Multimaterial structural topology optimization with a generalized Cahn–Hilliard model of multiphase transition

By Shiwei Zhou, Michael Y. Wang. 2006

295 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/a352d5c7cace73d3c4ceea3163bf85e450f02b34

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Materials Chemistry

Citations in the corpus

Multi-material topology optimization with multiple volume constraints: a general approach applied to ground structures with material nonlinearity (2017, methodology): “In addition to the density-based approach, phase-field (Wallin et al. 2015; Zhou and Wang 2007; Tavakoli and Mohseni 2014) and level set (Wang and Wang 2004; 2005; Wang et al. 2005; Mei and Wang 2004) approaches have also been used for multi-material topology optimization formulations.”
A topology optimization method based on the level set method incorporating a fictitious interface energy (2010, methodology): “Wei and Wang [65,66] proposed a piecewise constant level set method used in their topology optimization method.”
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].”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “They later investigated the phase-field method for compliance minimization based this time on the generalized Cahn-Hilliard equations for multiphase transitions (Zhou and Wang 2006, 2007).”
A multi-material level set-based topology and shape optimization method (2015, methodology): “Wang et al. [24] proposed an integrated optimization method for multi-material design problems, which involve optimal design of piezoelectric materials as actuation elements and topology optimization of elastic materials as the host structure.”
Multi-material topology optimization using ordered SIMP interpolation (2016, methodology): “Moreover, multi-material extension of the phase field method (Tavakoli 2014; Tavakoli and Mohseni 2013; Zhou and Wang 2007) and the level set method (Wang and Wang 2004) have also been developed.”
A mass constraint formulation for structural topology optimization with multiphase materials (2011, methodology): “In fact, the phase field method presented by Wang and Zhou [10, 11] is similar to UMMI-1 with the additional term.”
Topology optimization of multi-directional variable thickness thin plate with multiple materials (2019, unknown): “By using more additional stiff materials, multimaterial topology optimization may produce structures with higher stiffness and offer cost savings in comparison with single material structures (Tavakoli and Mohseni 2014; Zhou and Wang 2006).”
An improved soft-kill BESO algorithm for optimal distribution of single or multiple material phases (2015, methodology): “Apart from homogenization-based methods, different versions of level-set methods have also been introduced to solve multi-phase material distribution problems (see for example Zhou and Wang 2007; Wang and Wang 2004; Wang et al 2015).”
Isogeometric Analysis for Topology Optimization with a Phase Field Model (2012, methodology): “In [114, 115], the values differ from one test case to another; in [23, 102] the choice of γ appears to be arbitrary, while in [20] it is made by trial and error.”
A multi-resolution method for 3D multi-material topology optimization (2015, unknown): “Using the phase field approach with intrinsic volume preserving property based on Cahn–Hilliard equation, a multi-phase topology optimization approach was presented in [25,26].”
Multimaterial topology optimization by volume constrained Allen–Cahn system and regularized projected steepest descent method (2014, methodology): “Numerical results of the presented method illustrates that it is an order of magnitude faster than the generalized Cahn-Hilliad based topology optimization algorithm introduced in [8] (solving problem on H−1 function space).”