Morphology-based black and white filters for topology optimization

By Ole Sigmund. 2007

1,852 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/1ff78005c71b64d24a9a26dbc98cc5756adf52ef

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Length scale and manufacturability in density-based topology optimization (2016, methodology): “In [123], so-called morphological operators [108] are applied as filters in topology optimization.”
Multi-material topology optimization using ordered SIMP interpolation (2016, methodology): “Generally, a filter to either the sensitivities or the densities is used to achieve black-and-white structures (Sigmund 2007).”
Topology Optimization for Additive Manufacturing (2016, methodology): “, 1982; Lakes, 1987; Evans, 1991), often referred to as auxetic materials. A number of advantageous properties of such materials are predicted by the literature, and with its requirement of intricate, mechanism-like deformation patterns it is recognized as a difficult test problem for numerical opti”
Design of manufacturable 3D extremal elastic microstructure (2014, methodology): “Filters and projection methods are discussed in depth by Sigmund (2007) and more details on the robust optimization scheme are given in Section 3.”
Multi-material topology optimization of laminated composite beam cross sections (2012, background): “Continuation methods have been suggested in this context as a way to increase the possibility of obtaining a good design (see Sigmund and Petersson [6], Borrvall and Petersson [30], and Hvejsel et al. [31]).”
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.”
Exploiting Additive Manufacturing Infill in Topology Optimization for Improved Buckling Load (2016, background): “[11]), while the projection is determined by the threshold, η, and sharpness, β.”
Topology Optimization (2009, methodology): “An alternative formulation is the modified SIMP model [21]: 〈Ee〉 = Emin +ρ e ( E0 −Emin ) , (2.”
Efficient topology optimization in MATLAB using 88 lines of code (2011, methodology): “The modified SIMP approach has a number of advantages (Sigmund, 2007), most importantly that it allow s for a straightforward implementation of additional filters , a illustrated in section 5.”
An additive manufacturing filter for topology optimization of print-ready designs (2016, methodology): “The AM filter can be easily integrated in a conventional TO process, similar to other filters commonly used in density-based approaches (e.g. Bourdin (2001), Sigmund (2007)).”
Improving multiresolution topology optimization via multiple discretizations (2012, methodology): “In Reference [20], the design variable mesh and the density mesh are the same.”
Integrated topology optimization with embedded movable holes based on combined description by material density and level sets (2013, methodology): “Many techniques have been developed to overcome these numerical difficulties, including the sensitivity/densityfiltering techniques [14–16], theperimeter/slope”