A semi-implicit level set method for structural shape and topology optimization

Luo, Junzhao; Luo, Zhen; Chen, Liping; Tong, Liyong; Wang, Michael Yu

doi:10.1016/j.jcp.2008.02.003

Cited by 111 publications

(60 citation statements)

References 56 publications

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“…The traditional levelset optimization method uses shape derivatives to define a velocity function that is used to update the boundary by solving a Hamilton-Jacobi type PDE (Wang et al 2003;Allaire et al 2004). The traditional approach can be slow to converge (Luo et al 2008a;van Dijk et al 2013) and requires additional techniques to handle constraints beyond a simple volume constraint (Dunning and Kim 2015).…”

Section: Introductionmentioning

confidence: 99%

Minimum length-scale constraints for parameterized implicit function based topology optimization

Dunning

2018

Struct Multidisc Optim

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This paper introduces explicit minimum length-scale constraint functions suitable for parameterized implicit function based topology optimization methods. Length-scale control in topology optimization has many potential benefits, such as removing numerical artifacts, mesh independent solutions, avoiding thin, or single node hinges in compliant mechanism design and meeting manufacturing constraints. Several methods have been developed to control length-scale when using density-based or signed-distance-based level-set methods. In this paper a method is introduced to control length-scale for parameterized implicit function based topology optimization. Explicit constraint functions to control the minimum length in the structure and void regions are proposed and implementation issues explored in detail. Several examples are presented to show the efficacy of the proposed method. The examples demonstrate that the method can simultaneously control minimum structure and void length-scale, design hinge free compliant mechanisms and control minimum length-scale for three dimensional structures.

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Section: Introductionmentioning

confidence: 99%

Minimum length-scale constraints for parameterized implicit function based topology optimization

Dunning

2018

Struct Multidisc Optim

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“…Allaire and Jouve [26] combined the shape derivatives with topological derivatives to present a level set based optimisation method capable of automatic hole insertion. The proposed approach was shown to be independent from local minima but the implementation of topological derivatives is very difficult in numerical practice [27,28] because, the hole size is dependent on a single mesh cell which cannot be infinitesimally small as proposed in the method [26]. In addition, the resulting optimal structure depends on the values of various parameters which can affect the stability of the optimisation process [29].…”

Section: Introductionmentioning

confidence: 99%

Structural optimisation based on the boundary element and level set methods

Ullah

Trevelyan

Matthews

2014

Computers & Structures

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. (2014) 'Structural optimisation based on the boundary element and level set methods. ', Computers and structures., Further information on publisher's website:http://dx.doi.org/10. 1016/j.compstruc.2014.01.004 Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Computers Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version was subsequently published in Computers Structures, 137, 2014Structures, 137, , 10.1016Structures, 137, /j.compstruc.2014.01.004. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractA new method of structural topology optimisation is proposed in which an evolutionary approach is used with boundary element and level set methods. During the optimisation iterations, the proposed method automatically introduces internal cavities and does not rely on an initial guess topology with pre-existing holes. The zero level set contours describing both the external geometry and the internal cavities are converted to non-uniform rational B-splines (NURBS) for smooth boundary element meshing at each iteration. The optimal geometries generated by the proposed method for two-dimensional cases closely resemble to those available in the literature for a range of benchmark examples in the field of topology optimisation.

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“…The level set method is a powerful technique to model the motion of interfaces in many disciplines. The range of applications using the level set method has grown substantially, including investigations of electromigration [1], topology optimization [2], image processing [3], and evolving fluid interfaces [4]. First developed by Osher and Sethian [5] the level set method is based upon representing an interface as the zero level set of a higher dimensional function.…”

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confidence: 99%

A Semi-implicit Gradient Augmented Level Set Method

Kolahdouz¹,

Salac²

2013

SIAM J. Sci. Comput.

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Abstract. Here a semi-implicit formulation of the gradient augmented level set method is presented. By tracking both the level set and it's gradient accurate subgrid information is provided, leading to highly accurate descriptions of a moving interface. The result is a hybrid LagrangianEulerian method that may be easily applied in two or three dimensions. The new approach allows for the investigation of interfaces evolving by mean curvature and by the intrinsic Laplacian of the curvature. In this work the algorithm, convergence and accuracy results are presented. Several numerical experiments in both two and three dimensions demonstrate the stability of the scheme.

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A semi-implicit level set method for structural shape and topology optimization

Cited by 111 publications

References 56 publications

Minimum length-scale constraints for parameterized implicit function based topology optimization

Minimum length-scale constraints for parameterized implicit function based topology optimization

Structural optimisation based on the boundary element and level set methods

A Semi-implicit Gradient Augmented Level Set Method

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