Structural optimization using topological and shape sensitivity via a level set method

By Grégoire Allaire, Frédéric de Gournay, François Jouve, Anca-Maria Toader. 2005

431 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/bde4036958a92490cdc473e26cfa9e99035473bc

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Citations in the corpus

A topological derivative method for topology optimization (2007, methodology): “An extension of the level-set method in Allaire et al. (2002) is presented in Allaire et al. (2004a) , where the topological derivative is used to identify hole nucleation sites.”
An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions (2018, methodology): “Another way is to incorporate nucleation strategy, e.g. the topological derivative (Soko ł owski and Ż ochowski 1999), to create new holes by removing the least useful material during the optimization iterations (Burger et al. 2004; Mei and Wang 2004; Allaire et al. 2005).”
Introducing the sequential linear programming level-set method for topology optimization (2015, methodology): “This allows for some degree of topology optimization, although special techniques are often required to create new holes during optimization (Allaire et al. 2005; Park and Youn 2008; Dunning and Kim 2013).”
A topology optimization method based on the level set method incorporating a fictitious interface energy (2010, methodology): “In Allaire’s method [73], structural boundaries are updated based on smoothed shape sensitivities using the level set equation and holes are introduced during the optimization process.”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, background): “In response a number of works, including Burger et al. (2004), Allaire et al. (2005), Allaire and Jouve (2006), Wang et al. (2004a), and He et al. (2007), proposed different mechanisms to include topological derivatives in the level set problem.”
Application of spectral level set methodology in topology optimization (2006, background): “In two-dimensional problems, the level set methods have a major drawback: although they can easily remove holes, they are unable to create new ones in the interior of the interface (Sethian and Weigmann 2000; Allaire et al. 2004a ).”
Topology optimization approaches (2013, methodology): “Alternatively to using a reaction term in the Hamilton-Jacobi equation, holes are often generated in a separate, occasionally evoked step of the update procedure (Burger et al. 2004; Mei 2004; Allaire et al. 2005).”
Level Set Based Structural Topology Optimization for Minimizing Frequency Response (2011, background): “This is a known limitation of level sets in 2D as it has been previously widely discussed in literature [38,39].”
Isogeometric analysis for parameterized LSM-based structural topology optimization (2016, methodology): “At first, the LSM-based TO implemented the design optimization by solving Hamilton-Jacobi partial differential equation (PDE) that is naturally related to the shape derivative from the classical shape variational analysis [2,4,61,62].”
Piecewise constant level set method for structural topology optimization (2009, unknown): “It is well known that in the conventional level set method, nucleation of holes is very difficult, especially in two dimensions, and thus some dynamic schemes such as the bubble method and the topological derivative method may have to be implemented to overcome this shortcoming [26, 31, 32].”
Design of three dimensional isotropic microstructures for maximized stiffness and conductivity (2007, methodology): “The reader is referred to Allaire et al. (2004) for standard details of the level–set approach; only significant deviations from the standard method are mentioned here.”
Connections between topological sensitivity analysis and material interpolation schemes in topology optimization (2011, methodology): “This concept has been introduced in Eschenauer et al. (1994), mathematically justified in Garreau et al.”