Multimaterial topology optimization by volume constrained Allen–Cahn system and regularized projected steepest descent method

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A multi-material level set-based topology and shape optimization method (2015, methodology): “In the framework of the phase field method, Zhou and Wang [27] and Tavakoli [28] achieved multi-materials optimization.”
An improved soft-kill BESO algorithm for optimal distribution of single or multiple material phases (2015, background): “For other notable recent works in this area, the reader is referred to the works of Gao and Zhang (2011); Bruyneel (2011); Blasques and Stolpe (2012); Gao et al (2013); Tavakoli and Mohseni (2014); Tavakoli (2014); Park and Sutradhar (2015); Querin et al (2015).”
A new multi-material level set topology optimization method with the length scale control capability (2018, unknown): “In addition, multi-material topology optimization has also been performed under other frameworks, e.g., BESO (Bidirectional Evolutionary Structural Optimization) [37,38] and Phase field [39,40].”
Topology optimization of multi-directional variable thickness thin plate with multiple materials (2019, unknown): “Tavakoli (2014) proposed a new computational algorithm to solve multimaterial topology optimization problems based on the penalization of the objective functional by the multiphase volume constrained Ginzburg-Landau energy functional.”
Multi-material topology optimization using ordered SIMP interpolation (2016, methodology): “For instance, over 10(4) iterationswere commonly required to find a suitable solution (Tavakoli 2014).”