Evolutionary level set method for structural topology optimization

Jia, Haipeng; Beom, Hyeon Gyu; Wang, Yuxin; Lin, Su-Jien; Liu, Bo

doi:10.1016/j.compstruc.2010.11.003

Cited by 48 publications

(32 citation statements)

References 33 publications

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“…The hole insertion, evolution and merging continue throughout the optimisation process which finally ends, when the target volume fraction of 0.33 is reached, with a topology shown in Figure 7(o). This figure closely resembles optimal geometries for this benchmark example in the previous works [16,20,31,32,19,39,40].…”

Section: Example-1supporting

confidence: 84%

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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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Section: Example-1supporting

confidence: 84%

“…In addition, the resulting optimal structure depends on the values of various parameters which can affect the stability of the optimisation process [29]. Other examples of LSM combination with FEM-based structural optimisation schemes can be found in [29,30,31].…”

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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“…Allaire and Jouve [5] combined the shape derivatives with topological derivatives to present a level set based optimisation method capable of automatic hole insertion. Other examples of LSM-based structural optimisation schemes can be found in [6,7,8,9,10,11].…”

Section: Introductionmentioning

confidence: 99%

Correlation between hole insertion criteria in a boundary element and level set based topology optimisation method

Ullah

Trevelyan

2013

Engineering Analysis with Boundary Elements

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(2013) 'Correlation between hole insertion criteria in a boundary element and level set based topology optimisation method.', Engineering analysis with boundary elements., 37 (11). pp. 1457-1470.Further information on publisher's website:http://dx.doi.org/10. 1016/j.enganabound.2013.08.003 Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Engineering analysis with boundary elements. 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 Engineering analysis with boundary elements, 37, 11, 2013, 10.1016/j.enganabound.2013.08.003 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. AbstractThe research work presented in this paper is based on the correlation between two hole insertion criteria in a boundary element method (BEM) and level set method (LSM) based structural topology optimisation scheme for 2D elastic problems. The hole insertion criteria used in this work are based on the von Mises stress and the topological derivative approaches. During the optimisation process holes are automatically inserted in the design domain using each of the two criteria. The LSM is used to provide an implicit description of the structural geometry, and is also capable of automatically handling topological changes, i.e. holes merging with each other or with the boundary. The evolving structural geometry (i.e. the zero level set contours)is represented by NURBS, providing a smooth geometry throughout the optimisation process and completely eliminate jagged edges. In addition the optimal NURBS geometry can be used directly in other design processes.

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“…In the SIMP approach, one optimizes these material densities directly, whereas in the level set method, one optimizes the location of the material boundary, ∂Ω, and from the location of this boundary, one determines which elements are solid and which are void, as shown in (1). Due to this boundary-based parameterization, the level set method avoids meshdependence and checkerboarding [3,13] -two of the main numerical challenges associated with the SIMP method [14,15]. …”

Section: Problem Formulationmentioning

confidence: 99%

“…While the level set method is mesh-independent, the converged solution of the optimization problem is dependent upon the initial topology [3,13]. Therefore, one must carefully select the number of holes in the initial design according to the desired length scale for the final solution.…”

Section: Problem Formulationmentioning

confidence: 99%