A topology optimization method based on the level set method incorporating a fictitious interface energy

Yamada, Takayuki; Izui, Kazuhiro; Nishiwaki, Shinji; Takezawa, Akihiro

doi:10.1016/j.cma.2010.05.013

Cited by 511 publications

(379 citation statements)

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“…Another useful constraint for cast parts is the so-called "uniform cross-section surface constraint" [48], since it simplifies a lot the shape of the desired molds. To our knowledge, Yamada et al [48] were the first to study this type of constraint in shape and topology optimization using a combination of a phase-field and a levelset method.…”

Section: Uniform Cross-section Surface Constraintmentioning

confidence: 99%

“…To our knowledge, Yamada et al [48] were the first to study this type of constraint in shape and topology optimization using a combination of a phase-field and a levelset method. The constraint states that the cast part should have a uniform constant thickness along some direction d. An example of a uniform cross-section cantilever of thickness h is given in Figure 6.…”

Section: Uniform Cross-section Surface Constraintmentioning

confidence: 99%

“…Section 4 discusses the casting process while Section 5 introduces our new molding direction constraint. We also recall the approach of Xia et al [46,47], as well as the "uniform cross-section surface constraint" of Yamada et al [48], which simplifies a lot the shape of the desired molds. Section 6 is devoted to the computation of the shape derivatives of these molding constraints.…”

Section: Introductionmentioning

confidence: 99%

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Molding Direction Constraints in Structural Optimization via a Level-Set Method

Allaire

Jouve

Michailidis

2016

Variational Analysis and Aerospace Engineering

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Section: Uniform Cross-section Surface Constraintmentioning

confidence: 99%

Section: Uniform Cross-section Surface Constraintmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Molding Direction Constraints in Structural Optimization via a Level-Set Method

Allaire

Jouve

Michailidis

2016

Variational Analysis and Aerospace Engineering

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“…(Howell, 2001) No. 16-00178 [DOI: 10.1299 , , E-mail of corresponding author: kogiso@aero.osakafu-u.ac.jp (Sigmund, 1997, Frecker et al, 1997, Nishiwaki et al, 2001, Yamada et al, 2010, Otomori et al, 2011) (Seepersad et al, 2006, Chen et al, 2010, Takezawa et al, 2011) (Kogiso et al, 2008) 3 Pareto Pareto Pareto (Nakayama and Sawaragi, 1984) ( Kitayama and Yamazaki, 2014) (Toyoda and Kogiso, 2015) (Yamada et al, 2010) Pareto (Miettinen, 1999b) Pareto Pareto l p (Miettinen, 1999a) 2. Fig.…”

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confidence: 99%

Robust topology optimization of compliant mechanism using multiobjective optimization method

Nishino

Kogiso

Otomori³

et al. 2016

Transactions of the JSME (In Japanese)

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This study evaluates a robust optimum design of a compliant mechanism considering uncertainty of the load direction.For the topology optimization, this study adopts a level set based approach incorporating a fictitious interface energy term. The method is known to have several advantages such as the allowance of topological as well as shape changes, and the ability to qualitatively control the geometrical complexity of the obtained optimum configurations. The design objectives are to maximize the displacement at the gripping position and the robustness under variations of the applied load direction. In addition, the eigenfrequency maximization is considered to acquire the structural stiffness. The design problem is formulated as a multiobjective design problem. Conventionally, the robust design problem has been formulated as a weighted sum of the mean value and the standard deviation of the performance index. Integrating the multiobjective optimization to the level set-based topology optimization method, this study adopts the l p -norm method that can obtain the Pareto solution even when the Pareto frontier is a non-convex form. Through numerical examples of a compliant mechanism design, validity of the proposed method is verified. Then, the robustness of the obtained optimum configuration is discussed.

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“…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]. 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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. (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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A topology optimization method based on the level set method incorporating a fictitious interface energy

Cited by 511 publications

References 71 publications

Molding Direction Constraints in Structural Optimization via a Level-Set Method

Molding Direction Constraints in Structural Optimization via a Level-Set Method

Robust topology optimization of compliant mechanism using multiobjective optimization method

Structural optimisation based on the boundary element and level set methods

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