Shape and topology optimization based on the phase field method and sensitivity analysis

By Akihiro Takezawa, Shinji Nishiwaki, Mitsuru Kitamura. Journal of Computational Physics, 2010

409 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a69c217679fd88f69f592d264b67ce297626628e

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In Civil and Structural Engineering

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Citations in the corpus

Integrated topology optimization with embedded movable holes based on combined description by material density and level sets (2013, background): “It is also noted that, by introducing a density-like phase representation, a phase-field method has been developed for topology optimization problems [46].”
Isogeometric Analysis for Topology Optimization with a Phase Field Model (2012, methodology): “Initial solutions in the 0–1 configurations are also chosen in [102] for topology optimization problems formulated with the Cahn– Allen equation, which shows a strong dependence of the optimal solution on the initial one.”
Primal‐dual active set methods for Allen–Cahn variational inequalities with nonlocal constraints (2010, background): “There are only a few approaches considered, see [116, 30, 111].”
Introducing the sequential linear programming level-set method for topology optimization (2015, methodology): “There are also methods based on phase fields (Takezawa et al. 2010; Blank et al. 2010) where the implicit function is used to define the material phase of a point and the update is performed by solving a reaction–diffusion equation.”
Optimal topologies derived from a phase-field method (2012, methodology): “Takezawa et al. (2010) used a phase-field approach where a modified double well potential defines the driving force for redistribution of the material.”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “11 a A 2D domain represented by the phase field function and b a 1D illustration of the phase field function (from Takezawa et al. (2010))”
Adaptive topology optimization with independent error control for separated displacement and density fields (2014, methodology): “Over the past two decades, many topology optimization methods have been developed, including the homogenization method [4], the SIMP (Solid Isotropic Material with Penalization) method [5,6], the level set method [7–9], the ESO (Evolutionary Structural Optimization) method [10] and other alternative”