Volume preserving nonlinear density filter based on heaviside functions

By Shengli Xu, Yuanwu Cai, Gengdong Cheng. 2010

447 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Civil and Structural Engineering, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/27e780a9ad46a83e806cbc7ae040b1db655144d8

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Citations in the corpus

A general formulation of structural topology optimization for maximizing structural stiffness (2011, methodology): “2004), modified density filter with a Heaviside function (Sigmund 2007), volume preserving nonlinear density filter based on Heaviside functions (Xu et al. 2010).”
Compatibility in microstructural optimization for additive manufacturing (2019, methodology): “The elasticity tensor for linearly-varying volume constraint is fitted by a functional which replaces the SIMP model.”
On projection methods, convergence and robust formulations in topology optimization (2011, methodology): “The studies in Xu et al. (2010) and Kawamoto et al. (2010) indeed shows that the convergence for η close to 0.5 is smooth compared with the previous projection methods and almost discrete designs are obtained for lower β values.”
Robust topology optimization of photonic crystal waveguides with tailored dispersion properties (2011, unknown): “minimum length scale [14–22].”
Undercut and overhang angle control in topology optimization: A density gradient based integral approach (2017, methodology): “Heaviside projection of density To alleviate the grayscale transition between the black and white density in the optimized designs, density projection schemes have been used in the past [19, 35, 32].”
Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis (2015, methodology): “In this paper, the formulation of the optimization problem further relies on projection filters [21, 22, 23] for solving issues such as mesh-dependence of the optimal solution.”
Eliminating beta-continuation from Heaviside projection and density filter algorithms (2011, methodology): “This approach is simple and remarkably robust—it prevents the numerical issues discussed in Xu et al. (2010) .”
Concurrent topology optimization of multiscale structures with multiple porous materials under random field loading uncertainty (2017, methodology): “ogy optimization using volume preserving filtering (Xu et al. 2010).”
A mass constraint formulation for structural topology optimization with multiphase materials (2011, methodology): “Until now, a variety of techniques have been introduced, such as the perimeter control [20, 21] and its variant [5, 6], the density slope control [22, 23] and the filtering technique [24, 25].”
Topology optimization approaches (2013, methodology): “2004) provides a minimum length-scale on the material region; that the modified projection filter (Sigmund 2007) provides a minimum length-scale on the void regions; but that the intermediate projection filter (Xu et al. 2010) theoretically provides neither of the two (Wang et al.”
On filter boundary conditions in topology optimization (2017, methodology): “A density-based filter may be followed by a projection step (Guest et al, 2004; Xu et al, 2010) to force the design towards a 0/1 solution.”
Integrated topology optimization with embedded movable holes based on combined description by material density and level sets (2013, background): “constraint approaches [17,18], the higher-order/non-conforming finiteelementmethods [19,20]and theprojectionmethods [21–24].”