Piecewise constant level set method for structural topology optimization

By Peng Wei, Michael Y. Wang. 2009

207 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/75e8a98da89ff066152bcfbe8fe0c69ff4072d90

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In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

A new multi-material level set topology optimization method with the length scale control capability (2018, unknown): “Other level set related methods including the piecewise constant level set method [33] and the reconciled level set method (RLSM) [34,35] are also effective in deriving multi-material topological design.”
Multimaterial topology optimization by volume constrained Allen–Cahn system and regularized projected steepest descent method (2014, methodology): “The piecewise-constant variational level set method has been used in [28, 29] to improve the computational cost of multiple level set based approaches.”
An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions (2018, methodology): “Recently, some variational level set methods have been developed with nucleation capacity to alleviate the dependency of the final solution on the initial design (Wang and Wang 2006a; Wei and Wang 2009; Yamada et al. 2010).”
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 level set-based topology and shape optimization method (2015, methodology): “Another multi-material level set approach is to incorporate the piecewise constant level set model into topology optimization [15,45].”
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.”
Current and future trends in topology optimization for additive manufacturing (2018, methodology): “An alternative method is the piecewise constant level set method [149,150], in which different values of the level set functions split the design domain into different areas.”
Evolutionary level set method for structural topology optimization (2011, methodology): “penalty (SIMP) method [31], the LSM has some excellent aspects: no check-board phenomena, no mesh-dependency problems, and good numerical stability.”
Topology optimization approaches (2013, methodology): “To relax the CFL constraint semiimplicit schemes based on operator splitting methods can be used, which either operate separately on spatial dimensions of the problem or on the convective and diffusive terms (Luo et al. 2008a; Wei and Wang 2009).”
Topology optimization with multiple materials via moving morphable component (MMC) method (2018, unknown): “D Dt ∫Γt t ·udS 1⁄4 ∫Γt t ·udS · 1⁄4 DL Dt 1⁄4 L ð Þ · ; (16)”
Research supporting principles for design for additive manufacturing (2014, background): “See, for example, papers on ensuring connectivity of evolving solutions (Rozvany 2009), utilisation of topological sensitivity to improve computational efficiency (Suresh 2013), and alternative solution techniques such as level sets (Wei and Wang 2009).”
Multi-material topology optimization using ordered SIMP interpolation (2016, methodology): “Accordingly, piecewise constant level set method was proposed to treat geometries, eliminate reinitialization and naturally nucleate holes, where no new design variables are required (Luo et al. 2009; Wei and Wang 2009).”