
Primal‐dual active set methods for Allen–Cahn variational inequalities with nonlocal constraints (2010, methodology): “There are only a few approaches considered, see [116, 30, 111].”
Piecewise constant level set method for structural topology optimization (2009, methodology): “The PCLS scheme is also closely related to the phase-field models [12, 13].”
Shape and topology optimization based on the phase field method and sensitivity analysis (2010, methodology): “of gray scales or domain discontinuities, and a number of researchers have developed useful structural optimization methods that incorporate the phase field method [47, 48, 49, 50].”
Topology optimization of energy absorbing structures with maximum damage constraint (2017, methodology): “Various topology optimization methods have been proposed, which can be generally categorized into density-based methods [15, 16], level set methods [17, 18], phase field methods [19, 20], and evolutionary methods [21].”