A level-set method for shape optimization

By Grégoire Allaire, François Jouve, Anca-Maria Toader. 2002

691 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/c4d02e1ad06a68b75b57bc93f28bc9629bc73079

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In Civil and Structural Engineering

In Computational Mechanics

Citations in the corpus

Stress-constrained topology optimization: a topological level-set approach (2013, methodology): “On the other hand, in level-set methods (Allaire et al. 2002; Allaire and Jouve 2005; He et al. 2007; Wang et al. 2003), the topology is defined and controlled via an auxiliary function.”
A critical review of established methods of structural topology optimization (2009, methodology): “Topological derivative-based and level-set methods (e.g., Sokolowski and Zochowski 1999; Sethian and Wiegman 2000; Allaire et al. 2002, 2004; Wang et al. 2003, 2004, ranging to Norato et al. 2007) show tremendous promise, but have not reached the stage of regular industrial applications as yet.”
Minimum stress optimal design with the level set method. (2008, methodology): “The application of the level set method to structural optimization was pioneering in [6], [7], [27], [34], [40].”
Topology optimization of thermoelastic structures using level set method (2008, methodology): “[1, 2] proposed a similar implementation of the level-set method.”
Topology optimization approaches (2013, background): “…the concept has developed in a number of different directions, including: a) density (Bendsøe 1989; Zhou and Rozvany 1991; Mlejnek 1992); b) level set (Allaire et al. 2002, 2004; Wang et al. 2003); c) topological derivative (Sokołowski and Zochowski 1999); d) phase field (Bourdin and Chambolle…”
A geometry projection method for shape optimization (2004, background): “However, as indicated in Reference [16], they are so far unable to introduce new holes.”
An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures (2015, background): “, simplified isotropic material with penalization (SIMP)) [12,13], level set approach [14,15], evolutionary approaches (e.”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, background): “Independently, Allaire et al. (2002), Allaire et al. (2004) also developed a numerical framework for boundary design that linked the velocity of level set boundaries to adjoint shape sensitivity analysis for stiffness design and frequency maximization (Allaire and Jouve 2005).”