Color level sets: a multi-phase method for structural topology optimization with multiple materials

By Michael Y. Wang, Xiaoming Wang. 2004

503 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/04af593cef807585cdbf086fc9bcb0a6fd3c984e

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Topology optimization approaches (2013, methodology): “However, stabilization schemes like these are well-known from many methods of numerically solving PDEs and the need for such schemes should not be considered a fundamental weakness of topology optimization.”
Structural Shape and Topology Optimization Using an Implicit Free Boundary Parametrization Method (2006, methodology): “…and Sethian (1988)], have been applied to structural shape and topology optimization problems as an emerging and promising family of methods based on the moving free boundaries [Sethian and Wiegmann (2000); Allaire, Jouve, and Toader (2004); Wang, Wang, and Guo (2003); Wang and Wang (2004a)].”
Semi-Lagrange method for level-set-based structural topology and shape optimization (2006, background): “…(2003) for dynamic interfaces, is introduced for an implicit representation of the structural boundary (Allaire et al. 2004; Osher and Santosa 2001; Wang and Wang 2004, 2005; Wang et al. 2003, 2004), and 420 Qi Xia et al. thereafter, the boundary is evolved by the Hamilton–Jacobi equation with a…”
A multi-material topology optimization algorithm based on the topological derivative (2019, methodology): “The level set method based on shape sensitivities and a Hamilton-Jacobi equation was generalized to the multi-material case in [ 2, 29, 30 ] and similar techniques have also been used in image segmentation [ 28 ] .”
Current and future trends in topology optimization for additive manufacturing (2018, methodology): “11 Multi-material topology optimization through the “color” level set method (left) (Wang and Wang 2004) and the reconciled level set method (right) (Vogiatzis et al.”
Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis (2012, methodology): “In the work of Wang and Wang [23], a color level set method which represents n different material phases uses log2n level set functions by allowing overlap of the level set functions.”
Explicit level‐set‐based topology optimization using an exact Heaviside function and consistent sensitivity analysis (2012, background): “Some authors have included several constraints in their level-set-based formulation, for instance, [13, 33, 34].”
Multimaterial topology optimization by volume constrained Allen–Cahn system and regularized projected steepest descent method (2014, background): “In practice, the material interpolation is an artificial construction in the context of the topology optimization, because a successful procedure results in a distinct phase within each computational element at the final solution [11].”
Multi-material topology optimization with multiple volume constraints: a general approach applied to ground structures with material nonlinearity (2017, methodology): “…constraint to each material (e.g., Sigmund and Torquato (1997), Gibiansky and Sigmund (2000), Wallin et al. (2015), Zhou and Wang (2007), Tavakoli and Mohseni (2014), Wang and Wang (2004), and Wang et al. (2005)), which may impose higher demands on computational implementations and update schemes.”
A level set‐based parameterization method for structural shape and topology optimization (2008, methodology): “To shorten the length of the paper, we omit numerical details related to conventional level set-based methods [4, 23, 24].”