Structural optimization using sensitivity analysis and a level-set method

By Grégoire Allaire, François Jouve, Anca-Maria Toader. 2004

2,858 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6e50b1cb4131104e40dc18b4de5398e7bb892e03

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Citations in the corpus

Stress-based shape and topology optimization with the level set method (2018, background): “They usually take the form of boundary integrals [38].”
Piecewise constant level set method for structural topology optimization (2009, methodology): “Recently, the level set method, which was developed for tracing the propagation of fluid interfaces [2], has been successfully applied to a wide range of shape and topology optimization problems [3, 4].”
Design of multimaterial compliant mechanisms using level-set methods (2005, methodology): “This is a well-defined notion and it is derived in full detail in [34,35].”
A level-set method for vibration and multiple loads structural optimization (2005, methodology): “1 we refer to [6] in the single load case or to the classical works [25], [30], [33], [35].”
Detection of material interfaces using a regularized level set method in piezoelectric structures (2016, methodology): “In this work, the level set-based scheme [19,20] for structural optimization is employed to minimize the cost function.”
A level set approach for topology optimization with local stress constraints (2014, methodology): “It is shown in the literature (see, for example, [18, 19]) that choosing ı based on (31)”
A multi-material topology optimization algorithm based on the topological derivative (2019, methodology): “In the level set method for shape and topology optimization [ 4 ] , the evolution of the level set function ψ is guided by shape gradients by means of a Hamilton-Jacobi equation.”
Adaptive topology optimization with independent error control for separated displacement and density fields (2014, methodology): “Over the past two decades, many topology optimization methods have been developed, including the homogenization method [4], the SIMP (Solid Isotropic Material with Penalization) method [5,6], the level set method [7–9], the ESO (Evolutionary Structural Optimization) method [10] and other alternative”
Towards the stabilization of the low density elements in topology optimization with large deformation (2013, background): “In the linear geometric case, the strain energy density function is convex,withF being close to the identity, which means ∇u ≈ 0, and thus, rendering automatically a unique solution [1,17,21].”
Non-probabilistic reliability-based topology optimization with multidimensional parallelepiped convex model (2017, background): “Since the work of Bendsøe and Kikuchi (1988), topology optimization methods for continuum structures based on the material distribution model have experienced great popularity, such as solid isotropic material with penalization (SIMP) and its variants (Bendsøe and Sigmund 1999; Sigmund 2001), evolut”
Topology optimization of shell structures using adaptive inner-front (AIF) level set method (2008, background): “Some of the examples include structural optimization problems considering linear elasticity (Wang et al. 2003), nonlinear elasticity (Allaire et al. 2004; Kwak and Cho 2005), eigenfrequency (Allaire et al. 2004), compliant mechanism (Allaire et al. 2004), multi-materials and multiconstraints (Wang…”
An isogeometrical approach to structural topology optimization by optimality criteria (2012, methodology): “Recently several different approaches are devised that uses the level set methods (Sethian and Wiegmann 2000 ;W ang et al.2003; Allaire et al. 2004; Belytschko et al. 2003).”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, background): “In their introduction to level set topology design, Allaire et al. (2004) discussed a generalization of their method to nonlinear elasticity problems.”
A level set method for structural topology optimization and its applications (2004, background): “Meanwhile Allaire, Jouve and Toader [25,26] Yu, Xiaoming and Yulin [27–31] also studied structural 0965-9978/$ - see front matter q 2004 Elsevier Ltd.”
A survey on level set methods for inverse problems and optimal design (2005, methodology): “2 Nucleating holes In some applications one observes that the level set method does not lead to enough topological changes [9, 28], in particular the level set methods presented above cannot reconstruct inner contours like a ring-type structure in an automatic way.”