A new algorithm for topology optimization using a level-set method

By Samuel Amstutz, Heiko Andrä. Journal of Computational Physics, 2006

364 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c3050abdd426fe4da7f32ac4b9c24028c127083d

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Citations in the corpus

Topological derivative for multi‐scale linear elasticity models applied to the synthesis of microstructures (2010, methodology): “It has proved extremely useful in the treatment of a wide range of problems, including the topology optimization of load-bearing structures [1, 4, 39], inverse analysis [5, 18, 27] and image processing [8, 28, 32], and is currently a subject of great interest in applied mathematics circles [3, 19, 3”
Explicit level‐set‐based topology optimization using an exact Heaviside function and consistent sensitivity analysis (2012, background): “Another approach updates the level-set updates solely on topological derivative information rather than on shape sensitivity [16, 17].”
Topological optimization of structures subject to Von Mises stress constraints (2010, methodology): “Thus, the topological derivative has been successfully applied in the context of topology optimization [7, 13, 28], inverse problems [5, 12, 20, 29] and image processing [9, 25, 24, 26].”
Topology optimization of shell structures using adaptive inner-front (AIF) level set method (2008, background): “…inserting soft materials (Mei and Wang 2004; Burger et al. 2004), perforating level set function (Allaire et al. 2005), or adding forcing term (Amstutz and Andra 2006) at the local regions where the topological derivative attains its extreme value, topological changes can be carried out…”
Topological derivatives applied to fluid flow channel design optimization problems (2016, methodology): “Thus, following the original ideas due to Amstutz & Andrä [7], the results given by (3.”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “Other alternatives were proposed by Amstutz and Andrä (2006) and Norato et al.”
Level set methods for inverse scattering (2006, methodology): “Moreover, we again refer to [10, 28, 76, 78, 87, 145] and the further references given there for numerical approaches which are focusing on topology changes during the reconstruction.”
A multi-material topology optimization algorithm based on the topological derivative (2019, methodology): “As it is emphasized in [ 7, Sec.”
Connections between topological sensitivity analysis and material interpolation schemes in topology optimization (2011, background): “Therefore, the topological sensitivity may be advantageously combined with level set methods (Allaire et al. 2005; Amstutz and Andrä 2006; Burger et al. 2004).”
Topological derivative-based topology optimization of structures subject to Drucker–Prager stress constraints (2012, methodology): “representation of the structure domain has been proposed in [5] and shown to efficiently solve compliance minimization problems.”