A level-set method for vibration and multiple loads structural optimization

By Grégoire Allaire, François Jouve. 2005

237 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/b1f0384f0fe8fe93dec8d05650326b98f178b2a7

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In Civil and Structural Engineering

In Computational Mechanics

In Computer Graphics and Computer-Aided Design

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.”
Shape and topology optimization of the robust compliance via the level set method (2008, background): “The 3-d chair This problem has also been studied in [3].”
A new algorithm for topology optimization using a level-set method (2006, methodology): “As already noticed in [4], the multiple loads solution is much more realistic than the single load one.”
Support structure constrained topology optimization for additive manufacturing (2016, methodology): “There are several TO methods employed today to solve such TO problems; these include Solid Isotropic Material with Penalization (SIMP) [38]–[41], level-set [42], [42]–[44] and evolutionary [45] methods.”
A topology optimization method based on the level set method incorporating a fictitious interface energy (2010, methodology): “Allaire and Jouve [62] also extended their method to lowest eigen-frequency maximization problems and minimum compliance problems having multiple loads.”
PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab (2012, background): “The first is an extended domain for the design of a socket wrench and the other is domain for a suspension triangle which is presented as an industrial application of topology optimization in Allaire and Jouve (2005).”
Structural shape and topology optimization using a meshless Galerkin level set method (2012, methodology): “Actually, there are many methods that can be applied to treat this challenge in level set methods, including the ‘ersatz material’ model [7, 13], the variational finite element methods [42–44], and the meshless methods [28].”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “(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). A limitation of these direct methods are that algorithms cannot create new ”
Shape optimization with a level set based mesh evolution method (2014, unknown): “As in [9], the problem of finding the most rigid shape with respect to the N load cases is expressed as that of minimizing the sum of the individual compliances associated to each load case; the considered objective function thus reads:”
Minimum stress optimal design with the level set method. (2008, methodology): “Together with our previous works [10] (for eigenvalue and multiple loads optimization) and [11] (for robust or worst-case optimization), it clearly demonstrates that the level set method is a versatile tool for structural optimization which can tackle industrial, and not merely academic, problems.”
Efficient generation of large-scale pareto-optimal topologies (2013, background): “For eigen-value problems, one can show that [42], [43]:”