Nonlinear diffusions in topology optimization

By Michael Y. Wang, Shiwei Zhou, Han Ding. 2004

53 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/2948047f19097c5af2b325ab85b36f6d3bf3d065

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Topological design of structures and composite materials with multiobjectives (2007, methodology): “…meets some requirements as described in detail in Aubert and Kornprobst (2000), Charbonnier et al. (1997) and Wang et al. (2004), it can diffuse the densities along the tangential direction of the boundary but not across it so that the sharp edges are created and preserved (Wang et al., 2004).”
Topology optimization approaches (2013, background): “This requirement is satisfied in e.g. Wang et al. (2003, 2004b).”
Multimaterial structural topology optimization with a generalized Cahn–Hilliard model of multiphase transition (2006, methodology): “The most commonmethod is to use a filtering process such as linear filtering (Sigmund 1997; Bourdin 2001), nonlinear diffusion (Wang et al. 2004), or bilateral filtering (Wang and Wang 2005), averaging the material distribution in a small area covering several neighboring elements isotropic-wise or ”
A topology optimization method based on the level set method incorporating a fictitious interface energy (2010, methodology): “Key words: Topology Optimization, Finite Element Method, Level Set Method, Phase Field Method, Tikhonov Regularization Method”
Length scale and manufacturability in density-based topology optimization (2016, methodology): “Based on regularization strategies utilized in image processing [16] a time-dependent nonlinear diffusion regularization scheme in topology optimization is proposed in [150] where the focus is mainly on reducing the gray transition regions by tuning the diffusion coefficient along the design edges.”