A topology optimization method based on the level set method incorporating a fictitious interface energy

By Takayuki Yamada, Kazuhiro Izui, Shinji Nishiwaki, Akihiro Takezawa. 2010

668 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/6940fc3a6beb22d69f20ac759cb159d800482235

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Isogeometric Analysis for Topology Optimization with a Phase Field Model (2012, background): “However, it is shown in [112] by means of numerical examples that when the capability of hole nucleation is introduced in the level set method, the dependence of the optimal solution on the initial one is reduced.”
Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis (2012, methodology): “This method is based on a fixed mesh that works with the level set method firstly proposed by Osher and Sethian [9] to represent moving interfaces and has been extensively applied to structural optimization [14,20,16,17,22].”
Shape optimization of continua using NURBS as basis functions (2013, neutral): “in the level set approach[43].”
Integrated topology optimization with embedded movable holes based on combined description by material density and level sets (2013, methodology): “The second one is based on the geometrical boundary description model, such as the level set topology optimization methods [4–11], and the implicit description function method [12].”
Topology optimization for functionally graded cellular composites with metamaterials by level sets (2018, methodology): “LSM [40, 41] have been used as an alternative method for structural shape and topology optimization design problems [42, 43, 52-58].”
Topology optimization approaches (2013, methodology): “In some approaches, also labeled level set methods (Yamada et al. 2010; Otomori et al. 2011), the convective term is omitted and the reactive term is used solely to drive the evolution of the level set function.”
Multi-objective topology optimization of multi-component continuum structures via a Kriging-interpolated level set approach (2014, methodology): “Typical level set approaches (Wang et al. 2003; Allaire et al. 2004b; Wang and Wang 2006; Wei and Wang 2009; Yamada et al. 2010; James and Martins 2012) involve a Hamilton-Jacobi system of partial differential equations, with a large number of degrees of freedom, which in turn requires a gradient-ba”
A multi-material topology optimization algorithm based on the topological derivative (2019, methodology): “Moreover, the approach introduced in [31] has been extended to the multi-material case, e.”
Structural topology optimization based on non-local Shepard interpolation of density field (2011, background): “The most widely used ones can be broadly classified into material distribution models [1–6] and boundary description models, including the topology description function-based method [7], the level set-based method [8,9] and its variants [10–13].”