A boundary element approach for topology optimization problem using the level set method

Abe, Kazuhisa; Shunsuke, Kazama; Koro, Kazuhiro

doi:10.1002/cnm.919

Cited by 28 publications

(28 citation statements)

References 11 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: 83%

“…This geometry is required to be used in structural analysis in the next iteration. In the boundary element analysis if the zero level set intersection points are used directly as element nodal points (as in [32]), two intersection points can lie very close to each other (for example see Figure 6(c)), and this can cause difficulties and instabilities during the boundary element analysis. In addition the non-smoothness of the polygonal geometry can produce high stress concentrations, which can mislead the optimisation process.…”

Section: Nurbs Geometrymentioning

confidence: 99%

“…The available LSM and BEM based optimisation methods presented in [32,40] considered similar initial geometries as used for this example, and the optimal designs were obtained with 1500 and 2021 optimisation iterations, respectively. Although, in [32,40] the optimisation process always starts from initial designs with pre-existing holes.…”

Section: Example-1mentioning

confidence: 99%

“…Although, in [32,40] the optimisation process always starts from initial designs with pre-existing holes. However, with the proposed op-timisation methods, the optimal design has been obtained in less than 100…”

Section: Example-1mentioning

confidence: 99%

“…The use of BEM with the level set method in structural optimisation was first used by Abe et al [32]. During each optimisation iteration the evolving 5 structural boundary is re-constructed from the zero level set contours, which consists of line segments joining the zero level set intersection points.…”

Section: Introductionmentioning

confidence: 99%

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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: 83%

Section: Nurbs Geometrymentioning

confidence: 99%

Section: Example-1mentioning

confidence: 99%

Section: Example-1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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Editorial

Aliabadi

Gatmin

Sellier

2008

Commun. Numer. Meth. Engng.

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Owing to a technical problem in the submission process, selected presentations from the 7th International Conference on Boundary Elements, which took place in Paris, France, in September 2006 (http://beteq.engineeringconferences.net/), will not be published in a separate special issue. Links to these papers as they were published in the journal are listed at the end of this editorial. Copyright © 2008 John Wiley & Sons, Ltd.

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An immersed boundary element method for level‐set based topology optimization

Yamasaki

Yamada

Matsumoto

2012

Numerical Meth Engineering

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SUMMARY In this paper, we propose a new BEM for level‐set based topology optimization. In the proposed BEM, the nodal coordinates of the boundary element are replaced with the nodal level‐set function and the nodal coordinates of the Eulerian mesh that maintains the level‐set function. Because this replacement causes the nodal coordinates of the boundary element to disappear, the boundary element mesh appears to be immersed in the Eulerian mesh. Therefore, we call the proposed BEM an immersed BEM. The relationship between the nodal coordinates of the boundary element and the nodal level‐set function of the Eulerian mesh is clearly represented, and therefore, the sensitivities with respect to the nodal level‐set function are strictly derived in the immersed BEM. Furthermore, the immersed BEM completely eliminates grayscale elements that are known to cause numerical difficulties in topology optimization. By using the immersed BEM, we construct a concrete topology optimization method for solving the minimum compliance problem. We provide some numerical examples and discuss the usefulness of the constructed optimization method on the basis of the obtained results. Copyright © 2012 John Wiley & Sons, Ltd.

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A boundary element approach for topology optimization problem using the level set method

Cited by 28 publications

References 11 publications

Structural optimisation based on the boundary element and level set methods

Structural optimisation based on the boundary element and level set methods

Editorial

An immersed boundary element method for level‐set based topology optimization

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