Minimum stress optimal design with the level set method.

By Grégoire Allaire, François Jouve. 2008

175 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/1c7c057d75e66db20da0cdfe89fdfe4f5c6be7c9

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In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Shape optimization with a level set based mesh evolution method (2014, methodology): “In this last case, go back to stage (5), using a time step τ k +1 < τ k .”
Stress-based shape and topology optimization with the level set method (2018, methodology): “(a) Minimum compliance design (∼100), (b) Allaire and Jouve [16] (∼200), (c) Guo et al.”
Combined shape and topology optimization for minimization of maximal von Mises stress (2017, background): “…enforced in topology optimization problems (e.g. Duysinx and Sigmund (1998); Svanberg and Werme (2007); Bruggi and Venini (2008); Le et al (2010); Cheng and Jiang (1992); Allaire and Jouve (2008); Allaire et al (2011, 2014); Ha and Cho (2008); Yamasaki et al (2011)) and a number of other papers.”
Stress-based topology optimization using an isoparametric level set method (2012, methodology): “The following section builds on the framework introduced by Allaire and Jouve [25] and extends it to incorporate isoparametric finite elements.”
Topological derivative-based topology optimization of structures subject to Drucker–Prager stress constraints (2012, methodology): “The present procedure is not a member of the family usually referred to as level-set methods used, for instance, in [3].”
Topology optimization approaches (2013, background): “2013), level set approaches (Allaire and Jouve 2008) as well as for topological derivatives (Amstutz and Novotny 2010).”
Stress-constrained topology optimization: a topological level-set approach (2013, background): “One of the earliest implementation of level-set based stress-constrained topology optimization appears in Allaire and Jouve (2008) where the authors proposed to minimize a domain integral of stress subject to material volume constraint.”
Topological optimization of structures subject to Von Mises stress constraints (2010, background): “This is in contrast with the existing literature on the topic, where either dual methods are implemented [14, 16, 19, 31], with the well-known difficulties related to the irregularity of the Lagrange multiplier, or a simple power law penalization is considered [3, 4], generally leading to unfeasible”
Level Set Based Structural Topology Optimization for Minimizing Frequency Response (2011, background): “Meanwhile, a wide range of practical solid mechanics problems had been solved using the level set based structural topology optimization, such as the compliance optimization problem [19–25], the eigenfrequency optimization problem [18,26], and the stress optimization problem [27].”
A multi-material level set-based topology and shape optimization method (2015, methodology): “Up to date, the level set-based approaches have been widely applied to various design problems, such as eigenvalue maximization [37], stress minimization [38], designs with geometrical uncertainties [39], design of photonic nanostructures [40] and optimization of functional graded material [41].”